Polynomial approximation techniques for probabilistic amplitude shaping

Abstract

Various aspects of the present disclosure generally relate to wireless communications. In some aspects, a transmitter device may obtain a plurality of information bits. The transmitter device may form a polynomial approximation of the plurality of approximation factors. The transmitter device may obtain an approximation of a logarithm of a cumulative number of sequences using the polynomial approximations of the plurality of approximation factors. The transmitter device may perform an exponential operation on the approximation of the logarithm of the number of cumulative sequences, thereby obtaining an approximation of the number of cumulative sequences. The transmitter device may encode the plurality of information bits to obtain a sequence of symbols based at least in part on the approximation of the cumulative number of sequences. The transmitter device may transmit a message to one or more receiver devices based at least in part on the sequence of symbols. Numerous other aspects are described.

Description

Technical Field

[0001] Aspects of the present disclosure relate generally to wireless communications and to techniques and apparatus for polynomial approximation techniques for probability amplitude shaping. Background Art

[0002] Wireless communication systems are widely deployed to provide a variety of telecommunication services, such as telephony, video, data, messaging, and broadcasts. Typical wireless communication systems may employ multiple access technologies capable of supporting communication with multiple users by sharing available system resources (e.g., bandwidth, transmit power, etc.). Examples of such multiple access technologies include code division multiple access (CDMA) systems, time division multiple access (TDMA) systems, frequency division multiple access (FDMA) systems, orthogonal frequency division multiple access (OFDMA) systems, single-carrier frequency division multiple access (SC-FDMA) systems, time division synchronous code division multiple access (TD-SCDMA) systems, and long term evolution (LTE). LTE / LTE-Advanced is a set of enhancements to the Universal Mobile Telecommunications System (UMTS) mobile standard promulgated by the Third Generation Partnership Project (3GPP).

[0003] A wireless network may include one or more network nodes that support communication for wireless communication devices, such as user equipment (UE) or multiple UEs. The UE may communicate with the network node via downlink and uplink communications. A "downlink" (or "DL") refers to the communication link from the network node to the UE, and an "uplink" (or "UL") refers to the communication link from the UE to the network node. Some wireless networks may support device-to-device communication, such as via a local link (e.g., a sidelink (SL), a wireless local area network (WLAN) link, and / or a wireless personal area network (WPAN) link, etc.).

[0004] The above-mentioned multiple access technologies have been adopted in various telecommunication standards to provide a common protocol that enables different UEs to communicate at a city, country, region, and / or global level. New Radio (NR) (which may be referred to as 5G) is a set of enhancements to the LTE mobile standard promulgated by 3GPP. NR is designed to better support mobile broadband Internet access by: improving spectrum efficiency; reducing costs; improving services; utilizing new spectrum; and using orthogonal frequency division multiplexing (OFDM) with a cyclic prefix (CP) (CP-OFDM) on the downlink and CP-OFDM and / or single carrier frequency division multiplexing (SC-FDM) (also known as discrete Fourier transform spread OFDM (DFT-s-OFDM)) on the uplink to better integrate with other open standards; as well as supporting beamforming, multiple-input multiple-output (MIMO) antenna technology, and carrier aggregation. As the demand for mobile broadband access continues to increase, further improvements in LTE, NR, and other radio access technologies remain useful. Summary of the Invention

[0005] In some specific implementations, an apparatus for wireless communication at a transmitter device includes a memory and one or more processors coupled to the memory, the one or more processors configured to: obtain a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; form a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; use the polynomial approximation of the plurality of approximation factors to obtain an approximation of a logarithm of a cumulative number of sequences, the logarithm of the cumulative number of sequences being associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; perform an exponential operation on the approximation of the logarithm of the cumulative number of sequences, thereby obtaining an approximation of the cumulative number of sequences; encode the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a symbol sequence having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the symbol sequence belongs to a second alphabet having a second alphabet size; and send a message to one or more receiver devices based at least in part on the symbol sequence.

[0006] In some specific implementations, a method of wireless communication performed by a transmitter device includes: obtaining a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; forming a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; using the polynomial approximation of the plurality of approximation factors to obtain an approximation of a logarithm of a cumulative number of sequences, the logarithm of the cumulative number of sequences being associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; performing an exponential operation on the approximation of the logarithm of the cumulative number of sequences, thereby obtaining an approximation of the cumulative number of sequences; encoding the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a symbol sequence having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the symbol sequence belongs to a second alphabet having a second alphabet size; and sending a message to one or more receiver devices based at least in part on the symbol sequence.

[0007] In some specific implementations, a non-transitory computer-readable medium storing an instruction set for wireless communication includes one or more instructions that, when executed by one or more processors of a transmitter device, cause the transmitter device to: obtain a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; form a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; use the polynomial approximation of the plurality of approximation factors to obtain an approximation of a logarithm of a cumulative number of sequences, the logarithm of the cumulative number of sequences being associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; perform an exponential operation on the approximation of the logarithm of the cumulative number of sequences, thereby obtaining an approximation of the cumulative number of sequences; encode the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a symbol sequence having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the symbol sequence belongs to a second alphabet having a second alphabet size; and send a message to one or more receiver devices based at least in part on the symbol sequence.

[0008] In some embodiments, an apparatus for wireless communication includes: means for obtaining a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; means for forming a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; means for obtaining an approximation of a logarithm of a cumulative number of sequences using the polynomial approximation of the plurality of approximation factors, the logarithm of the cumulative number of sequences being associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; means for performing an exponential operation on the approximation of the logarithm of the cumulative number of sequences to thereby obtain an approximation of the cumulative number of sequences; means for encoding the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a symbol sequence having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the symbol sequence belongs to a second alphabet having a second alphabet size; and means for sending a message to one or more receiver devices based at least in part on the symbol sequence.

[0009] The various aspects generally include methods, apparatus, systems, computer program products, non-transitory computer-readable media, user equipment, base stations, network entities, network nodes, transmitter devices, wireless communication devices, and / or processing systems as fully described herein with reference to the accompanying drawings and description and as illustrated in the accompanying drawings and description.

[0010] The features and technical advantages of the examples according to the present disclosure have been outlined quite broadly above so that the detailed description that follows may be better understood. Additional features and advantages will be described below. The concepts and specific examples disclosed may be readily utilized as a basis for modifying or designing other structures for achieving the same purposes of the present disclosure. Such equivalent constructions do not depart from the scope of the appended claims. The characteristics of the concepts disclosed herein, both in terms of their organization and method of operation, and the associated advantages will be better understood by considering the following description in conjunction with the accompanying drawings. Each of the figures in the accompanying drawings is provided for the purpose of illustration and description and not as a definition of limitations of the claims.

[0011] Although various aspects are described in the present disclosure by illustrating some examples, it will be understood by those skilled in the art that such aspects can be implemented in many different arrangements and scenarios. The technology described herein can be implemented using different platform types, devices, systems, shapes, sizes and / or packaging arrangements. For example, some aspects can be implemented via integrated chip implementations or other devices based on non-module components (e.g., end-user devices, vehicles, communication equipment, computing equipment, industrial equipment, retail / shopping equipment, medical equipment and / or artificial intelligence devices). Various aspects can be implemented in chip-level components, modular components, non-modular components, non-chip-level components, device-level components and / or system-level components. The equipment incorporated into the various aspects and features described may include additional components and features for implementing and practicing the various aspects claimed and described. For example, the transmission and reception of wireless signals may include one or more components (e.g., hardware components, including antennas, radio frequency (RF) chains, power amplifiers, modulators, buffers, processors, interleavers, adders and / or summers) for analog and digital purposes. The various aspects described herein are intended to be practiced in various devices, components, systems, distributed arrangements and / or end-user devices of various sizes, shapes and compositions. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order that the above-mentioned features of the present disclosure may be fully understood, a more particular description of the invention briefly summarized above may be obtained by reference to various aspects (some of which are illustrated in the accompanying drawings). It should be noted, however, that the drawings illustrate only certain typical aspects of the present disclosure and are not therefore to be considered limiting of its scope, as the description may admit to other equally effective aspects. The same reference numerals in different drawings may identify the same or similar elements.

[0013] Figure 1 is a diagram illustrating an example of a wireless network according to the present disclosure.

[0014] Figure 2 is a diagram illustrating an example of communication between a network node and a user equipment (UE) in a wireless network according to the present disclosure.

[0015] Figure 3 is a diagram illustrating an example decomposed base station architecture according to the present disclosure.

[0016] Figure 4 is a diagram illustrating an example of a transmitter chain according to the present disclosure.

[0017] Figure 5 is a diagram illustrating an example of the logarithm of the cumulative number of sequences according to the present disclosure.

[0018] Figure 6 is a diagram illustrating an example of an absolute error of an approximation according to the present disclosure.

[0019] Figure 7 is a diagram illustrating an example associated with a polynomial approximation technique for probability amplitude shaping according to the present disclosure.

[0020] Figure 8A and Figure 8B is a diagram illustrating an example 800 associated with an approximate absolute error according to the present disclosure.

[0021] Figure 9 is a diagram illustrating an example associated with an approximate area according to the present disclosure.

[0022] Figure 10 is a diagram illustrating an example associated with an approximate area according to the present disclosure.

[0023] Figure 11A and Figure 11B is a diagram illustrating an example associated with a first interval structure according to the present disclosure.

[0024] Figure 12 is a diagram illustrating an example associated with a first additional interval structure according to the present disclosure.

[0025] Figure 13 is a diagram illustrating an example associated with the second interval structure according to the present disclosure.

[0026] Figure 14 is a diagram illustrating an example associated with a search according to the present disclosure.

[0027] Figure 15 is a diagram illustrating an example associated with a lookup table for storing polynomial coefficients according to the present disclosure.

[0028] Figure 16 is a diagram illustrating an example process associated with a polynomial approximation technique for probability amplitude shaping according to the present disclosure.

[0029] Figure 17 is a diagram of an example apparatus for wireless communications according to the present disclosure. DETAILED DESCRIPTION

[0030] Various aspects of the present disclosure are described more fully below with reference to the accompanying drawings. However, the present disclosure can be embodied in many different forms and should not be interpreted as being limited to any specific structure or function presented throughout the present disclosure. Instead, these aspects are provided so that the present disclosure will be thorough and complete, and the scope of protection of the present disclosure will be fully conveyed to those skilled in the art. Those skilled in the art will appreciate that the scope of the present disclosure is intended to cover any aspect of the present disclosure disclosed herein, whether it is implemented independently or in combination with any other aspect of the present disclosure. For example, any number of aspects set forth herein can be used to implement a device or practice method. In addition, the scope of the present disclosure is intended to cover such devices or methods implemented using other structures, functionality, or structure and functionality in addition to or different from the various aspects of the disclosure set forth herein. It should be understood that any aspect of the disclosure disclosed herein can be embodied by one or more elements of the present claims.

[0031] Several aspects of telecommunication systems will now be presented with reference to various devices and techniques. These devices and techniques will be described in the following detailed description and illustrated in the accompanying drawings by various blocks, modules, components, circuits, steps, processes, or algorithms (collectively, "elements"). These elements can be implemented using hardware, software, or a combination thereof. Whether such elements are implemented as hardware or software depends on the specific application and the design constraints imposed on the overall system.

[0032] Although various aspects may be described herein using terminology generally associated with 5G or New Radio (NR) radio access technology (RAT), various aspects of the present disclosure may be applicable to other RATs, such as 3G RAT, 4G RAT, and / or post-5G (e.g., 6G) RATs.

[0033] Figure 11 is a diagram illustrating an example of a wireless network 100 according to the present disclosure. The wireless network 100 may be a 5G (e.g., NR) network and / or a 4G (e.g., Long Term Evolution (LTE)) network, or may include elements of a 5G (e.g., NR) network and / or elements of a 4G (e.g., Long Term Evolution (LTE)) network, etc. The wireless network 100 may include one or more network nodes 110 (illustrated as network node 110a, network node 110b, network node 110c, and network node 110d), user equipment (UE) 120 or multiple UEs 120 (illustrated as UE 120a, UE 120b, UE 120c, UE 120d, and UE 120e), and / or other entities. The network node 110 is a network node that communicates with the UE 120. As shown in the figure, the network node 110 may include one or more network nodes. For example, the network node 110 may be a converged network node, meaning that the converged network node is configured to utilize a radio protocol stack that is physically or logically integrated within a single radio access network (RAN) node (e.g., within a single device or unit). As another example, the network node 110 may be a disaggregated network node (sometimes referred to as a disaggregated base station), meaning that the network node 110 is configured to utilize a protocol stack that is physically or logically distributed between two or more nodes (such as one or more central units (CUs), one or more distributed units (DUs), or one or more radio units (RUs)).

[0034] In some examples, network node 110 is or includes a network node (such as an RU) that communicates with UE 120 via a radio access link. In some examples, network node 110 is or includes a network node (such as a DU) that communicates with other network nodes 110 via a fronthaul link or a midhaul link. In some examples, network node 110 is or includes a network node (such as a CU) that communicates with other network nodes 110 via a midhaul link or communicates with a core network via a backhaul link. In some examples, network node 110 (such as a converged network node 110 or a decomposed network node 110) may include multiple network nodes, such as one or more RUs, one or more CUs, and / or one or more DUs. Network node 110 may include, for example, an NR base station, an LTE base station, a Node B, an eNB (e.g., in 4G), a gNB (e.g., in 5G), an access point, a transmit receive point (TRP), a DU, an RU, a CU, a mobility element of a network, a core network node, a network element, network equipment, a RAN node, or a combination thereof. In some examples, network nodes 110 may be interconnected to each other or to one or more other network nodes 110 in wireless network 100 using any suitable transport network via various types of fronthaul interfaces, midhaul interfaces, and / or backhaul interfaces, such as direct physical connections, air interfaces, or virtual networks.

[0035] In some examples, network node 110 may provide communication coverage for a particular geographic area. In the Third Generation Partnership Project (3GPP), the term "cell" may refer to the coverage area of ​​network node 110 and / or a network node subsystem serving that coverage area, depending on the context in which the term is used. Network node 110 may provide communication coverage for a macrocell, a picocell, a femtocell, and / or another type of cell. A macrocell may cover a relatively large geographic area (e.g., a radius of several kilometers) and may allow unrestricted access by UEs 120 with service subscriptions. A picocell may cover a relatively small geographic area and may allow unrestricted access by UEs 120 with service subscriptions. A femtocell may cover a relatively small geographic area (e.g., a home) and may allow restricted access by UEs 120 associated with the femtocell (e.g., UEs 120 in a closed subscriber group (CSG)). A network node 110 for a macrocell may be referred to as a macro network node. A network node 110 for a picocell may be referred to as a pico network node. The network node 110 for a femto cell may be referred to as a femto network node or a home network node. Figure 1 In the example shown, network node 110a may be a macro network node for macro cell 102a, network node 110b may be a pico network node for pico cell 102b, and network node 110c may be a femto network node for femto cell 102c. A network node may support one or more (e.g., three) cells. In some examples, the cells may not necessarily be stationary, and the geographic area of ​​the cells may move depending on the location of a mobile network node 110 (e.g., a mobile network node).

[0036] In some aspects, the term "base station" or "network node" may refer to a converged base station, a decomposed base station, an integrated access and backhaul (IAB) node, a relay node, or one or more components thereof. For example, in some aspects, a "base station" or "network node" may refer to a CU, a DU, a RU, a near real-time (near-RT) RAN intelligent controller (RIC), or a non-real-time (non-RT) RIC, or a combination thereof. In some aspects, the term "base station" or "network node" may refer to a device configured to perform one or more functions, such as those described herein in conjunction with network node 110. In some aspects, the term "base station" or "network node" may refer to multiple devices configured to perform one or more functions. For example, in some distributed systems, each of multiple different devices (which may be located in the same geographic location or in different geographic locations) may be configured to perform at least a portion of a function, or to repeatedly perform at least a portion of the function, and the term "base station" or "network node" may refer to any one or more of these different devices. In some aspects, the term "base station" or "network node" may refer to one or more virtual base stations or one or more virtual base station functions. For example, in some aspects, two or more base station functions may be instantiated on a single device. In some aspects, the term "base station" or "network node" may refer to one of the base station functions but not another base station function. In this way, a single device may include more than one base station.

[0037] The wireless network 100 may include one or more relay stations. A relay station is a network node that can receive transmissions of data from an upstream node (e.g., a network node 110 or a UE 120) and transmit transmissions of data to a downstream node (e.g., a UE 120 or a network node 110). A relay station may be a UE 120 that can relay transmissions for other UEs 120. Figure 1 In the example shown in , a network node 110 d (e.g., a relay network node) may communicate with a network node 110 a (e.g., a macro network node) and a UE 120 d to facilitate communications between the network node 110 a and the UE 120 d. A network node 110 that relays communications may be referred to as a relay station, a relay base station, a relay network node, a relay node, a relay, etc.

[0038] The wireless network 100 may be a heterogeneous network that includes different types of network nodes 110, such as macro network nodes, pico network nodes, femto network nodes, relay network nodes, etc. These different types of network nodes 110 may have different transmit power levels, different coverage areas, and / or different impacts on interference in the wireless network 100. For example, a macro network node may have a high transmit power level (e.g., 5 watts to 40 watts), while a pico network node, a femto network node, and a relay network node may have a lower transmit power level (e.g., 0.1 watt to 2 watts).

[0039] The network controller 130 may be coupled to or in communication with a set of network nodes 110 and may provide coordination and control for the network nodes 110. The network controller 130 may communicate with the network nodes 110 via a backhaul communication link or a midhaul communication link. The network nodes 110 may also communicate directly with each other or indirectly via a wireless backhaul communication link or a wired backhaul communication link. In some aspects, the network controller 130 may be or may include a CU or a core network device.

[0040] UEs 120 may be dispersed throughout wireless network 100, and each UE 120 may be stationary or mobile. UE 120 may include, for example, an access terminal, a terminal, a mobile station, and / or a subscriber unit. UE 120 may be a cellular phone (e.g., a smartphone), a personal digital assistant (PDA), a wireless modem, a wireless communication device, a handheld device, a laptop computer, a cordless phone, a wireless local loop (WLL) station, a tablet computer, a camera, a gaming device, a netbook, a smartbook, an ultrabook, a medical device, a biometric device, a wearable device (e.g., a smart watch, smart clothing, smart glasses, a smart wristband, smart jewelry (e.g., a smart ring or smart bracelet)), an entertainment device (e.g., a music device, a video device, and / or a satellite radio), a vehicle component or sensor, a smart meter / sensor, industrial manufacturing equipment, a global positioning system device, a UE function of a network node, and / or any other suitable device configured to communicate via a wireless or wired medium.

[0041] Some UEs 120 may be considered machine type communication (MTC) or evolved or enhanced machine type communication (eMTC) UEs. MTC UEs and / or eMTC UEs may include, for example, robots, drones, remote devices, sensors, meters, monitors, and / or location tags that can communicate with a network node, another device (e.g., a remote device), or some other entity. Some UEs 120 may be considered Internet of Things (IoT) devices and / or may be implemented as NB-IoT (narrowband IoT) devices. Some UEs 120 may be considered customer premises equipment. The UE 120 may be included within a housing that houses components of the UE 120, such as a processor component and / or a memory component. In some examples, the processor component and the memory component may be coupled together. For example, the processor component (e.g., one or more processors) and the memory component (e.g., memory) may be operatively coupled, communicatively coupled, electronically coupled, and / or electrically coupled.

[0042] Generally speaking, any number of wireless networks 100 may be deployed in a given geographic area. Each wireless network 100 may support a specific RAT and may operate on one or more frequencies. A RAT may be referred to as a radio technology, air interface, etc. A frequency may be referred to as a carrier, frequency channel, etc. Each frequency may support a single RAT in a given geographic area to avoid interference between wireless networks of different RATs. In some cases, NR or 5G RAT networks may be deployed.

[0043] In some examples, two or more UEs 120 (e.g., shown as UE 120a and UE 120e) can communicate directly using one or more sidelink channels (e.g., without using network node 110 as an intermediary to communicate with each other). For example, UE 120 can communicate using peer-to-peer (P2P) communication, device-to-device (D2D) communication, vehicle-to-everything (V2X) protocols (e.g., which may include vehicle-to-vehicle (V2V) protocols, vehicle-to-infrastructure (V2I) protocols, or vehicle-to-pedestrian (V2P) protocols), and / or mesh networks. In such examples, UE 120 can perform scheduling operations, resource selection operations, and / or other operations described elsewhere herein as being performed by network node 110.

[0044] The devices of the wireless network 100 can communicate using an electromagnetic spectrum, which can be subdivided into various categories, bands, channels, etc. based on frequency or wavelength. For example, the devices of the wireless network 100 can communicate using one or more operating bands. In 5G NR, two initial operating bands have been identified as frequency range designations FR1 (410 MHz–7.125 GHz) and FR2 (24.25 GHz–52.6 GHz). It should be understood that although a portion of FR1 is greater than 6 GHz, FR1 is often (interchangeably) referred to as the “sub-6 GHz” band in various documents and articles. A similar naming issue sometimes occurs with respect to FR2, which is often (interchangeably) referred to as the “millimeter wave” band in documents and articles, although it is different from the extremely high frequency (EHF) band (30 GHz–300 GHz) identified as the “millimeter wave” band by the International Telecommunication Union (ITU).

[0045] Frequencies between FR1 and FR2 are generally referred to as mid-band frequencies. Recent 5G NR research has identified the operating band for these mid-band frequencies as frequency range designation FR3 (7.125 GHz–24.25 GHz). The frequency bands falling within FR3 can inherit FR1 characteristics and / or FR2 characteristics, thus effectively extending the features of FR1 and / or FR2 to mid-band frequencies. In addition, higher frequency bands are currently being explored to extend 5G NR operation to more than 52.6 GHz. For example, three higher operating bands have been identified as frequency range designations FR4a or FR4-1 (52.6 GHz–71 GHz), FR4 (52.6 GHz–114.25 GHz), and FR5 (114.25 GHz–300 GHz). Each of these higher frequency bands falls within the EHF band.

[0046] With the above examples in mind, unless otherwise specifically stated, it should be understood that if the term "sub-6 GHz" or the like is used herein, the term may broadly refer to frequencies that may be lower than 6 GHz, may be within FR1, or may include mid-band frequencies. Furthermore, unless otherwise specifically stated, it should be understood that if the term "millimeter wave" or the like is used herein, the term may broadly refer to frequencies that may include mid-band frequencies, may be within FR2, FR4, FR4-a, FR4-1, and / or FR5, or may be within the EHF band. It is contemplated that the frequencies included in these operating bands (e.g., FR1, FR2, FR3, FR4, FR4-a, FR4-1, and / or FR5) may be modified, and the techniques described herein are applicable to those modified frequency ranges.

[0047] In some aspects, a transmitter device (e.g., UE 120 or network node 110) may include a communication manager 140 or a communication manager 150. As described in greater detail elsewhere herein, the communication manager 140 or the communication manager 150 may obtain a plurality of information bits for a probabilistic shaping scheme associated with an energy threshold; form a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; obtain an approximation of a logarithm of a cumulative number of sequences using the polynomial approximation of the plurality of approximation factors, the logarithm of the cumulative number of sequences associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; perform an exponential operation on the approximation of the logarithm of the cumulative number of sequences to thereby obtain an approximation of the cumulative number of sequences; encode the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a symbol sequence having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the symbol sequence belongs to a second alphabet having a second alphabet size; and transmit a message to one or more receiver devices based at least in part on the symbol sequence. Additionally or alternatively, communications manager 140 or communications manager 150 may perform one or more other operations described herein.

[0048] As indicated above, Figure 1 are provided as examples. Other examples can be found in the Figure 1 The examples described are different.

[0049] Figure 2 2 is a diagram illustrating example 200 of a network node 110 communicating with a UE 120 in a wireless network 100 according to the present disclosure. The network node 110 may be equipped with a set of antennas 234a through 234t, such as T antennas (T ≥ 1). The UE 120 may be equipped with a set of antennas 252a through 252r, such as R antennas (R ≥ 1). The network node 110 of example 200 includes one or more radio frequency components, such as antennas 234 and a modem 232. In some examples, the network node 110 may include an interface, a communication component, or another component that facilitates communication with the UE 120 or another network node. Some network nodes 110 may not include radio frequency components, such as one or more CUs or one or more DUs, that facilitate direct communication with the UE 120.

[0050] At network node 110, transmit processor 220 may receive data intended for UE 120 (or a set of UEs 120) from data source 212. Transmit processor 220 may select one or more modulation and coding schemes (MCS) for UE 120 based at least in part on one or more channel quality indicators (CQIs) received from UE 120. Network node 110 may process (e.g., encode and modulate) the data for UE 120 based at least in part on the MCS selected for UE 120 and may provide data symbols for UE 120. Transmit processor 220 may process system information (e.g., for semi-static resource allocation information (SRPI)) and control information (e.g., CQI requests, grants, and / or upper layer signaling) and provide overhead symbols and control symbols. Transmit processor 220 may generate reference symbols for reference signals (e.g., cell-specific reference signals (CRS) or demodulation reference signals (DMRS)) and synchronization signals (e.g., primary synchronization signals (PSS) or secondary synchronization signals (SSS)). The transmit (TX) multiple-input, multiple-output (MIMO) processor 230 may perform spatial processing (e.g., precoding) on ​​data symbols, control symbols, overhead symbols, and / or reference symbols, as applicable, and may provide a set of output symbol streams (e.g., T output symbol streams) to a corresponding set of modems 232 (e.g., T modems) (shown as modems 232a through 232t). For example, each output symbol stream may be provided to a modulator component (shown as MOD) of the modem 232. Each modem 232 may process a corresponding output symbol stream (e.g., for OFDM) using a corresponding modulator component to obtain an output sample stream. Each modem 232 may also process (e.g., convert to analog, amplify, filter, and / or frequency upconvert) the output sample stream using a corresponding modulator component to obtain a downlink signal. The modems 232a through 232t may transmit a set of downlink signals (e.g., T downlink signals) via a corresponding set of antennas 234 (e.g., T antennas) (shown as antennas 234a through 234t).

[0051] At the UE 120, a set of antennas 252 (shown as antennas 252a through 252r) may receive downlink signals from the network node 110 and / or other network nodes 110 and may provide a set of received signals (e.g., R received signals) to a set of modems 254 (e.g., R modems) (shown as modems 254a through 254r). For example, each received signal may be provided to a demodulator component (shown as DEMOD) of the modem 254. Each modem 254 may use a corresponding demodulator component to condition (e.g., filter, amplify, downconvert, and / or digitize) the received signal to obtain input samples. Each modem 254 may use the demodulator component to further process the input samples (e.g., for OFDM) to obtain received symbols. A MIMO detector 256 may obtain received symbols from the modem 254, may perform MIMO detection on the received symbols, if applicable, and may provide detected symbols. The receive processor 258 may process (e.g., demodulate and decode) the detected symbols, may provide decoded data for the UE 120 to a data sink 260, and may provide decoded control information and system information to a controller / processor 280. The term "controller / processor" may refer to one or more controllers, one or more processors, or a combination thereof. The channel processor may determine, among other things, a reference signal received power (RSRP) parameter, a received signal strength indicator (RSSI) parameter, a reference signal received quality (RSRQ) parameter, and / or a CQI parameter. In some examples, one or more components of the UE 120 may be included in a housing 284.

[0052] The network controller 130 may include a communication unit 294, a controller / processor 290, and a memory 292. The network controller 130 may include, for example, one or more devices in a core network. The network controller 130 may communicate with the network node 110 via the communication unit 294.

[0053] One or more antennas (e.g., antennas 234a to 234t and / or antennas 252a to 252r) may include or be included within one or more antenna panels, one or more antenna groups, one or more groups of antenna elements, and / or one or more antenna arrays, etc. An antenna panel, antenna group, group of antenna elements, and / or antenna array may include one or more antenna elements (within a single housing or multiple housings), a group of coplanar antenna elements, a group of non-coplanar antenna elements, and / or be coupled to one or more transmit and / or receive components (such as, Figure 2 One or more antenna elements of one or more components in.

[0054] On the uplink, at the UE 120, a transmit processor 264 may receive and process data from a data source 262 and control information (e.g., for reports including RSRP, RSSI, RSRQ, and / or CQI) from the controller / processor 280. The transmit processor 264 may generate reference symbols for one or more reference signals. The symbols from the transmit processor 264 may be pre-decoded by the TX MIMO processor 266, if applicable, further processed by the modem 254 (e.g., for DFT-s-OFDM or CP-OFDM), and transmitted to the network node 110. In some examples, the modem 254 of the UE 120 may include a modulator and a demodulator. In some examples, the UE 120 includes a transceiver. The transceiver may include any combination of an antenna 252, a modem 254, a MIMO detector 256, a receive processor 258, a transmit processor 264, and / or a TX MIMO processor 266. The transceiver may be used by a processor (eg, controller / processor 280) and memory 282 to execute the instructions herein (eg, reference Figures 7 to 17 )Aspects of any of the methods described.

[0055] At network node 110, uplink signals from UE 120 and / or other UEs may be received by antenna 234, processed by modem 232 (e.g., a demodulator component (shown as DEMOD) of modem 232), detected by MIMO detector 236 (if applicable), and further processed by receive processor 238 to obtain decoded data and control information transmitted by UE 120. Receive processor 238 may provide the decoded data to a data sink 239 and the decoded control information to controller / processor 240. Network node 110 may include a communication unit 244 and may communicate with network controller 130 via communication unit 244. Network node 110 may include a scheduler 246 to schedule one or more UEs 120 for downlink and / or uplink communications. In some examples, modem 232 of network node 110 may include a modulator and a demodulator. In some examples, network node 110 includes a transceiver. The transceiver may include any combination of antenna 234, modem 232, MIMO detector 236, receive processor 238, transmit processor 220, and / or TX MIMO processor 230. The transceiver may be used by a processor (e.g., controller / processor 240) and memory 242 to execute the instructions herein (e.g., reference 242). Figures 7 to 17 )Aspects of any of the methods described.

[0056] The controller / processor 240 of the network node 110, the controller / processor 280 of the UE 120, and / or Figure 2 Any other components of may perform one or more techniques associated with polynomial approximation for probability amplitude shaping, as described in more detail elsewhere herein. In some aspects, the transmitter device described herein is a network node 110, is included in a network node 110, or includes Figure 2 One or more components of the network node 110 shown. In some aspects, the transmitter device described herein is a UE 120, is included in a UE 120, or includes Figure 2 One or more components of the UE 120 are shown. For example, the controller / processor 240 of the network node 110, the controller / processor 280 of the UE 120, and / or Figure 2 Any other component that can execute or guide e.g. Figure 16 1600 and / or operations of other processes as described herein. Memory 242 and memory 282 may store data and program codes for network node 110 and UE 120, respectively. In some examples, memory 242 and / or memory 282 may include a non-transitory computer-readable medium storing one or more instructions (e.g., code and / or program code) for wireless communication. For example, the one or more instructions, when executed (e.g., directly or after compilation, conversion, and / or interpretation) by one or more processors of network node 110 and / or UE 120, may cause the one or more processors, UE 120, and / or network node 110 to perform or direct, for example, Figure 16 The operations of process 1600 and / or other processes as described herein. In some examples, executing instructions may include running instructions, converting instructions, compiling instructions, and / or interpreting instructions, among others.

[0057] In some aspects, a transmitter device (e.g., UE 120 or network node 110) includes: means for obtaining a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; means for forming a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; means for obtaining an approximation of a logarithm of a cumulative number of sequences using the polynomial approximation of the plurality of approximation factors, the logarithm of the cumulative number of sequences being associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; means for performing an exponential operation on the approximation of the logarithm of the cumulative number of sequences to thereby obtain the approximation of the cumulative number of sequences; means for encoding the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a symbol sequence having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the symbol sequence belongs to a second alphabet having a second alphabet size; and / or means for sending a message to one or more receiver devices based at least in part on the symbol sequence. In some aspects, means for a transmitter device to perform operations described herein may include, for example, one or more of the communication manager 150, transmit processor 220, TX MIMO processor 230, modem 232, antenna 234, MIMO detector 236, receive processor 238, controller / processor 240, memory 242, or scheduler 246. In some aspects, means for a transmitter device to perform operations described herein may include, for example, one or more of the communication manager 140, antenna 252, modem 254, MIMO detector 256, receive processor 258, transmit processor 264, TX MIMO processor 266, controller / processor 280, or memory 282.

[0058] Although Figure 2 The blocks in FIG. 2 are illustrated as distinct components, but the functionality described above with respect to these blocks may be implemented in a single hardware, software, or combined component or in various combinations of components. For example, the functionality described with respect to the transmit processor 264, the receive processor 258, and / or the TX MIMO processor 266 may be performed by or under the control of the controller / processor 280.

[0059] As indicated above, Figure 2 are provided as examples. Other examples can be found in the Figure 2 The examples described are different.

[0060] The deployment of a communication system such as a 5G NR system can be arranged in a variety of ways with various components or constituent parts. In a 5G NR system or network, a network node, a network entity, a mobility element of the network, a RAN node, a core network node, a network element, a base station or network equipment may be implemented in an aggregated architecture or a decomposed architecture. For example, a base station (such as a node B (NB), an evolved NB (eNB), an NR base station, a 5G NB, an access point (AP), a TRP or a cell, etc.) or one or more units (or one or more components) performing base station functionality may be implemented as an aggregated base station (also referred to as an independent base station or a monolithic base station) or a decomposed base station. A “network entity” or a “network node” may refer to a decomposed base station or one or more units of a decomposed base station (such as one or more CUs, one or more DUs, one or more RUs or a combination thereof).

[0061] A converged base station (e.g., a converged network node) may be configured to utilize a radio protocol stack that is physically or logically integrated within a single RAN node (e.g., within a single device or unit). A decomposed base station (e.g., a decomposed network node) may be configured to utilize a protocol stack that is physically or logically distributed between two or more units (such as one or more CUs, one or more DUs, or one or more RUs). In some examples, the CU may be implemented within a network node, and one or more DUs may be co-located with the CU, or alternatively, may be geographically or virtually spread across one or more other network nodes. The DU may be implemented to communicate with one or more RUs. Each of the CU, DU, and RU may also be implemented as a virtual unit, such as a virtual central unit (VCU), a virtual distributed unit (VDU), or a virtual radio unit (VRU), among others.

[0062] Base station type operation or network design may take into account the aggregated nature of base station functionality. For example, a disaggregated base station may be utilized in an IAB network, an open radio access network (O-RAN (such as a network configuration initiated by the O-RAN Alliance)), or a virtualized radio access network (vRAN, also known as a cloud radio access network (C-RAN)) to facilitate scaling of the communication system by separating base station functionality into one or more units that can be deployed separately. A disaggregated base station may include functionality implemented across two or more units at various physical locations, as well as functionality implemented virtually for at least one unit, which may enable flexibility in network design. Each unit of the disaggregated base station may be configured for wired or wireless communication with at least one other unit of the disaggregated base station.

[0063] Figure 3FIG2 is a diagram illustrating an example decomposed base station architecture 300 according to the present disclosure. The decomposed base station architecture 300 may include a CU 310 that may communicate directly with a core network 320 via a backhaul link, or indirectly with the core network 320 through one or more decomposed control units (such as a near-RT RIC 325 via an E2 link, a non-RT RIC 315 associated with a service management and orchestration (SMO) framework 305, or both). The CU 310 may communicate with one or more DUs 330 via respective midhaul links (such as via an F1 interface). Each of the DUs 330 may communicate with one or more RUs 340 via respective fronthaul links. Each of the RUs 340 may communicate with one or more UEs 120 via respective radio frequency (RF) access links. In some implementations, a UE 120 may be served simultaneously by multiple RUs 340.

[0064] Each of the units (including the CU 310, DU 330, RU 340) and the near-RT RIC 325, the non-RT RIC 315, and the SMO framework 305 may include or be coupled to one or more interfaces configured to receive or transmit signals, data, or information (collectively, signals) via a wired or wireless transmission medium. Each of the units, or an associated processor or controller that provides instructions to one or more communication interfaces of the corresponding unit, may be configured to communicate with one or more of the other units via the transmission medium. In some examples, each of the units may include a wired interface configured to receive signals or transmit signals to one or more of the other units via a wired transmission medium, and a wireless interface that may include a receiver, a transmitter, or a transceiver (such as an RF transceiver) configured to receive signals or transmit signals to one or more of the other units via a wireless transmission medium, or both.

[0065] In some aspects, the CU 310 may host one or more higher layer control functions. Such control functions may include radio resource control (RRC) functions, packet data convergence protocol (PDCP) functions, or service data adaptation protocol (SDAP) functions, among others. Each control function may be implemented using an interface that is configured to communicate signals with other control functions hosted by the CU 310. The CU 310 may be configured to handle user plane functionality (e.g., central unit-user plane (CU-UP) functionality), control plane functionality (e.g., central unit-control plane (CU-CP) functionality), or a combination thereof. In some implementations, the CU 310 may be logically split into one or more CU-UP units and one or more CU-CP units. When implemented in an O-RAN configuration, the CU-UP unit may communicate bidirectionally with the CU-CP unit via an interface (such as an E1 interface). As needed, the CU 310 may be implemented to communicate with the DU 330 for network control and signaling.

[0066] Each DU 330 may correspond to a logical unit that includes one or more base station functions for controlling the operation of one or more RUs 340. In some aspects, the DU 330 may host one or more of a radio link control (RLC) layer, a medium access control (MAC) layer, and one or more higher physical (PHY) layers, at least in part according to a functional split (such as that defined by 3GPP). In some aspects, the one or more higher PHY layers may be implemented by one or more modules for forward error correction (FEC) encoding and decoding, scrambling, modulation and demodulation, and the like. In some aspects, the DU 330 may also host one or more lower PHY layers, such as those implemented by one or more modules for fast Fourier transform (FFT), inverse FFT (iFFT), digital beamforming, or physical random access channel (PRACH) extraction and filtering. Each layer (which may also be referred to as a module) may be implemented using an interface configured to communicate signals with other layers (and modules) hosted by the DU 330 or with control functions hosted by the CU 310.

[0067] Each RU 340 may implement lower layer functionality. In some deployments, the RU 340 controlled by the DU 330 may correspond to a logical node that hosts RF processing functions or low PHY layer functions based on functional split (e.g., functional split defined by 3GPP) (such as lower layer functional split), such as performing FFT, performing iFFT, digital beamforming, or PRACH extraction and filtering, etc. In this architecture, each RU 340 may be operated to handle over-the-air (OTA) communications with one or more UEs 120. In some specific implementations, real-time and non-real-time aspects of control plane and user plane communications with the RU 340 may be controlled by the corresponding DU 330. In some scenarios, this configuration may enable each DU 330 and CU 310 to be implemented in a cloud-based RAN architecture (such as a vRAN architecture).

[0068] The SMO framework 305 can be configured to support RAN deployment and provisioning of both non-virtualized and virtualized network elements. For non-virtualized network elements, the SMO framework 305 can be configured to support the deployment of dedicated physical resources for RAN coverage requirements, which can be managed via an operations and maintenance interface (such as the O1 interface). For virtualized network elements, the SMO framework 305 can be configured to interact with a cloud computing platform (such as the Open Cloud (O-Cloud) platform 390) to perform network element lifecycle management (such as instantiating virtualized network elements) via a cloud computing platform interface (such as the O2 interface). Such virtualized network elements can include, but are not limited to, CU 310, DU 330, RU 340, non-RT RIC 315, and near-RT RIC 325. In some implementations, the SMO framework 305 can communicate with hardware aspects of the 4G RAN (such as the Open eNB (O-eNB) 311) via the O1 interface. Additionally, in some implementations, the SMO framework 305 can communicate directly with each of the one or more RUs 340 via a corresponding O1 interface. The SMO framework 305 can also include a non-RT RIC 315 configured to support the functionality of the SMO framework 305.

[0069] The non-RT RIC 315 can be configured to include logic that enables non-real-time control and optimization of RAN elements and resources, artificial intelligence / machine learning (AI / ML) workflows including model training and updating, or policy-based guidance of applications / features in the near-RT RIC 325. The non-RT RIC 315 can be coupled to or in communication with the near-RT RIC 325 (e.g., via an A1 interface). The near-RT RIC 325 can be configured to include logic that enables near-real-time control and optimization of RAN elements and resources through data collection and actions over an interface (e.g., via an E2 interface) that connects one or more CUs 310, one or more DUs 330, or both, and the O-eNB with the near-RT RIC 325.

[0070] In some implementations, the non-RT RIC 315 can receive parameters or external enrichment information from an external server to generate an AI / ML model to be deployed in the near-RT RIC 325. Such information can be utilized by the near-RT RIC 325 and can be received from non-network data sources or from network functions at the SMO framework 305 or the non-RT RIC 315. In some examples, the non-RT RIC 315 or the near-RT RIC 325 can be configured to tune RAN behavior or performance. For example, the non-RT RIC 315 can monitor long-term trends and patterns in performance and employ AI / ML models to perform corrective actions through the SMO framework 305 (such as via reconfiguration of the O1 interface) or through the creation of RAN management policies (such as A1 interface policies).

[0071] As indicated above, Figure 3 are provided as examples. Other examples can be found in the Figure 3 The examples described are different.

[0072] In wireless networks, a transmitting node may encode information according to a forward error correction (FEC) coding scheme to improve transmission reliability. The transmitting node may then modulate the encoded information according to a modulation scheme for transmission. A modulation scheme may have a constellation with certain constellation points, which may also be referred to as modulation symbols. Transmissions using a modulation scheme may carry information represented by modulation symbols from a set of constellation points defined for the modulation scheme.

[0073] Traditional signal constellations, such as amplitude-shift keying (ASK) and quadrature amplitude modulation (QAM), are characterized by equally spaced constellation points, each transmitted with equal probability. Unfortunately, such constellations result in a gap with the Shannon limit. To narrow this gap and improve spectral efficiency, constellation shaping can be applied. For additive white Gaussian noise (AWGN) channels, constellation shaping can provide a signal-to-noise ratio (SNR) gain of up to 1.53 decibels (dB), referred to as shaping gain, by utilizing a Gaussian-shaped constellation.

[0074] Advantageous performance, with data rates close to the channel capacity, can be achieved with constellations having a Gaussian-like distribution. Geometric constellation shaping (GCS) and probabilistic amplitude shaping (PAS) are specific examples of constellations that provide non-uniform distributions using QAM. For GCS, each constellation point can be used with equal probability, while the positions of the constellation points are unequally spaced and arranged to mimic the capacity realization distribution. For PAS, or more generally, probabilistic constellation shaping (PCS), constellations, such as ASK or QAM, can be used in which the constellation points are equidistant and different probabilities can be assigned to different constellation points.

[0075] The transmitter chain in the transmitter device may be associated with an energy-based PAS architecture. The transmitter chain may be considered to have a modulation order of 2 M ASK constellation. The ASK constellation can be composed of a constellation with an amplitude alphabet {1,3,…,2 M {±1,±3,…,±(2 M -1)}. The energy-based PAS architecture can be naturally extended to the constellation with modulation order 2 2M The QAM constellation can be composed of a QAM constellation with an amplitude alphabet {1,3,…,2 M {±1,±3,…,±(2 M -1)}×{±1,±3,…,±(2 M -1)}. In energy-based probability shaping, The energy of can be constrained to be below an energy threshold The energy threshold E can refer to the maximum sequence energy. to induce a target non-uniform distribution on the amplitude sign.

[0076] Figure 4 is a diagram illustrating an example 400 of a transmitter chain according to the present disclosure.

[0077] like Figure 4 As shown, the transmitter chain in the transmitter device may include an energy-based amplitude shaper. The input to the energy-based amplitude shaper may be u k, and the output of the energy-based amplitude shaper can be The symbol to bit mapper may receive the output of the energy based amplitude shaper. The symbol to bit mapper may be coupled to a system FEC encoder which may be coupled to the bit to symbol mapper. The output of the bit to symbol mapper may be

[0078] As indicated above, Figure 4 are provided as examples. Other examples can be found in the Figure 4 The examples described are different.

[0079] In the transmitter chain of the transmitter device, with rate The amplitude shaper can encode k information bits as Amplitude symbols. Sequence u k =(u1,u2,…,u k ) may include k information bits. May include Amplitude symbols. Induced by the energy-based amplitude shaper A non-uniform symbol-by-symbol marginal distribution over the amplitude symbols can be closer to the capacity-achieving input distribution than a uniform distribution. For example, the non-uniform distribution can be a Maxwell-Boltzmann (MB) distribution for an AWGN channel. The sequence Can be converted to length The (M-1) bit sequence (given by express). Each of the magnitude symbols may correspond to (M-1) bits, which may each contribute 1 bit to the bit sequence, which yields a total of Amplitude bits. Amplitude bit sum extra information bits (by can be combined to form The bits can be used at a rate of R c =(M-1+γ) / M is input to the system FEC encoder. The FEC encoder can generate Indicated parity bit. parity bits together with γn additional information bits (which together constitute ) can be converted to A flag bit. The flag bit can be used with in The transmission rate associated with the transmitter chain can be R t =R as +γ.

[0080] About the alphabet Can be a second alphabet size The second alphabet of Each element of can be called a symbol. Sort on such that for any a i i+1 (For example, ). For 1 and For every integer m between It can be represented by the symbol a i Composed of A subset of where all i≤m such that For example, and and May be referred to as the first alphabet and may have a first alphabet size m, and may be a subset of or equal to the second alphabet.

[0081] Regarding symbol energy, at a given size The second alphabet In the case of E(a i ) can represent the symbol a of each i i The symbol energies can be different, and for example for any The induced ordering can exist in the energy such that 0≤E(a i ) <E(a i+1 ).

[0082] About the 2M-ary ASK constellation and symbolic energy examples, Make m=2 M-1 (for example, m depends on the modulation order), and Corresponding to 2 M In this case, a i =2i-1, so that In the first example, for each i, the symbol a i Energy E(a i ) can be E(a i )=(2i-1) 2 In the second example, for each i, the symbol a i Energy E(a i ) can be E(a i )=i(i-1) / 2. Since 8E(a i )+1=(2i-1)​2 , so E(a i ) may be related to (2i-1) in the first example 2 Shift scaling.

[0083] Regarding sequence energy, for the first alphabet of size m It is possible to consider a first sequence length n and The sequence s in the n ). The length of the sequence may be equal to n, and each element of the sequence may belong to the first alphabet The energy of a sequence s, denoted by E(s), may be defined as the accumulation (eg, sum) of all its symbol energies according to:

[0084]

[0085] About the cumulative number of sequences It can be the first alphabet of size m that satisfies the following condition: for each i∈{1,2,…,m}, the symbol a i With energy E(a i ).also, can be represented as having length n and The set of all sequences in , such that each sequence in the set has an energy at most equal to the energy E of the first sequence. In addition, Can represent The cardinality of the set (e.g., The total number of different sequences in ), such that When the alphabet size m is clear from the context, the superscript " [m] " can be omitted and N can be written c (n,E) as a substitute. For a given m, N c (n,E) can be a two-variable integer-valued function of n and E.

[0086] Cumulative number of sequences N c Can be associated with energy-based shaping. In energy-based shaping schemes, given a symbol alphabet Sequence length and energy threshold In the case of The coding technique can induce the k The set of digit sequences to The encoding technique can be adopted by the distribution matcher in the PAS architecture.

[0087] Regarding computational complexity and storage complexity, generally, may be relatively small, while the sequence length and energy threshold Coding techniques generally require knowledge of the dynamic range for one or more values ​​of n and E and m. in and Direct calculation of the value of may have a computational complexity quadratic to n. Furthermore, such values ​​may be of relatively large magnitude, so that a direct tabulation technique for accurately storing all such values ​​for a wide range of values ​​of n and E may have prohibitively large storage complexity.

[0088] Figure 5 is a diagram illustrating an example 500 of accumulating logarithms of the number of sequences according to the present disclosure.

[0089] like Figure 5 As shown, you can define the alphabet log N c (n, E), where n ranges from 1 to 1000, and for each n, E ranges from 0 to 6n. The symbol energies can be E(a1) = 0, E(a2) = 1, E(a3) = 3, and E(a4) = 6. In other words, is shown as a two-variable function of n and E with respect to m.

[0090] As indicated above, Figure 5 are provided as examples. Other examples can be found in the Figure 5 The examples described are different.

[0091] Executable for N c The approximation of log N can ensure ultra-high approximation accuracy, but may require further reduction of complexity. c (n,E) can be approximated by represents and can be determined based on:

[0092]

[0093] log N c Another approximation for (n,E) can be determined from:

[0094]

[0095] Among them H sat is the same as the underlying alphabet The associated saturation entropy function.

[0096] In addition, the normalized energy can be obtained by The concentrated and scaled energy can be expressed as indicates that, and The uniform energy within can be expressed as follows:

[0097]

[0098] Except for c(E), each of the remaining functions may depend on the underlying alphabet

[0099] When the normalized energy ω is less than Uniform energy ω u The saturation entropy function H evaluated at the normalized energy ω is sat The value is equal to The value of the Shannon entropy associated with the Maxwell-Boltzmann (MB) distribution with parameter β, which is equal to the saturation entropy function H evaluated at the normalized energy ω. sat When the value of the normalized energy ω is greater than or equal to Uniform energy ω u When , the saturation entropy function H evaluated at the normalized energy ω is sat equal The logarithm of the magnitude of ; that is, logm.

[0100] Regarding complexity considerations, evaluating each of the above terms for any pair of n and E may be of moderate complexity. The evaluation of each of the above terms may involve solving the root λ=λ(ω) of the polynomial equation Z1(λ) / Z0(λ)=ω, which may be based on the following:

[0101] as well as

[0102]

[0103] The evaluation of each of the above items may involve taking e.g. The logarithm of the real positive number in the term. The evaluation of each of the above terms may involve taking a real number to a power, where the power increases with m. Like the saturation entropy function H sat The function can be [0,E(a m )] within a smooth function. Therefore, the approximate log N c (n,E) may involve using simpler alternatives to approximate these functions.

[0104] Figure 6 is a diagram illustrating an example 600 of approximated absolute error according to the present disclosure.

[0105] like Figure 6 As shown, it can be calculated with The associated approximation, where log N cis associated with a truth value, and is associated with an approximation. The approximation may be associated with an absolute error of the approximation in log-10 scale. The approximation may be in terms of n and E. The calculation may be associated with a very high approximation accuracy, but may involve a relatively high complexity.

[0106] As indicated above, Figure 6 are provided as examples. Other examples can be found in the Figure 6 The examples described are different.

[0107] In various aspects of the techniques and apparatuses described herein, a transmitter device (eg, a UE or a network node) may obtain a plurality of information bits (k information bits) for a probabilistic shaping scheme. The probabilistic shaping scheme may be combined with an energy threshold. Energy threshold The transmitter device may form a polynomial approximation of the plurality of approximation factors as part of the probability shaping scheme. The transmitter device may use the polynomial approximation of the plurality of approximation factors to obtain the cumulative number of sequences (N c The logarithm of the cumulative number of sequences can be approximated by the first alphabet with the first alphabet size (m). The first sequence length (n) is associated with the first sequence energy (E). The transmitter device may perform an exponential operation on an approximation of the logarithm of the cumulative sequence quantity to obtain an approximation of the cumulative sequence quantity. The transmitter device may encode a plurality of information bits based at least in part on the approximation of the cumulative sequence quantity as part of a probability shaping scheme to obtain a symbol sequence The symbol sequence may have a second sequence length equal to The length and energy less than or equal to the energy threshold Each symbol in the symbol sequence may belong to a second alphabet having a size The second alphabet A transmitter device may transmit a message to one or more receiver devices based at least in part on a symbol sequence. In some aspects, by using polynomial approximation, very high approximation accuracy can be achieved with reduced complexity, which can improve the performance of the transmitter device. For example, implementing polynomial approximation can reduce power consumption of the transmitter device.

[0108] Figure 7 is a diagram illustrating an example 700 associated with a polynomial approximation technique for probability amplitude shaping according to the present disclosure. Figure 7 As shown, example 700 includes communications between a transmitter device (e.g., UE 120 or network node 110) and a receiver (e.g., network node 110 or UE 120). In some aspects, the transmitter device and receiver may be included in a wireless network such as wireless network 100.

[0109] As shown in reference numeral 702, the transmitter device may obtain a plurality of information bits (k information bits) for a probability shaping scheme. The probability shaping scheme may be combined with an energy threshold The probability shaping scheme may be an energy-based probability amplitude shaping scheme involving polynomial approximation.

[0110] As shown at 704, the transmitter device may form a polynomial approximation of the plurality of approximation factors as part of the probabilistic shaping scheme. In some aspects, when forming the polynomial approximation of the plurality of approximation factors, the transmitter device may determine a normalized energy (ω) corresponding to a ratio between the first sequence energy (E) and the first sequence length (n). The transmitter device may obtain a uniform energy (ω) u ), where uniform energy can be compared with the first alphabet The transmitter device may obtain a sub-interval of the interval based at least in part on the normalized energy (an example of an interval is shown in FIG. Figure 11A 、 Figure 11B 、 Figure 12 and Figure 13 ). The transmitter device may use the subinterval of the interval and the normalized energy to form at least one polynomial approximation of the plurality of approximation factors.

[0111] In some aspects, an interval may be associated with a first alphabet. An interval may include a plurality of subintervals, and the interval may correspond to a disjoint union of the plurality of subintervals. Each of the plurality of subintervals of the interval may correspond to a respective left subinterval boundary of the plurality of left subinterval boundaries.

[0112] In some aspects, each of the plurality of subintervals of an interval may be associated with one or more respective approximate region indices (examples of approximate regions are described in Figure 9 and Figure 10 ). Each respective approximation region index of the one or more respective approximation region indices may be associated with a respective reference point of the plurality of reference points, a respective additional index, and / or one or more respective polynomial coefficient indices, wherein each polynomial coefficient index of the one or more respective polynomial coefficient indices may be associated with a respective multiplication index of the plurality of multiplication indices and a respective type indicator of the plurality of type indicators.

[0113] In some aspects, one or more reference points in the plurality of reference points may correspond to binary numbers. One or more left subinterval boundaries of the plurality of subintervals of the interval may correspond to binary numbers. One or more reference points in the plurality of reference points may coincide with one or more corresponding left subinterval boundaries of the plurality of left subinterval boundaries. The total number of reference points in the plurality of reference points may be less than the total number of left subinterval boundaries of the plurality of subintervals of the interval. In some aspects, the plurality of left subinterval boundaries may be stored as a binary tree structure having a root node, a plurality of internal nodes, and a plurality of leaf nodes. Each of the plurality of internal nodes may store a key corresponding to the corresponding left subinterval boundary. Each of the plurality of leaf nodes may store a subinterval index corresponding to the corresponding subinterval of the plurality of subintervals of the interval.

[0114] In some aspects, the transmitter device may perform a binary search by traversing a path from a root node to a leaf node of a plurality of leaf nodes in a binary tree structure when obtaining a subinterval of an interval (an example of a subinterval search is described in Figure 14 ). A leaf node of the plurality of leaf nodes may store a subinterval index corresponding to a subinterval of the interval. The transmitter device may identify a subinterval of the interval based at least in part on the subinterval index. The transmitter device may determine an approximate region index based at least in part on the first sequence length and the identification of the subinterval of the interval. The transmitter device may identify one or more polynomial coefficient indices, wherein the one or more polynomial coefficient indices may be associated with the approximate region index. The transmitter device may identify a corresponding multiplication index for each of the one or more polynomial coefficient indices. The transmitter device may identify a corresponding type indicator for each of the one or more polynomial coefficient indices.

[0115] In some aspects, when performing the binary search, the transmitter device may determine a difference between the normalized energy and a reference point corresponding to a subinterval of the interval. The difference may refer to a subtraction between the normalized energy and the reference point. In other words, the difference refers to the normalized energy minus the reference point. In some aspects, when performing the binary search, the transmitter device may determine a difference between a lumped and scaled energy (v) and a reference point corresponding to a subinterval of the interval, where the lumped and scaled energy may correspond to a square root of the length of the first sequence multiplied by the difference between the normalized energy and the uniform energy.

[0116] In some aspects, when utilizing a subinterval of an interval and a normalized energy, a transmitter device may calculate one or more polynomial values, wherein each of the one or more polynomial values ​​may correspond to a corresponding polynomial coefficient index in one or more polynomial coefficient indices. The transmitter device may determine one or more multiplication factors, wherein each of the one or more multiplication factors may be associated with a corresponding polynomial coefficient index in the one or more polynomial coefficient indices based at least in part on the multiplication index. The transmitter device may determine one or more approximations, wherein each of the one or more approximations may be based at least in part on a product of a corresponding polynomial value in the one or more polynomial values ​​and a corresponding multiplication factor in the one or more multiplication factors.

[0117] In some aspects, each respective polynomial approximation may be based at least in part on a plurality of polynomial coefficients and a polynomial degree. The plurality of polynomial coefficients and the polynomial degree may be stored in a memory of the transmitter device (an example of storage of polynomial coefficients is provided in Figure 15 ). Multiple polynomial coefficients may be stored in a lookup table.

[0118] In some aspects, when forming a polynomial approximation of the plurality of approximation factors, the transmitter device may determine an approximation region based at least in part on the first sequence length and the first sequence energy. The approximation region may be associated with a first alphabet. The transmitter device may identify an approximation form corresponding to the approximation region. The transmitter device may form a polynomial approximation of the plurality of approximation factors based at least in part on the identification of the approximation form. In some aspects, when forming the polynomial approximation of the plurality of approximation factors, the transmitter device may remove singularities from at least one of the polynomial approximations of the plurality of approximation factors.

[0119] As shown at reference numeral 706, the transmitter device may use a polynomial approximation of a plurality of approximation factors to obtain the cumulative number of sequences (N c (n, E)). The logarithm of the cumulative number of sequences may be associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy. The cumulative number of sequences may define a cardinality of a set of all sequences over the first alphabet. Each sequence in the set of all sequences over the first alphabet may have a respective length equal to the first sequence length and a respective energy less than or equal to the first sequence energy.

[0120] In some aspects, when obtaining an approximation of the logarithm of the cumulative sequence quantity, the transmitter device may multiply each polynomial approximation of a plurality of approximation factors by a corresponding multiplication factor. The corresponding multiplication factor may be based at least in part on the first sequence length. The transmitter device may obtain a plurality of approximation terms based at least in part on the multiplication of each polynomial approximation. Each approximation term in the plurality of approximation terms may correspond to a corresponding polynomial approximation of the plurality of approximation factors. The transmitter device may sum the plurality of approximation terms to obtain the approximation of the logarithm of the cumulative sequence quantity.

[0121] In some aspects, the polynomial approximation of the plurality of approximation factors may include a saturation entropy function (H sat ). The saturated entropy function may correspond to a first approximation factor of the plurality of approximation factors. The saturated entropy function may be associated with a first alphabet. The polynomial approximation of the plurality of approximation factors may include a respective piecewise polynomial approximation corresponding to each of the one or more additional functions. Each of the one or more additional functions may be a function of normalized energy or a lumped and scaled energy.

[0122] The transmitter device may perform an exponential operation on an approximation of the logarithm of the cumulative sequence number, thereby obtaining an approximation of the cumulative sequence number, as indicated by reference numeral 708. The logarithm of the cumulative sequence number is base 2, and the transmitter device may perform an exponential operation on the base 2.

[0123] As indicated at reference numeral 710, a transmitter device may encode a plurality of information bits to obtain a symbol sequence based at least in part on an approximation of the cumulative sequence quantity as part of a probabilistic shaping scheme. The symbol sequence may have a second sequence length equal to The length of the symbol sequence and the energy less than or equal to the energy threshold. Each symbol in the symbol sequence may belong to a second alphabet having a size The second alphabet The probability shaping scheme may be associated with a second alphabet and a second sequence length. The second alphabet size may be greater than 1. The second alphabet may include multiple amplitude symbols. The first alphabet may be a subset of the second alphabet or equal to the second alphabet. The first sequence length may be less than or equal to the second sequence length. The first sequence energy may be less than or equal to an energy threshold. The second sequence length may be a power of 2. The first sequence length may be a power of 2. In other words, the second sequence length and the first sequence length may be equal to a number that is a power of 2 (e.g., the number 16, which is 2 4 ), or may be equal to an integer power of 2.

[0124] As shown at reference numeral 712, a transmitter device may transmit a message to one or more receiver devices based at least in part on the symbol sequence. For example, a UE may transmit a message to another UE or a network node based at least in part on the symbol sequence. A network node may transmit a message to another network node or a UE based at least in part on the symbol sequence.

[0125] As indicated above, Figure 7 are provided as examples. Other examples can be found in the Figure 7 The examples described are different.

[0126] In some aspects, a transmitter device (e.g., a UE or a network node) may obtain k information bits. The transmitter device may encode the k information bits into a symbol sequence based at least in part on an energy-based probability shaping scheme involving polynomial approximation. Polynomial approximation can involve targeting the first alphabet One or more values ​​of the associated first alphabet size m, first sequence length n and / or first sequence energy E are associated with the cumulative number of sequences N. c Piecewise polynomial approximation of (n,E). k information bits to symbol sequence The encoding may be based at least in part on the cumulative number of sequences N c (n,E). k information bits to symbol sequence The encoding can be for the second alphabet Second sequence length and energy threshold Polynomial approximation can be used to approximate N for one or more values ​​of m, n, and E c (n,E), and such values ​​can be used for encoding. Can be the second alphabet The first sequence length n may be less than or equal to the second sequence length The first sequence energy E may be less than or equal to the energy threshold

[0127] In some aspects, the transmitter device may perform a polynomial approximation to obtain the cumulative sequence number N c (n, E). When performing the polynomial approximation, the transmitter device may perform an interval search based at least in part on the interval to obtain a subinterval. Given a first sequence length n and a first sequence energy E, the transmitter device may perform an interval search based at least in part on the interval to obtain a subinterval. The interval search may be based at least in part on a binary search tree structure. The binary search tree structure may be based at least in part on the normalized energy ω or the lumped and scaled energy v. One or more reference points may be obtained based at least in part on the interval for use in polynomial evaluation associated with polynomial approximation. The transmitter device may determine an approximation form based at least in part on the first sequence length n and the subinterval. The polynomial coefficient index associated with the subinterval may correspond to a polynomial coefficient stored in a lookup table.

[0128] In some aspects, the transmitter device may calculate the value of each polynomial of the normalized energy ω or the lumped and scaled energy v to obtain a polynomial value. The transmitter device may calculate the value of each of the one or more approximation terms of the approximation form based at least in part on the first sequence length n and the polynomial value. The transmitter device may approximate the cumulative number of sequences N based at least in part on the sum of the approximation terms. c The logarithm of (n,E). The transmitter device can accumulate the number of sequences N c The approximate exponential of the logarithm of (n,E) is used to obtain the cumulative number of sequences N c Approximation of (n,E).

[0129] Figure 8A and Figure 8B is a diagram illustrating an example 800 associated with an approximate absolute error according to the present disclosure.

[0130] In some aspects, numerical evaluation using m=8 and QAM-256 can be based at least in part on piecewise polynomial approximation techniques. Figure 8A The high accuracy scenario for m=8 may have a worst case absolute error of 0.0007 for all n≥32. ​​The total number of polynomial segments may be 152. All polynomials may have degree 3. The fixed storage of polynomial coefficients may be 1824 bytes, with 3 bytes per coefficient. Figure 8B As shown, the low accuracy example for m=8 may have a worst-case absolute error of 0.0014 for all n≥32. ​​The total number of polynomial segments may be 67. All polynomials may have degree 3. Fixed storage of polynomial coefficients may be 804 bytes, 3 bytes per coefficient.

[0131] As indicated above, Figure 8A and Figure 8B are provided as examples. Other examples can be found in the Figure 8A and Figure 8B The examples described are different.

[0132] In some aspects, the first alphabet The first feasible region and the second feasible region The first feasible region and the second feasible region Each of the one or more subsets may be a disjoint union of the one or more subsets. Each subset in the one or more subsets may correspond to an approximation region. The approximation region may be associated with an approximation form. The approximation form may be a sum of one or more approximation terms. Each of the one or more approximation terms may include an approximation factor corresponding to a polynomial of the normalized energy ω or the concentrated and scaled energy v. Each of the one or more approximation terms may include a multiplication factor that depends on the length n of the first sequence. An approximation term may be a function of the energy E of the first sequence.

[0133] In some aspects, the approximation region can be customized to make a relatively fast and accurate approximation. E(a i ) can be symbol a i energy, so that E(a m ) is the maximum symbol energy. For integer n min and n max , such that 1≤n min <n max ,and Associated feasible region and Can be defined as:

[0134]

[0135] Here, n min and n max is n min =1 and n max =1024, and ω u Can be with The associated uniform energy. Each feasible region or It can be a disjoint union of one or more subsets. Each subset can be called an approximate region, and the total number of approximate regions can be given by J m and K m Therefore:

[0136]

[0137] For example, i indexes the approximate region, and Can be an approximate area (for example, when It can be written when it is clear As substituted for).

[0138] In some aspects, each approximation region can be associated with an approximation form. Each approximation form can be written as a sum of one or more approximation terms. Each approximation term can be composed of approximation factors corresponding to a polynomial of the normalized energy ω or the concentrated and scaled energy ν. Each approximation term can be composed of a multiplicative factor that depends only on n (e.g., a factor such as n, log n, or 1). The approximation term can be a function of E, the value of which can be tabulated.

[0139] Figure 9 is a diagram illustrating an example 900 associated with an approximate region according to the present disclosure.

[0140] In some aspects, the normalized energy ω can be zero and the first alphabet The associated uniform energy ω u The first feasible region A plurality of approximation regions may be included. An approximation region in the plurality of approximation regions may be based at least in part on using a lookup table, a first sequence length n, a saturation entropy function H sat , normalized energy ω, first sequence energy E and / or concentrated and scaled energy ν versus cumulative sequence number N c Storage of (n,E).

[0141] like Figure 9 As shown, The approximate region in can be for m=4, 1≤n≤1024 and 0≤ω<ω u For example, 1, 10, 16, 32, 128, 256, 512, or 1024, and 0, 0.3125, 1.25, 1.5, 2.215, or 2.5 can be used to distinguish The boundary of the approximate region in . The approximate area in may include (surface), and c(E), and

[0142] about Approximate form, approximate area It can correspond to using a lookup table to N c (n,E) or log N c Storage (e.g., fixed read-only memory (ROM) storage) of (n, E). For example, the approximate area corresponding to ω at 0 and ω u and n is less than or equal to 10. In other words, when n and ω are within these specified ranges, The tabulated values ​​can be used to approximate where E = ωn. For the approximate region or The associated approximate forms can be given by:

[0143]

[0144] The logarithm can be base 2, but other choices are possible (e.g., natural logarithm). For example, the approximate region corresponds to the case when ω is between 0 and 0.3125 and n is between 32 and 1024. The symbols in brackets (e.g., for and ) can be used to partially indicate the approximation factor associated with the corresponding approximation region. The associated approximate forms can be given by:

[0145]

[0146] For example, the approximate area This corresponds to the case when ω is between 0.3125 and 1.25 and n is between 10 and 32. For the approximate region or The associated approximate form can be given by:

[0147]

[0148] For example, the approximate area For the case where ω is between 0.3125 and 1.5 and n is between 32 and 128, the approximate region corresponds to the case when ω is between 0.3125 and 2.125 and n is between 128 and 512, and the approximate region This corresponds to the case where ω is between 0.3125 and 2.125 and n is between 512 and 1024. For the approximate region The associated approximate form can be given by:

[0149]

[0150] For the approximate area or The associated approximate form can be given by:

[0151]

[0152] For example, the approximate area corresponds to the case when ω is between 2.125 and 2.5 and n is between 256 and 512, and the approximate region This corresponds to the case where ω is between 2.125 and 2.5 and n is between 512 and 1024.

[0153] As indicated above, Figure 9 are provided as examples. Other examples can be found in the Figure 9 The examples described are different.

[0154] Figure 10 is a diagram illustrating an example 1000 associated with an approximate region according to the present disclosure.

[0155] In some aspects, the normalized energy ω may be obtained by multiplying the uniform energy ω by the given value. u and the maximum symbol energy E(a m ), the uniform energy and the first alphabet The second feasible region A plurality of approximation regions may be included. An approximation region in the plurality of approximation regions may be based at least in part on the cumulative number of sequences N using a lookup table, a first sequence length n, a first alphabet size m, and / or a focused and scaled energy v. c Storage of (n,E).

[0156] like Figure 10 As shown, The approximate region in can be for m=4, 1≤n≤1024 and ω u ≤ω <E(a m For example, 1, 10, 16, 32, 128, 256, 512, or 1024 and 0, 4, 7.5, 8.5, or 112 can be used to distinguish The boundary of the approximate region in . The approximate area in may include (surface), and (For example, using H in this area sat (ω) = lgo m is sufficient).

[0157] about Approximate form, approximate area It can correspond to using a lookup table to N c (n,E) or lgo N c Storage (e.g., fixed ROM storage) of (n, E). For example, the approximate area This corresponds to the case when n is less than or equal to 10. For the approximate region The associated approximate form can be given by:

[0158]

[0159] in is the multiplication factor, is an approximation factor, and is an approximate term. For example, the approximate area Corresponds to the case when ν is between 0 and 4 and n is between 10 and 256 and when ν is between 4 and 7.5 and n is between 10 and 32. The symbols in brackets (e.g., for and ) can be used to partially indicate the approximation factor associated with the corresponding approximation region. The associated approximate form can be given by:

[0160]

[0161] For example, the approximate area This corresponds to the case where v is between 0 and 4, n is between 256 and 1024, and when v is between 4 and 7.5, n is between 32 and 1024. The associated approximate form can be given by:

[0162]

[0163] For example, the approximate area This corresponds to the case when ν is between 7.5 and 8.5 and n is between 10 and 1024. For the approximate region The associated approximate form can be given by:

[0164]

[0165] For example, the approximate area This corresponds to the case where v is between 8.5 and 112 and n is between 10 and 1024.

[0166] As indicated above, Figure 10 are provided as examples. Other examples can be found in the Figure 10 The examples described are different.

[0167] In some aspects, the piecewise polynomial approximation may be associated with polynomial coefficients and degrees. A device (eg, a transmitter device) may not need to know the exact function (eg, the saturation entropy function H sat ). Instead, the device may only need to have a process to locate the correct polynomial and then assemble the polynomial. Therefore, a polynomial approximation of an approximation factor may not imply that the device actually knows the approximation factor (e.g., function).

[0168] Corresponding to The associated saturation entropy function H sat The approximate factors of can be obtained by piecewise polynomial Associated Hsat (ω) represents. The associated approximation factor multiplied by log n (e.g., the function ) can be expressed by piecewise polynomials Related Indicates. The associated approximation factor multiplied by a negative power of n (e.g., a function where i∈{0,1,2} ) can be represented by piecewise polynomials Related Indicates. Associated multiplication Approximate factors of negative powers of (e.g., functions where i∈{0,1 / 2,1} ) can be expressed by piecewise polynomials Related In some aspects, using piecewise polynomial approximation can provide several advantages. For example, the evaluation calculation can be relatively easy (e.g., involving addition and multiplication). Furthermore, the polynomial can be easily described (e.g., only requiring the storage of polynomial coefficients and corresponding degrees). The piecewise polynomial approximation can be associated with the addition and multiplication polynomial evaluation calculations. The polynomial coefficients and corresponding degrees associated with the piecewise polynomial can be stored in a memory of the transmitter device.

[0169] In some aspects, the interval can be a uniform interval across multiple approximations. The interval includes the first alphabet The first interval may be a disjoint union of subintervals. Each subinterval of the first interval may be associated with: a reference point, one or more approximation region indices and / or one or more additional indices, one or more polynomial coefficient indices (where each polynomial coefficient index may be associated with an approximation region index), one or more multiplication indices (where each multiplication index may be associated with a polynomial coefficient index), and one or more type indicators (where each type indicator may be associated with a polynomial coefficient index). The interval may be

[0170] So is the first letter of the alphabet The first additional interval may be associated with a first additional interval. The first additional interval may be a disjoint union of subintervals. Each subinterval of the first additional interval may be associated with: a reference point, one or more approximation region indices, one or more polynomial coefficient indices (where each polynomial coefficient index may be associated with an approximation region index), and one or more multiplication indices (where each multiplication index may be associated with a polynomial coefficient index).

[0171] In some aspects, with respect to the interval structure, a uniform interval can span multiple approximations. Can be used with The first interval It can be L i Sorting and presentation The disjoint union of subintervals where Each subinterval of the first interval may be associated with: a reference point, one or more approximation region indices and / or one or more additional indices, one or more polynomial coefficient indices (each of which may be associated with an approximation region index), one or more multiplication indices (each of which may be associated with a polynomial coefficient index), and one or more type indicators (each of which may be associated with a polynomial coefficient index). Can be used with The first additional interval Can be sorted and represented by L′i The disjoint union of subintervals where Each subinterval of the first additional interval may be associated with: a reference point, one or more approximation region indices, one or more polynomial coefficient indices (each of which may be associated with an approximation region index), and one or more multiplication indices (each of which may be associated with a polynomial coefficient index).

[0172] Figure 11A and Figure 11B is a diagram illustrating an example 1100 associated with a first interval structure according to the present disclosure.

[0173] In some aspects, the first interval may be a disjoint union of a plurality of subintervals. The first interval may be based at least in part on the first alphabet. Each of the plurality of subintervals of the first interval may be associated with one or more respective approximation indices. Each of the one or more respective approximation region indices may be associated with a respective reference point of the plurality of reference points, a respective additional index, and / or one or more respective polynomial coefficient indices, wherein each of the one or more respective polynomial coefficient indices may be associated with a respective multiplication index of the plurality of multiplication indices and a respective type indicator of the plurality of type indicators. Additionally, each approximation region index of each respective subinterval of the plurality of subintervals may be associated with a respective minimum integer and a respective maximum integer, wherein the respective minimum integer and the respective maximum integer indicate a respective integer range, wherein each integer in the respective integer range is greater than or equal to the respective minimum integer and less than or equal to the respective maximum integer.

[0174] like Figure 11A As shown, ω u yes (which is equal to 2.5). The first interval is [0, 2.5). The subinterval [11 / 128, 22 / 128) of the plurality of subintervals of the first interval is the same as the approximate region index ( The approximate region index associated with the subinterval [11 / 128, 22 / 128) may be associated with the reference point α1, which has a value of 30 / 128. The approximate region index may be associated with the first polynomial index (for H sat The first polynomial index is associated with the first multiplication index (Mul-IDX1) and the first type indicator (type a). The approximate region index may be associated with the second polynomial index (for The second polynomial index is associated with a third multiplication index (Mul-IDX3) and a second type indicator (type b). The approximate region index may be associated with the third polynomial index (for The approximate region index may be associated with the fourth polynomial index (for The fourth polynomial index is associated with the sixth multiplication index (Mul-IDX6). Additionally, the approximate region index of the subinterval [11 / 128, 22 / 128) is associated with The minimum integer and the maximum integer may be associated. For example, the minimum integer may be equal to 11 and the maximum integer may be equal to 31.

[0175] In some aspects, after locating the subinterval, multiple approximation region indices may still be available. The approximation form to be selected may depend on the first sequence length n. In other words, each approximation region index may be associated with a minimum value n and a maximum value n, so that the first sequence n belonging to a particular range may determine which approximation form to use.

[0176] The subinterval [11 / 128, 22 / 128] of the plurality of subintervals of the first interval is associated with the approximate region index ( The approximate region index associated with the subinterval [11 / 128, 22 / 128) may be associated with the reference point α1. The approximate region index may be associated with the first polynomial index (for H sat The first polynomial index is associated with the first multiplication index (Mul-IDX1) and the first type indicator (type a). The approximate region index may be associated with the second polynomial index (for The second polynomial index is associated with the third multiplication index (Mul-IDX3) and the second type indication (type b). The approximate region index can be associated with the third polynomial index (for The third polynomial index is associated with the fifth multiplication index (Mul-IDX5) and the second type indicator (type c). Additionally, the approximate region index (with The minimum integer and the maximum integer may be associated. For example, the minimum integer may be equal to 32 and the maximum integer may be equal to 1024.

[0177] The subinterval [109 / 128, 132 / 128) in the plurality of subintervals of the first interval is associated with the approximate region index ( The approximate region index associated with the subinterval [109 / 128, 132 / 128) may be associated with the reference point α2, where the value of α2 is 90 / 128. The approximate region index may be associated with the fifth polynomial index (for H sat The fifth polynomial index is associated with the first multiplication index (Mul-IDX1). The approximate region index can be associated with the sixth polynomial index (for The sixth polynomial index is associated with the third multiplication index (Mul-IDX3). The approximate region index can be associated with the seventh polynomial index (for The seventh polynomial index is associated with the fifth multiplication index (Mul-IDX5). The approximate region index can be associated with the eighth polynomial index (for The eighth polynomial index is associated with the sixth multiplication index (Mul-IDX6). Additionally, the approximate region index of the subinterval [109 / 128, 132 / 128) is associated with The minimum integer and the maximum integer may be associated. For example, the minimum integer may be equal to 11 and the maximum integer may be equal to 31.

[0178] Similarly, the approximate region index (with Associated with), approximate region index (with associated with) and approximate region indexes (associated with associated) can be associated with the reference point α2 and each polynomial index and multiplication index, such as Figure 11A As shown. Approximate area index (with The approximate region index (associated with The approximate region index (associated with The minimum integer and the maximum integer may be associated. For example, the minimum integer may be equal to 512 and the maximum integer may be equal to 1024.

[0179] In some aspects, with respect to the multiplication index, Mul-IDX1 may be associated with n (e.g., the multiplication index Mul-IDX1 indicates that the first sequence length n is to be multiplied by the corresponding polynomial approximation), Mul-IDX2 may be associated with logn (e.g., the multiplication index Mul-IDX2 indicates that the logarithm of the first sequence length n is to be multiplied by the corresponding polynomial approximation), Mul-IDX3 may be associated with 1 (e.g., the multiplication index Mul-IDX3 indicates that 1 is to be multiplied by the corresponding polynomial approximation), and Mul-IDX4 may be associated with Associated (eg, multiplication index Mul-IDX4 indicates will be multiplied by the corresponding polynomial approximation), Mul-IDX5 may be associated with 1 / n (eg, the multiplication index Mul-IDX5 indicates that 1 / n will be multiplied by the corresponding polynomial approximation), and Mul-IDX6 may be associated with 1 / n 2 Associated (eg, multiplication index Mul-IDX6 indicates 1 / n 2 will be multiplied by the corresponding polynomial approximation).

[0180] like Figure 11B As shown, the subintervals [272 / 128, 320 / 128) in the plurality of subintervals of the first interval are associated with the approximate region index ( The approximate region index associated with the subinterval [272 / 128, 320 / 128) may be associated with the reference point α4, which has a value of 229 / 128. The approximate region index may be associated with the fifteenth polynomial index (for H sat The fifteenth polynomial index is associated with the first multiplication index (Mul-IDX1). The approximate region index can be associated with the sixteenth polynomial index (for The approximate region index may be associated with the seventeenth polynomial index (for The seventeenth polynomial index is associated with the fifth multiplication index (Mul-IDX5). Additionally, the approximate region index of the subinterval [272 / 128, 320 / 128) is associated with The minimum integer and the maximum integer may be associated. For example, the minimum integer may be equal to 11 and the maximum integer may be equal to 255.

[0181] Similarly, the approximate region index (with associated with) and approximate region indexes (associated with associated) can be associated with the reference point α4 and each polynomial index and multiplication index, such as Figure 11B As shown. Approximate area index (with The approximate region index (associated with The minimum integer and the maximum integer may be associated. For example, the minimum integer may be equal to 512 and the maximum integer may be equal to 1024.

[0182] In some aspects, when the additional index is T, then the first additional interval Can be used to determine polynomials where i∈{0,1 / 2,1}, this may be because and The approximate form of can be obtained by one or more approximation factors Furthermore, each polynomial evaluation can be relative to a reference point.

[0183] As indicated above, Figure 11A and Figure 11B are provided as examples. Other examples can be found in the Figure 11A and Figure 11B The examples described are different.

[0184] Figure 12 is a diagram illustrating an example 1200 associated with a first additional interval structure according to the present disclosure.

[0185] In some aspects, the first additional interval may be a disjoint union of a plurality of subintervals. The first additional interval may be based at least in part on the first alphabet Each of the plurality of subintervals of the first additional interval may be associated with one or more respective approximation indices. Each of the one or more respective approximation region indices may be associated with a respective reference point of the plurality of reference points, a respective additional index, and / or one or more respective polynomial coefficient indices, wherein each of the one or more respective polynomial coefficient indices may be associated with a respective multiplication index of the plurality of multiplication indices and a respective type indicator of the plurality of type indicators. Additionally, each approximation region index of each respective subinterval of the plurality of subintervals may be associated with a respective minimum integer and a respective maximum integer, wherein the respective minimum integer and the respective maximum integer indicate a respective integer range, wherein each integer in the respective integer range is greater than or equal to the respective minimum integer and less than or equal to the respective maximum integer.

[0186] In some aspects, each polynomial coefficient index may indicate an index into a lookup table in which the polynomial coefficients are stored.Multiple polynomials may be associated with a common maximum degree.

[0187] like Figure 12 As shown, the subinterval [-4,0) in the plurality of subintervals of the first additional interval is consistent with the approximate region index ( The approximate region index associated with the subinterval [-4,0) may be associated with the reference point b3, the value of b3 being -4. The approximate region index may be associated with the nineteenth polynomial index (for The nineteenth polynomial index is associated with the third multiplication index (Mul-IDX3). The approximate region index can be associated with the twentieth polynomial index (for The approximate region index may be associated with the 21st polynomial index (for The twenty-first polynomial index is associated with the fifth multiplication index (Mul-IDX5). Additionally, the approximate region index of the subinterval [-4,0) is associated with The minimum integer and the maximum integer may be associated. For example, the minimum integer may be equal to 11 and the maximum integer may be equal to 255.

[0188] Similarly, the approximate region index (with associated with) and approximate region indexes (associated with associated with the reference point And each polynomial index is associated with the multiplication index, such as Figure 12 As shown. Approximate area index (with The approximate region index (associated with The minimum integer and the maximum integer may be associated. For example, the minimum integer may be equal to 512 and the maximum integer may be equal to 1024.

[0189] As indicated above, Figure 12 are provided as examples. Other examples can be found in the Figure 12 The examples described are different.

[0190] In some aspects, the interval can be a uniform interval across multiple approximations. The interval can be a uniform interval with the first alphabet. The second interval may be a disjoint union of subintervals. Each subinterval of the second interval may be associated with: a reference point, one or more approximation region indices, one or more polynomial coefficient indices (where each polynomial coefficient index may be associated with an approximation region index), and one or more multiplication indices. The reference point may be a subinterval boundary point of the interval. The polynomial evaluation may be based at least in part on a polynomial of the difference between the normalized energy ω and the reference point. The subinterval boundary point may be a binary number.

[0191] In some aspects, with respect to the interval structure, a uniform interval can span multiple approximations. Can be used with The second interval It can be made by R i According to the following sorting and expression The disjoint union of subintervals, where

[0192]

[0193] Each subinterval of the second interval may be associated with: a reference point, one or more approximate region indices, one or more polynomial coefficient indices (each of which may be associated with an approximate region index), and one or more multiplication indices (each of which may be associated with a polynomial coefficient index).

[0194] In some aspects, with respect to reference points and interval boundaries, the reference point may be a subinterval boundary point of the first interval, the first additional interval, or the second interval. Each polynomial evaluation may be relative to the reference point. For example,

[0195]

[0196] Where d is the degree of the polynomial, c i are polynomial coefficients, and α4 is a reference point. In other words, the polynomial evaluation may involve a polynomial of the difference between the normalized energy ω and the reference point. Furthermore, all subinterval boundaries may be, for example, of the form α / 2 for some integers a and l. l The binary number of .

[0197] Figure 13 is a diagram illustrating an example 1300 associated with a second interval structure according to the present disclosure.

[0198] In some aspects, the second interval may be a disjoint union of the plurality of subintervals. The second interval may be based at least in part on the first alphabet. Each of the plurality of subintervals of the second interval may be associated with one or more respective approximation indices. Each of the one or more respective approximation region indices may be associated with a respective reference point of the plurality of reference points, a respective additional index, and / or one or more respective polynomial coefficient indices, wherein each of the one or more respective polynomial coefficient indices may be associated with a respective multiplication index of the plurality of multiplication indices and a respective type indicator of the plurality of type indicators. Additionally, each approximation region index of each of the plurality of subintervals of the second interval may be associated with a respective minimum integer and a respective maximum integer, wherein the respective minimum integer and the respective maximum integer indicate a respective integer range, wherein each integer in the respective integer range is greater than or equal to the respective minimum integer and less than or equal to the respective maximum integer.

[0199] like Figure 13 As shown, the subinterval [0,4) in the plurality of subintervals of the second interval is associated with the approximate region index ( Associated). The approximate region index of the subinterval [0,4) (with associated with the reference point Related, The value of is 0. Approximate area index (with associated with) can be associated with the twenty-second polynomial index (for The 22nd polynomial index is associated with the third multiplication index (Mul-IDX3). associated with) can be associated with the twenty-third polynomial index (for The twenty-third polynomial index is associated with the fourth multiplication index (Mul-IDX4). associated with) can be associated with the twenty-fourth polynomial index (for The twenty-fourth polynomial index is associated with the fifth multiplication index (Mul-IDX5). Additionally, the approximate region index of the subinterval [0,4) (with ) can be associated with a minimum integer and a maximum integer. For example, the minimum integer can be equal to 11 and the maximum integer can be equal to 255. Similarly, the subinterval [0,4) can be associated with an approximate region index (associated with Associated). The approximate region index of the subinterval [0,4) (with associated with the reference point Additionally, the approximate region index of the subinterval [0,4) (with For example, the minimum integer may be equal to 256 and the maximum integer may be equal to 1024. Figure 12 shown.

[0200] like Figure 13 As shown, the subinterval [4,7.5) in the plurality of subintervals of the second interval is consistent with the approximate region index (with Associated). The approximate region index of the subinterval [4,7.5) (with associated with the reference point Related, The value of is 4. Approximate area index (with associated with) can be associated with the twenty-fifth polynomial index (for The 25th polynomial index is associated with the third multiplication index (Mul-IDX3). associated with) can be associated with the twenty-sixth polynomial index (for The twenty-sixth polynomial index is associated with the fourth multiplication index (Mul-IDX4). associated with) can be associated with the twenty-seventh polynomial index (for The twenty-seventh polynomial index is associated with the fifth multiplication index (Mul-IDX5). Additionally, the approximate region index of the subinterval [4,7.5) is associated with ) can be associated with a minimum integer and a maximum integer. For example, the minimum integer can be equal to 11 and the maximum integer can be equal to 31. Similarly, the subinterval [4,7.5) can be associated with an approximate region index (associated with ) is associated with). The approximate region index of the subinterval [4,7.5) (with ) can be associated with a reference point Additionally, the approximate region index of the subinterval [4,7.5) (with The minimum integer and the maximum integer may be associated. For example, the minimum integer may be equal to 32 and the maximum integer may be equal to 1024.

[0201] like Figure 13 As shown, the subinterval [7.5, 8.5) in the plurality of subintervals of the second interval is consistent with the approximate region index ( Associated). Approximate region index of subinterval [7.5,8.5) (with associated with the reference point Related, The value of is 7.5. Approximate area index (with associated with) can be associated with the twenty-eighth polynomial index (for The twenty-eighth polynomial index is associated with the third multiplication index (Mul-IDX3).

[0202] As indicated above, Figure 13 are provided as examples. Other examples can be found in the Figure 13 The examples described are different.

[0203] In some aspects, a binary search tree structure may be associated with an interval. The binary search tree structure may be used to store subinterval boundaries including a reference point. Each interval node of the binary search tree structure may store a key corresponding to a subinterval boundary in the subinterval boundaries. Each leaf node of the binary search tree structure may store a subinterval index corresponding to a subinterval. The binary search tree structure may be traversed from a root node to a leaf node to perform a binary search for a subinterval associated with the normalized energy ω or the lumped and scaled energy v.

[0204] In some aspects, a search (e.g., an interval search or a subinterval search) may be performed for a polynomial approximation. A binary tree structure may be used for the search. The search may be associated with the binary tree search. A corresponding binary tree structure may be associated with each of the first interval, the first additional interval, or the second interval. The binary tree structure may be used to store subinterval boundaries (e.g., including reference points). Each internal node may store a key corresponding to a subinterval boundary. The subinterval boundaries may have a special structure, such as a binary number. When the key associated with an internal node is a reference point, the internal node may be a special node. Each leaf node may store a subinterval index corresponding to a subinterval. The binary tree structure may be constructed such that traversing a path from the root to a leaf node simulates a binary search for a subinterval, where the normalized energy ω or the concentrated and scaled energy v is in the subinterval.

[0205] In some aspects, the transmitter device may perform a search that may be based at least in part on the first alphabet size m. When performing the search, the transmitter device may determine a normalized energy ω. The transmitter device may compare the normalized energy ω with the uniform symbol energy ω. u In other words, given n and E, the normalized energy ω can be determined and compared with the uniform symbol energy ω u The transmitter device can be compared based on whether ω-ω u <0 to determine the binary search tree structure is started for the interval, wherein the interval can be one of the first interval or the second interval. u <0, a binary tree may be started for the first interval. Otherwise, a binary tree may be selected for the second interval. The sender device may traverse the binary search tree structure from the root node of the binary search tree structure. The sender device may use the key ω associated with the internal node key To perform the subtraction ω-ω keyAt each internal node, the key ω associated with the internal node is available key To perform subtraction ω-ω key When the internal node is special, for example its key is a reference point, then the difference can be tracked. The transmitter device can be based at least in part on ω-ω key < 0 to move to the left child of an internal node, or at least partially based on ω-ω key ≥0 to move to the right child of the internal node. In other words, when ω-ω key <0, the search may involve going to the left child of the internal node, and when ω-ω key ≥0, the search may involve going to the right child node of the internal node. The sender device may determine the subinterval index stored at the leaf node and the most recent difference ω-ω after reaching the leaf node of the binary search tree structure. ref , where ω ref is the most recently visited reference point along the path traversed from the root node to the leaf node. After finding the subinterval index, the corresponding subinterval may be associated with more than one approximate region index. In these cases, the first sequence length n may be used to determine which approximate region index to select. In other words, based at least in part on the subinterval index, the approximate region index may be determined based at least in part on the first sequence length n and the identification of the subinterval index. After determining the approximate region index, the process described earlier may be applied.

[0206] Figure 14 is a diagram illustrating an example 1400 associated with a search according to the present disclosure.

[0207] like Figure 14 As shown, the search in the case of m=4 may involve one or more of reference points α1, α2, α3, or α4. The binary tree in which the search is performed may be associated with reference points α1, α2, α3, and α4. In this example, after the search, the difference ω-α4 and the subinterval index 14 may be available.

[0208] As indicated above, Figure 14 are provided as examples. Other examples can be found in the Figure 14 The examples described are different.

[0209] In some aspects, the polynomial coefficients may be stored in one or more lookup tables based at least in part on fixed ROM storage. The polynomial coefficient index may be used for table lookup. A row of the lookup table may correspond to a polynomial coefficient corresponding to a polynomial index of a subinterval. Each column of the lookup table may correspond to the most recent difference ω-ω refIn some aspects, the storage of polynomial coefficients may be based at least in part on fixed ROM storage, which may be independent of n. Regarding the storage of polynomial coefficients, one or more lookup tables may be used to store the polynomial coefficients. A polynomial index may be used for table lookup. The polynomial coefficients may be stored in different forms depending on the specific implementation (e.g., truncated precision or binary approximation of real-valued coefficients).

[0210] Figure 15 is a diagram illustrating an example 1500 associated with a lookup table for storing polynomial coefficients according to the present disclosure.

[0211] like Figure 15 As shown, the lookup table may be composed of a plurality of rows and a plurality of columns (e.g., five rows and four columns). Each row may correspond to a polynomial coefficient corresponding to a polynomial index of a certain subinterval. For example, a particular row may correspond to the polynomial:

[0212]

[0213] Furthermore, each column may correspond to ω-ω ref The power of .

[0214] As indicated above, Figure 15 are provided as examples. Other examples can be found in the Figure 15 The examples described are different.

[0215] In some respects, H sat The characteristic term of may be related to H for relatively small ω sat Singularities in . Special terms can be added to H sat When the type indicator is type a, then H sat The approximation can be determined as: Here, L H Corresponding to H sat In some aspects, regarding the specific implementation of ωlogω, since ω=E / n, the following can be derived:

[0216] nH sat An approximation of (ω) can be It can be equal to:

[0217]

[0218] In other words, the approximation can involve nL H (ω) minus the product of the first sequence energy E and the difference between the logarithm of the first sequence energy E and the logarithm of the first sequence length n (eg, E(log E-log n)).

[0219] In some respects, and The characteristic term of may involve for relatively small ω and Special terms can be added to Polynomial approximation of . Approximation factor Can be associated with a type indicator, where the approximation factor Can be associated with an approximate region. When the type indicator is type b, then Indicated The approximation can be determined as:

[0220]

[0221] here, Corresponds to In some aspects, special terms can be added to Polynomial approximation of . Approximation factor Can be associated with a type indicator, where the approximation factor Can be associated with an approximate region. When the type indicator is type c, then Indicated The approximation can be determined as:

[0222]

[0223] here, Corresponds to Polynomial approximation of .

[0224] In some aspects, regarding the specific implementation of -1 / 2log ω and -1 / (12ω), since E=ωn, An approximation can be It can be equal to:

[0225]

[0226] Since E = ωn, An approximation can be It can be equal to:

[0227]

[0228] In some aspects, c(E) can be a function of the energy variable E. The function c may not depend on the first alphabet And it can be used when the first sequence energy E meets the threshold. The term c(E) can be used only for relatively small (eg, very small) E (eg, or ). When the logarithm of the approximation is to base e, the approximation can have the following parametric form as a function of E:

[0229]

[0230] The value of c(E) can be (approximately) tabulated. The function c(c(E)) of the first sequence energy E can be approximately tabulated for a plurality of first sequence energy E values. For example, when E ranges between 1 and 7, the value of E can be associated with the value of c(E), respectively. In this example, E=1 can be associated with c(E)≈2.2719×10 -3 E = 2 can be associated with c(E)≈3.2597×10 -4 E = 3 can be associated with c(E)≈9.9852×10 -5 E = 4 can be associated with c(E)≈4.2661×10 -5 E = 5 can be associated with c(E)≈2.1975×10 -5 E = 6 can be associated with c(E)≈1.2760×10 -5 and E = 7 can be associated with c(E)≈8.0520×10 -6 associated.

[0231] Figure 16 is a diagram illustrating an example process 1600, performed, for example, by a transmitter device, in accordance with the present disclosure. Example process 1600 is an example in which a transmitter device (eg, UE 120 or network node 110) performs operations associated with a polynomial approximation technique for probability amplitude shaping.

[0232] like Figure 16 As shown, in some aspects, process 1600 may include obtaining a plurality of information bits for a probabilistic shaping scheme associated with an energy threshold (block 1610). For example, a transmitter device (e.g., using Figure 17 The communication manager 1706 depicted in may obtain a plurality of information bits for a probabilistic shaping scheme that is associated with an energy threshold, as described above.

[0233] like Figure 16 As further shown, in some aspects, process 1600 may include forming a polynomial approximation of a plurality of approximation factors as part of a probabilistic shaping scheme (block 1620). For example, a transmitter device (e.g., using Figure 17 The communication manager 1706 depicted in may form a polynomial approximation of multiple approximation factors as part of a probabilistic shaping scheme, as described above.

[0234] like Figure 16As further shown, in some aspects, process 1600 may include using a polynomial approximation of a plurality of approximation factors to obtain an approximation of a logarithm of a cumulative number of sequences associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy (block 1630). For example, a transmitter device (e.g., using Figure 17 The communication manager 1706 depicted in may use a polynomial approximation of a plurality of approximation factors to obtain an approximation of a logarithm of a cumulative number of sequences associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy, as described above.

[0235] like Figure 16 As further shown, in some aspects, process 1600 may include performing an exponential operation on an approximation of the logarithm of the cumulative number of sequences, thereby obtaining an approximation of the cumulative number of sequences (block 1640). Figure 17 The communication manager 1706 depicted in FIG. 17 may perform an exponential operation on an approximation of the logarithm of the cumulative number of sequences, thereby obtaining an approximation of the cumulative number of sequences, as described above.

[0236] like Figure 16 As further shown, in some aspects, process 1600 may include encoding a plurality of information bits based at least in part on an approximation of a cumulative number of sequences as part of a probabilistic shaping scheme to obtain a symbol sequence having a length equal to a second sequence length and an energy less than or equal to an energy threshold, wherein each symbol in the symbol sequence belongs to a second alphabet having a second alphabet size (block 1650). For example, a transmitter device (e.g., using Figure 17 The communication manager 1706 depicted in the figure may encode a plurality of information bits based at least in part on an approximation of a cumulative number of sequences as part of a probabilistic shaping scheme to obtain a sequence of symbols having a length equal to a second sequence length and an energy less than or equal to an energy threshold, wherein each symbol in the sequence of symbols belongs to a second alphabet having a second alphabet size, as described above.

[0237] like Figure 16 As further shown, in some aspects, process 1600 may include sending a message to one or more receiver devices based at least in part on the symbol sequence (block 1660). Figure 17 The transmitting component 1704 and / or the communication manager 1706 depicted in can transmit a message to one or more receiver devices based at least in part on the sequence of symbols, as described above.

[0238] Process 1600 may include additional aspects, such as any single aspect or any combination of aspects described below and / or in conjunction with one or more other processes described elsewhere herein.

[0239] In a first aspect, process 1600 includes determining a normalized energy corresponding to a ratio between a first sequence energy and a first sequence length; obtaining a uniform energy associated with a first alphabet; obtaining a subinterval of an interval based at least in part on the normalized energy; and forming at least one polynomial approximation of a plurality of approximation factors using the subinterval of the interval and the normalized energy.

[0240] In a second aspect, either alone or in combination with the first aspect, at least one interval of the interval is associated with a first alphabet, the interval comprises a plurality of subintervals, and the interval corresponds to a disjoint union of the plurality of subintervals, or each of the plurality of subintervals of the interval corresponds to a respective left subinterval boundary of a plurality of left subinterval boundaries.

[0241] In a third aspect, either alone or in combination with one or more of the first and second aspects, each subinterval of a plurality of subintervals of an interval is associated with one or more corresponding approximate region indices, each corresponding approximate region index of the one or more corresponding approximate region indices is associated with a corresponding reference point of a plurality of reference points, a corresponding additional index, or at least one of one or more corresponding polynomial coefficient indices, and each polynomial coefficient index of the one or more corresponding polynomial coefficient indices is associated with a corresponding multiplication index of a plurality of multiplication indices and a corresponding type indicator of a plurality of type indicators.

[0242] In a fourth aspect, alone or in combination with one or more of the first to third aspects, at least one reference point of the one or more reference points in the plurality of reference points corresponds to a binary number, one or more left subinterval boundaries of the plurality of subintervals of the interval correspond to a binary number, one or more reference points in the plurality of reference points coincide with one or more corresponding left subinterval boundaries of the plurality of left subinterval boundaries, or the total number of reference points in the plurality of reference points is less than the total number of left subinterval boundaries of the plurality of subintervals of the interval.

[0243] In a fifth aspect, alone or in combination with one or more of the first to fourth aspects, multiple left subinterval boundaries are stored as a binary tree structure having a root node, multiple internal nodes, and multiple leaf nodes, each of the multiple internal nodes stores a key corresponding to the corresponding left subinterval boundary, and each of the multiple leaf nodes stores a subinterval index corresponding to the corresponding subinterval of the multiple subintervals of the interval.

[0244] In a sixth aspect, alone or in combination with one or more of the first to fifth aspects, process 1600 includes: performing a binary search by traversing a path from a root node to a leaf node of a plurality of leaf nodes of a binary tree structure, wherein the leaf node of the plurality of leaf nodes stores a subinterval index corresponding to a subinterval of the interval; identifying a subinterval of the interval based at least in part on the subinterval index; determining an approximate region index based at least in part on the first sequence length and the identification of the subinterval of the interval; identifying one or more polynomial coefficient indices associated with the approximate region index; identifying a corresponding multiplication index for each of the one or more polynomial coefficient indices; and identifying a corresponding type indicator for each of the one or more polynomial coefficient indices.

[0245] In a seventh aspect, alone or in combination with one or more of the first to sixth aspects, process 1600 includes determining a difference between a normalized energy and a reference point corresponding to a subinterval of an interval, or determining a difference between a concentrated and scaled energy and a reference point corresponding to a subinterval of an interval, wherein the concentrated and scaled energy corresponds to a square root of the length of the first sequence multiplied by a difference between: the normalized energy and the uniform energy.

[0246] In an eighth aspect, alone or in combination with one or more of the first to seventh aspects, process 1600 comprises calculating one or more polynomial values, each polynomial value in the one or more polynomial values ​​corresponding to a corresponding polynomial coefficient index in one or more polynomial coefficient indices; determining one or more multiplication factors, each multiplication factor in the one or more multiplication factors being associated with a corresponding polynomial coefficient index in the one or more polynomial coefficient indices based at least in part on the multiplication index; and determining one or more approximations, each approximation in the one or more approximations being based at least in part on a product of a corresponding polynomial value in the one or more polynomial values ​​and a corresponding multiplication factor in the one or more multiplication factors.

[0247] In a ninth aspect, either alone or in combination with one or more of the first to eighth aspects, each respective polynomial approximation is based at least in part on a plurality of polynomial coefficients and a polynomial degree stored in a memory of the transmitter device.

[0248] In a tenth aspect, alone or in combination with one or more of the first to ninth aspects, the plurality of polynomial coefficients are stored in a lookup table.

[0249] In an eleventh aspect, alone or in combination with one or more of aspects one to ten, process 1600 comprises determining an approximation region based at least in part on a first sequence length and a first sequence energy, the approximation region being associated with a first alphabet; identifying an approximation form corresponding to the approximation region, wherein forming a polynomial approximation of a plurality of approximation factors is based at least in part on the identification of the approximation form.

[0250] In a twelfth aspect, alone or in combination with one or more of the first to eleventh aspects, the cumulative number of sequences defines a cardinality of a set of all sequences within a first alphabet, each sequence in the set of all sequences within the first alphabet having a respective length equal to the length of the first sequence and a respective energy less than or equal to the energy of the first sequence.

[0251] In a thirteenth aspect, alone or in combination with one or more of aspects one to twelfth, process 1600 comprises multiplying each polynomial approximation of a plurality of approximation factors by a corresponding multiplication factor, the corresponding multiplication factor being based at least in part on a first sequence length; obtaining a plurality of approximation terms based at least in part on the multiplication, each approximation term of the plurality of approximation terms corresponding to a corresponding polynomial approximation of the plurality of approximation factors; and summing the plurality of approximation terms to obtain an approximation of a logarithm of a cumulative number of sequences.

[0252] In a fourteenth aspect, alone or in combination with one or more of aspects one to thirteen, the polynomial approximation of the plurality of approximation factors comprises at least one of: a first piecewise polynomial approximation of a saturated entropy function of the normalized energy, the saturated entropy function corresponding to a first approximation factor among the plurality of approximation factors, and the saturated entropy function being associated with a first alphabet; or a corresponding piecewise polynomial approximation corresponding to each of one or more additional functions, each of the one or more additional functions being a function of the normalized energy or concentrated and scaled energy.

[0253] In a fifteenth aspect, alone or in combination with one or more of the first to fourteenth aspects, process 1600 includes removing singularities from at least one polynomial approximation of the plurality of approximation factors.

[0254] In a sixteenth aspect, alone or in combination with one or more of the first to fifteenth aspects, the logarithm of the cumulative sequence quantity is base 2, and the exponential operation is performed in base 2.

[0255] In a seventeenth aspect, either alone or in combination with one or more of the first to sixteenth aspects, at least one of the following conditions exists: the probabilistic shaping scheme is associated with the second alphabet and the second sequence length, the second alphabet size is greater than 1, or the second alphabet includes multiple amplitude symbols.

[0256] In an eighteenth aspect, either alone or in combination with one or more of aspects one to seventeen, the first alphabet is a subset of or equal to the second alphabet, the first sequence length is less than or equal to the second sequence length, and the first sequence energy is less than or equal to an energy threshold.

[0257] In a nineteenth aspect, alone or in combination with one or more of the first to eighteenth aspects, at least one of the following situations exists: the second sequence length is a power of 2, or the first sequence length is a power of 2.

[0258] In a twentieth aspect, alone or in combination with one or more of the first to nineteenth aspects, the probability shaping scheme and the transmitting are performed by a UE.

[0259] In a twenty-first aspect, alone or in combination with one or more of the first to twentieth aspects, the probabilistic shaping scheme and the transmitting are performed by a network node.

[0260] although Figure 16 Example blocks of process 1600 are shown, but in some aspects, process 1600 may include Figure 16 1600. In some embodiments, the process 1600 may include additional blocks, fewer blocks, different blocks, or blocks arranged in a different manner than those depicted in FIG. Additionally or alternatively, two or more blocks of the blocks of process 1600 may be executed in parallel.

[0261] Figure 17 1 is a diagram of an example apparatus 1700 for wireless communication according to the present disclosure. Apparatus 1700 may be a transmitter device, or a transmitter device may include apparatus 1700. In some aspects, apparatus 1700 includes a receiving component 1702, a transmitting component 1704, and / or a communication manager 1706, which may communicate with each other (e.g., via one or more buses and / or one or more other components). In some aspects, communication manager 1706 is a communication manager that is configured to communicate with one another. Figure 1 The depicted communication manager 140 or communication manager 150. As shown, the device 1700 can utilize a receiving component 1702 and a sending component 1704 to communicate with another device 1708, such as a UE or a network node, such as a CU, DU, RU, or base station.

[0262] In some aspects, the apparatus 1700 may be configured to perform Figure 7 、 Figures 8A to 8B 、 Figures 9 and 10 、 Figures 11A to 11B and Figures 12 to 15 Additionally or alternatively, the apparatus 1700 may be configured to perform one or more of the processes described herein, such as Figure 16The process 1600. In some aspects, Figure 17 The illustrated apparatus 1700 and / or one or more components may include a combination of Figure 2 Additionally or alternatively, one or more components of the transmitter device described. Figure 17 One or more of the components shown may be combined Figure 2 Additionally or alternatively, one or more components in a set of components may be implemented at least in part as software stored in a memory. For example, a component (or a portion of a component) may be implemented as instructions or code that are stored in a non-transitory computer-readable medium and can be executed by a controller or processor to perform the function or operation of the component.

[0263] The receiving component 1702 may receive communications, such as reference signals, control information, data communications, or a combination thereof, from the device 1708. The receiving component 1702 may provide the received communications to one or more other components of the device 1700. In some aspects, the receiving component 1702 may perform signal processing (such as filtering, amplification, demodulation, analog-to-digital conversion, demultiplexing, deinterleaving, demapping, equalization, interference cancellation, or decoding, etc.) on the received communications and may provide the processed signals to one or more other components of the device 1700. In some aspects, the receiving component 1702 may include in conjunction with Figure 2 One or more antennas, modems, demodulators, MIMO detectors, receive processors, controllers / processors, memories, or combinations thereof of the described transmitter devices.

[0264] The transmitting component 1704 may transmit communications, such as reference signals, control information, data communications, or a combination thereof, to the apparatus 1708. In some aspects, one or more other components of the apparatus 1700 may generate communications and may provide the generated communications to the transmitting component 1704 for transmission to the apparatus 1708. In some aspects, the transmitting component 1704 may perform signal processing (such as filtering, amplification, modulation, digital-to-analog conversion, multiplexing, interleaving, mapping, or encoding, etc.) on the generated communications and may transmit the processed signals to the apparatus 1708. In some aspects, the transmitting component 1704 may include a combination of Figure 2 One or more antennas, modems, modulators, transmit MIMO processors, transmit processors, controllers / processors, memories, or combinations thereof of the described transmitter devices. In some aspects, the transmit component 1704 can be co-located with the receive component 1702 in a transceiver.

[0265] The communications manager 1706 can support the operations of the receiving component 1702 and / or the sending component 1704. For example, the communications manager 1706 can receive information associated with configuring the receipt of communications by the receiving component 1702 and / or the sending of communications by the sending component 1704. Additionally or alternatively, the communications manager 1706 can generate and / or provide control information to the receiving component 1702 and / or the sending component 1704 to control the receipt and / or sending of communications.

[0266] The communication manager 1706 may obtain a plurality of information bits for a probabilistic shaping scheme associated with an energy threshold. The communication manager 1706 may form a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme. The communication manager 1706 may use the polynomial approximation of the plurality of approximation factors to obtain an approximation of a logarithm of a cumulative number of sequences, the logarithm of the cumulative number of sequences associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy. The communication manager 1706 may perform an exponential operation on the approximation of the logarithm of the cumulative number of sequences to obtain an approximation of the cumulative number of sequences. The communication manager 1706 may, as part of the probabilistic shaping scheme, encode the plurality of information bits based at least in part on the approximation of the cumulative number of sequences to obtain a symbol sequence having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the symbol sequence belongs to a second alphabet having a second alphabet size. The transmitting component 1704 may transmit a message to one or more receiver devices based at least in part on the symbol sequence.

[0267] The communication manager 1706 may determine a normalized energy corresponding to a ratio between the first sequence energy and the first sequence length. The communication manager 1706 may obtain a uniform energy associated with the first alphabet. The communication manager 1706 may obtain a subinterval of the interval based at least in part on the normalized energy. The communication manager 1706 may form at least one polynomial approximation of a plurality of approximation factors using the subinterval of the interval and the normalized energy.

[0268] The communication manager 1706 may perform a binary search by traversing a path of a binary tree structure from a root node to a leaf node of a plurality of leaf nodes, wherein the leaf node of the plurality of leaf nodes stores a subinterval index corresponding to a subinterval of the interval. The communication manager 1706 may identify a subinterval of the interval based at least in part on the subinterval index. The communication manager 1706 may determine an approximate region index based at least in part on the first sequence length and the identification of the subinterval of the interval. The communication manager 1706 may identify one or more polynomial coefficient indices associated with the approximate region index. The communication manager 1706 may identify a corresponding multiplication index for each of the one or more polynomial coefficient indices. The communication manager 1706 may identify a corresponding type indicator for each of the one or more polynomial coefficient indices.

[0269] The communication manager 1706 may determine a difference between the normalized energy and a reference point corresponding to a subinterval of the interval. The communication manager 1706 may determine a difference between a lumped and scaled energy and a reference point corresponding to a subinterval of the interval, wherein the lumped and scaled energy corresponds to a square root of the length of the first sequence multiplied by a difference between the normalized energy and the uniform energy.

[0270] The communication manager 1706 may calculate one or more polynomial values, each polynomial value in the one or more polynomial values ​​corresponding to a corresponding polynomial coefficient index in the one or more polynomial coefficient indices. The communication manager 1706 may determine one or more multiplication factors, each multiplication factor in the one or more multiplication factors being associated with a corresponding polynomial coefficient index in the one or more polynomial coefficient indices based at least in part on the multiplication index. The communication manager 1706 may determine one or more approximations, each approximation in the one or more approximations being based at least in part on a product of a corresponding polynomial value in the one or more polynomial values ​​and a corresponding multiplication factor in the one or more multiplication factors.

[0271] The communication manager 1706 may determine an approximation region based at least in part on the first sequence length and the first sequence energy, the approximation region being associated with the first alphabet. The communication manager 1706 may identify an approximation form corresponding to the approximation region, wherein forming a polynomial approximation of the plurality of approximation factors is based at least in part on identifying the approximation form.

[0272] The communication manager 1706 may multiply each polynomial approximation of the plurality of approximation factors by a corresponding multiplication factor, the corresponding multiplication factor being based at least in part on the first sequence length. The communication manager 1706 may obtain, based at least in part on the multiplication, a plurality of approximation terms, each of the plurality of approximation terms corresponding to a corresponding polynomial approximation of the plurality of approximation factors. The communication manager 1706 may sum the plurality of approximation terms to obtain an approximation of a logarithm of the cumulative sequence length. The communication manager 1706 may remove singularities from at least one of the polynomial approximations of the plurality of approximation factors.

[0273] Figure 17 The number and arrangement of components shown are provided as examples. In practice, there may be Figure 17 The components shown may include additional components, fewer components, different components, or components arranged in a different manner than those shown. Figure 17 Two or more components shown may be implemented in a single component, or Figure 17 The single component shown may be implemented as multiple distributed components. Additionally or alternatively, Figure 17 The illustrated set of components (one or more) may be described as being executable by Figure 17 Another group of components is shown performing one or more functions.

[0274] The following provides an overview of some aspects of the disclosure:

[0275] Aspect 1: A method of wireless communication performed by a transmitter device, the method comprising: obtaining a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; forming a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; using the polynomial approximation of the plurality of approximation factors to obtain an approximation of a logarithm of a cumulative number of sequences, the logarithm of the cumulative number of sequences being associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; performing an exponential operation on the approximation of the logarithm of the cumulative number of sequences, thereby obtaining an approximation of the cumulative number of sequences; encoding the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a symbol sequence having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the symbol sequence belongs to a second alphabet having a second alphabet size; and sending a message to one or more receiver devices based at least in part on the symbol sequence.

[0276] Aspect 2: A method according to Aspect 1, wherein forming the polynomial approximation of the multiple approximation factors further includes: determining a normalized energy corresponding to the ratio between the first sequence energy and the first sequence length; obtaining a uniform energy, the uniform energy being associated with the first alphabet; obtaining a subinterval of an interval based at least in part on the normalized energy; and using the subinterval of the interval and the normalized energy to form at least one polynomial approximation of the polynomial approximation of the multiple approximation factors.

[0277] Aspect 3: The method according to Aspect 2, wherein at least one of the following situations exists: the interval is associated with the first alphabet; the interval includes multiple sub-intervals, and the interval corresponds to a disjoint union of the multiple sub-intervals; or each sub-interval of the multiple sub-intervals of the interval corresponds to a corresponding left sub-interval boundary among multiple left sub-interval boundaries.

[0278] Aspect 4: A method according to aspect 3, wherein each subinterval of the multiple subintervals of the interval is associated with one or more corresponding approximate area indices, each corresponding approximate area index of the one or more corresponding approximate area indices is associated with at least one of the following: a corresponding reference point of multiple reference points, a corresponding additional index, or one or more corresponding polynomial coefficient indices, and each polynomial coefficient index of the one or more corresponding polynomial coefficient indices is associated with a corresponding multiplication index of multiple multiplication indices and a corresponding type indicator of multiple type indicators.

[0279] Aspect 5: The method according to Aspect 4, wherein at least one of the following situations exists: one or more reference points among the multiple reference points correspond to binary numbers; one or more left subinterval boundaries of the multiple subintervals of the interval correspond to binary numbers; one or more reference points among the multiple reference points coincide with one or more corresponding left subinterval boundaries among the multiple left subinterval boundaries; or the total number of reference points among the multiple reference points is less than the total number of left subinterval boundaries of the multiple subintervals of the interval.

[0280] Aspect 6: The method according to Aspect 4, wherein: the multiple left sub-interval boundaries are stored as a binary tree structure having a root node, multiple internal nodes and multiple leaf nodes; each of the multiple internal nodes stores a key corresponding to the corresponding left sub-interval boundary; and each of the multiple leaf nodes stores a sub-interval index corresponding to the corresponding sub-interval of the multiple sub-intervals of the interval.

[0281] Aspect 7: A method according to aspect 6, wherein obtaining the subinterval of the interval further comprises: performing a binary search by traversing a path from the root node to a leaf node among the plurality of leaf nodes of the binary tree structure, wherein the leaf node among the plurality of leaf nodes stores a subinterval index corresponding to the subinterval of the interval; identifying the subinterval of the interval based at least in part on the subinterval index; determining an approximate region index based at least in part on the first sequence length and the identification of the subinterval of the interval; identifying one or more polynomial coefficient indices, the one or more polynomial coefficient indices being associated with the approximate region index; identifying a corresponding multiplication index for each of the one or more polynomial coefficient indices; and identifying a corresponding type indicator for each of the one or more polynomial coefficient indices.

[0282] Aspect 8: A method according to Aspect 7, wherein performing the binary search further includes: determining the difference between the normalized energy and a reference point corresponding to the subinterval of the interval; or determining the difference between the concentrated and scaled energy and a reference point corresponding to the subinterval of the interval, wherein the concentrated and scaled energy corresponds to the square root of the length of the first sequence multiplied by the difference between the following two terms: the normalized energy and the uniform energy.

[0283] Aspect 9: A method according to Aspect 8, wherein utilizing the subinterval of the interval and the normalized energy further comprises: calculating one or more polynomial values, each polynomial value in the one or more polynomial values ​​corresponding to a corresponding polynomial coefficient index in the one or more polynomial coefficient indices; determining one or more multiplication factors, each multiplication factor in the one or more multiplication factors being associated with a corresponding polynomial coefficient index in the one or more polynomial coefficient indices based at least in part on a multiplication index; and determining one or more approximations, each approximation in the one or more approximations being based at least in part on a product of a corresponding polynomial value in the one or more polynomial values ​​and a corresponding multiplication factor in the one or more multiplication factors.

[0284] Aspect 10: The method of any one of aspects 1 to 9, wherein each respective polynomial approximation is based at least in part on a plurality of polynomial coefficients and a polynomial degree, the plurality of polynomial coefficients and the polynomial degree being stored in a memory of the transmitter device.

[0285] Aspect 11: The method of aspect 10, wherein the plurality of polynomial coefficients are stored in a lookup table.

[0286] Aspect 12: A method according to any one of Aspects 1 to 11, wherein the polynomial approximation of the multiple approximation factors is formed, including: determining an approximation region based at least in part on the first sequence length and the first sequence energy, the approximation region being associated with the first alphabet; identifying an approximation form corresponding to the approximation region, wherein the polynomial approximation of the multiple approximation factors is formed at least in part on the identification of the approximation form.

[0287] Aspect 13: A method according to any one of Aspects 1 to 12, wherein the cumulative number of sequences defines the cardinality of the set of all sequences within the first alphabet, each sequence in the set of all sequences within the first alphabet having a corresponding length equal to the length of the first sequence and a corresponding energy less than or equal to the energy of the first sequence.

[0288] Aspect 14: A method according to any one of Aspects 1 to 13, wherein obtaining the approximation of the logarithm of the cumulative number of sequences further comprises: multiplying each of the polynomial approximations of the plurality of approximation factors by a corresponding multiplication factor, the corresponding multiplication factor being based at least in part on the first sequence length; obtaining a plurality of approximation terms based at least in part on the multiplication, each of the plurality of approximation terms corresponding to a corresponding polynomial approximation of the polynomial approximations of the plurality of approximation factors; and summing the plurality of approximation terms to obtain the approximation of the logarithm of the cumulative number of sequences.

[0289] Aspect 15: A method according to any one of Aspects 1 to 14, wherein the polynomial approximation of the multiple approximation factors includes at least one of the following: a first piecewise polynomial approximation of a saturated entropy function of the normalized energy, the saturated entropy function corresponding to the first approximation factor among the multiple approximation factors, and the saturated entropy function is associated with the first alphabet; or a corresponding piecewise polynomial approximation corresponding to each of one or more additional functions, each of the one or more additional functions being a function of the normalized energy or the concentrated and scaled energy.

[0290] Aspect 16: The method according to any one of aspects 1 to 15, wherein forming the polynomial approximation of the plurality of approximation factors further comprises: removing singular points from at least one of the polynomial approximations of the plurality of approximation factors.

[0291] Aspect 17: The method according to any one of aspects 1 to 16, wherein the logarithm of the cumulative number of sequences is base 2 and the performing of the exponential operation is base 2.

[0292] Aspect 18: A method according to any one of Aspects 1 to 17, wherein at least one of the following situations exists: the probabilistic shaping scheme is associated with the second alphabet and the second sequence length; the second alphabet size is greater than 1; or the second alphabet includes multiple amplitude symbols.

[0293] Aspect 19: A method according to any one of Aspects 1 to 18, wherein: the first alphabet is a subset of the second alphabet or is equal to the second alphabet; the first sequence length is less than or equal to the second sequence length; and the first sequence energy is less than or equal to the energy threshold.

[0294] Aspect 20: The method according to any one of aspects 1 to 19, wherein at least one of the following situations exists: the second sequence length is a power of 2; or the first sequence length is a power of 2.

[0295] Aspect 21: The method according to any one of aspects 1 to 20, wherein the probabilistic shaping scheme and the transmitting are performed by a user equipment (UE).

[0296] Aspect 22: The method according to any one of aspects 1 to 21, wherein the probabilistic shaping scheme and the sending are performed by a network node.

[0297] Aspect 23: An apparatus for wireless communication at a device, the apparatus comprising: a processor; a memory coupled to the processor; and instructions stored in the memory and executable by the processor to cause the apparatus to perform one or more of the methods described in aspects 1 to 22.

[0298] Aspect 24: A device for wireless communication, the device comprising: a memory and one or more processors coupled to the memory, the one or more processors configured to perform the method according to one or more of aspects 1 to 22.

[0299] Aspect 25: An apparatus for wireless communication, the apparatus comprising at least one component for performing the method according to one or more of aspects 1 to 22.

[0300] Aspect 26: A non-transitory computer-readable medium storing code for wireless communication, the code comprising instructions executable by a processor to perform the method according to one or more of aspects 1 to 22.

[0301] Aspect 27: A non-transitory computer-readable medium storing an instruction set for wireless communication, the instruction set comprising one or more instructions that, when executed by one or more processors of a device, cause the device to perform one or more of the methods described in aspects 1 to 22.

[0302] While the foregoing disclosure provides illustration and description, it is not intended to be exhaustive or to limit the aspects to the precise forms disclosed. Modifications and variations are possible in light of the above disclosure or may be acquired from practice of these aspects.

[0303] As used herein, the term "component" is intended to be broadly interpreted as a combination of hardware and / or hardware and software. Whether referred to as software, firmware, middleware, microcode, hardware description language or other names, "software" should be broadly interpreted as meaning instructions, instruction sets, codes, code segments, program codes, programs, subroutines, software modules, applications, software applications, software packages, routines, subroutines, objects, executable files, threads of execution, processes and / or functions, etc. As used herein, a "processor" is implemented in a combination of hardware and / or hardware and software. It will be apparent that the systems and / or methods described herein can be implemented by a combination of different forms of hardware and / or hardware and software. The actual dedicated control hardware or software code used to implement these systems and / or methods does not limit various aspects. Therefore, no reference is made herein to specific software code to describe the operation and behavior of the systems and / or methods, as those skilled in the art will appreciate that software and hardware can be designed to implement the systems and / or methods based at least in part on the description herein.

[0304] As used herein, "satisfying a threshold" may mean that a value is greater than a threshold, greater than or equal to a threshold, less than a threshold, less than or equal to a threshold, equal to a threshold, not equal to a threshold, etc., depending on the context.

[0305] Although specific combinations of features are set forth in the claims and / or disclosed in the specification, these combinations are not intended to limit the disclosure of various aspects. Many of these features can be combined in a manner not specifically described in the claims and / or not disclosed in the specification. The disclosure of various aspects includes each dependent claim combined with each other claim in the claim set. As used herein, a phrase referring to "at least one of" a list of items refers to any combination of these items (which includes a single member). As an example, "at least one of a, b, or c" is intended to encompass a, b, c, a+b, a+c, b+c, and a+b+c, as well as any combination of multiple identical elements (e.g., a+a, a+a+a, a+a+b, a+a+c, a+b+b, a+c+c, b+b, b+b+b, b+b+c, c+c, and c+c+c, or any other arrangement of a, b, and c).

[0306] Any element, action or instruction used herein should not be interpreted as key or necessary, unless explicitly described as such. In addition, as used herein, the articles "one" and "a kind of" are intended to include one or more projects and can be used interchangeably with "one or more". In addition, as used herein, the article "said" is intended to include one or more projects connected with the article "said", and can be used interchangeably with "one or more". In addition, as used herein, the terms "group" and "cluster" are intended to include one or more projects and can be used interchangeably with "one or more". If only want to refer to a project, then use the phrase "only one" or similar terms. In addition, as used herein, the terms "have", "possess", "have" etc. are intended to be open terms, which do not limit the elements they modify (for example, "an element having" A can also have B). In addition, the phrase "based on" is intended to represent "at least partially based on", unless explicitly stated otherwise. Furthermore, as used herein, the term "or" when used in a series is intended to be open-ended and used interchangeably with "and / or" unless explicitly stated otherwise (e.g., if used in conjunction with "either" or "only one of").

Claims

1. An apparatus for wireless communication at a transmitter device, the apparatus comprising: Memory; and one or more processors coupled to the memory and configured to: obtaining a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; forming a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; obtaining an approximation of a logarithm of a cumulative number of sequences using the polynomial approximation of the plurality of approximation factors, the logarithm of the cumulative number of sequences associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; performing an exponential operation on the approximation of the logarithm of the cumulative sequence quantity, thereby obtaining an approximation of the cumulative sequence quantity; encoding the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a sequence of symbols, the sequence of symbols having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the sequence of symbols belongs to a second alphabet having a second alphabet size; as well as A message is sent to one or more receiver devices based at least in part on the sequence of symbols.

2. The apparatus of claim 1 , wherein to form the polynomial approximation of the plurality of approximation factors, the one or more processors are configured to: determining a normalized energy corresponding to a ratio between the first sequence energy and the first sequence length; obtaining a uniform energy, the uniform energy being associated with the first alphabet; obtaining a subinterval of an interval based at least in part on the normalized energy; as well as At least one polynomial approximation of the polynomial approximations of the plurality of approximation factors is formed using the subinterval of the interval and the normalized energy.

3. The apparatus of claim 2 , wherein at least one of the following conditions exists: said interval being associated with said first alphabet; The interval includes a plurality of subintervals, and the interval corresponds to a disjoint union of the plurality of subintervals; or Each subinterval of the plurality of subintervals of the interval corresponds to a respective left subinterval boundary of a plurality of left subinterval boundaries.

4. The apparatus of claim 3 , wherein each subinterval of the plurality of subintervals of the interval is associated with one or more respective approximate region indexes, each respective approximate region index of the one or more respective approximate region indexes being associated with at least one of: a corresponding reference point among multiple reference points, Append the index accordingly, or One or more respective polynomial coefficient indices, each polynomial coefficient index of the one or more respective polynomial coefficient indices being associated with a respective multiplication index of the plurality of multiplication indices and a respective type indicator of the plurality of type indicators.

5. The apparatus of claim 4, wherein at least one of the following conditions exists: One or more reference points of the plurality of reference points correspond to binary numbers; One or more left subinterval boundaries of the plurality of subintervals of the interval correspond to binary numbers; One or more reference points of the plurality of reference points coincide with one or more corresponding left subinterval boundaries of the plurality of left subinterval boundaries; or A total number of reference points in the plurality of reference points is less than a total number of left subinterval boundaries of the plurality of subintervals of the interval.

6. The device according to claim 4, wherein: The plurality of left subinterval boundaries are stored as a binary tree structure having a root node, a plurality of internal nodes, and a plurality of leaf nodes; Each of the plurality of internal nodes stores a key corresponding to a corresponding left subinterval boundary; and Each leaf node of the plurality of leaf nodes stores a subinterval index corresponding to a corresponding subinterval of the plurality of subintervals of the interval.

7. The apparatus of claim 6, wherein to obtain the subinterval of the interval, the one or more processors are configured to: performing a binary search by traversing a path of the binary tree structure from the root node to a leaf node of the plurality of leaf nodes, wherein the leaf node of the plurality of leaf nodes stores a subinterval index corresponding to the subinterval of the interval; identifying the subinterval of the interval based at least in part on the subinterval index; determining an approximate region index based at least in part on the first sequence length and the identification of the subinterval of the interval; identifying one or more polynomial coefficient indices, the one or more polynomial coefficient indices being associated with the approximation region index; identifying a corresponding multiplication index for each of the one or more polynomial coefficient indices; as well as A respective type indicator is identified for each of the one or more polynomial coefficient indices.

8. The apparatus of claim 7, wherein to perform the binary search, the one or more processors are configured to: determining a difference between the normalized energy and a reference point corresponding to the subinterval of the interval; or A difference is determined between a centered and scaled energy and a reference point corresponding to the subinterval of the interval, wherein the centered and scaled energy corresponds to a square root of the first sequence length multiplied by a difference between: the normalized energy and the uniform energy.

9. The apparatus of claim 8, wherein to utilize the subinterval of the interval and the normalized energy, the one or more processors are configured to: calculating one or more polynomial values, each polynomial value of the one or more polynomial values ​​corresponding to a respective polynomial coefficient index of the one or more polynomial coefficient indices; determining one or more multiplication factors, each multiplication factor of the one or more multiplication factors being associated with a corresponding polynomial coefficient index of the one or more polynomial coefficient indices based at least in part on a multiplication index; as well as One or more approximations are determined, each of the one or more approximations being based at least in part on a product of a corresponding polynomial value of the one or more polynomial values ​​and a corresponding multiplication factor of the one or more multiplication factors.

10. The apparatus of claim 1, wherein each respective polynomial approximation is based at least in part on a plurality of polynomial coefficients and a polynomial degree, the plurality of polynomial coefficients and the polynomial degree being stored in a memory of the transmitter device. The apparatus of claim 10 , wherein the plurality of polynomial coefficients are stored in a lookup table.

12. The apparatus of claim 1 , wherein to form the polynomial approximation of the plurality of approximation factors, the one or more processors are configured to: determining an approximate region based at least in part on the first sequence length and the first sequence energy, the approximate region being associated with the first alphabet; and An approximation form corresponding to the approximation region is identified, wherein the polynomial approximation forming the plurality of approximation factors is based at least in part on the identification of the approximation form.

13. The apparatus of claim 1 , wherein the cumulative number of sequences defines a cardinality of a set of all sequences within the first alphabet, each sequence in the set of all sequences within the first alphabet having a respective length equal to the length of the first sequence and a respective energy less than or equal to the energy of the first sequence.

14. The apparatus of claim 1 , wherein to obtain the approximation of the logarithm of the cumulative number of sequences, the one or more processors are configured to: multiplying each polynomial approximation of the plurality of approximation factors by a corresponding multiplication factor, the corresponding multiplication factor being based at least in part on the first sequence length; obtaining a plurality of approximations based at least in part on the multiplying, each approximation in the plurality of approximations corresponding to a respective polynomial approximation in the polynomial approximations of the plurality of approximation factors; and The plurality of approximations are summed to obtain the approximation of the logarithm of the cumulative sequence quantity.

15. The apparatus of claim 1 , wherein the polynomial approximation of the plurality of approximation factors comprises at least one of: a first piecewise polynomial approximation of a saturated entropy function of the normalized energy, the saturated entropy function corresponding to a first approximation factor of the plurality of approximation factors, and the saturated entropy function being associated with the first alphabet; or A respective piecewise polynomial approximation corresponds to each of one or more additional functions, each of the one or more additional functions being a function of the normalized energy or the lumped and scaled energy.

16. The apparatus of claim 1 , wherein to form the polynomial approximation of the plurality of approximation factors, the one or more processors are configured to: Singularities are removed from at least one polynomial approximation of the polynomial approximations of the plurality of approximation factors.

17. The apparatus of claim 1, wherein the logarithm of the cumulative sequence quantity is base 2 and the performing of the exponential operation is base 2.

18. The apparatus of claim 1, wherein at least one of the following conditions exists: the probabilistic shaping scheme is associated with the second alphabet and the second sequence length; The second alphabet size is greater than 1; or The second alphabet includes a plurality of magnitude symbols.

19. The apparatus of claim 1, wherein: the first alphabet is a subset of or equal to the second alphabet; The first sequence length is less than or equal to the second sequence length; and The first sequence energy is less than or equal to the energy threshold.

20. The apparatus of claim 1, wherein at least one of the following conditions exists: The second sequence length is a power of 2; or The first sequence length is a power of 2.

21. The apparatus of claim 1, wherein the probabilistic shaping scheme and the sending of the message are performed by a user equipment (UE).

22. The apparatus of claim 1, wherein the probabilistic shaping scheme and the sending of the message are performed by a network node.

23. A method of wireless communication performed by a transmitter device, the method comprising: obtaining a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; forming a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; obtaining an approximation of a logarithm of a cumulative number of sequences using the polynomial approximation of the plurality of approximation factors, the logarithm of the cumulative number of sequences associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; performing an exponential operation on the approximation of the logarithm of the cumulative sequence quantity, thereby obtaining an approximation of the cumulative sequence quantity; encoding the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a sequence of symbols, the sequence of symbols having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the sequence of symbols belongs to a second alphabet having a second alphabet size; as well as A message is sent to one or more receiver devices based at least in part on the sequence of symbols.

24. The method of claim 23, wherein forming the polynomial approximation of the plurality of approximation factors further comprises: determining a normalized energy corresponding to a ratio between the first sequence energy and the first sequence length; obtaining a uniform energy, the uniform energy being associated with the first alphabet; obtaining a subinterval of an interval based at least in part on the normalized energy; as well as At least one polynomial approximation of the polynomial approximations of the plurality of approximation factors is formed using the subinterval of the interval and the normalized energy.

25. The method of claim 24, wherein at least one of the following conditions exists: said interval being associated with said first alphabet; The interval includes a plurality of subintervals, and the interval corresponds to a disjoint union of the plurality of subintervals; or Each subinterval of the plurality of subintervals of the interval corresponds to a respective left subinterval boundary of a plurality of left subinterval boundaries.

26. The method of claim 25, wherein each subinterval of the plurality of subintervals of the interval is associated with one or more respective approximate region indices, each respective approximate region index of the one or more respective approximate region indices being associated with at least one of: a corresponding reference point among multiple reference points, Append the index accordingly, or One or more respective polynomial coefficient indices, each polynomial coefficient index of the one or more respective polynomial coefficient indices being associated with a respective multiplication index of the plurality of multiplication indices and a respective type indicator of the plurality of type indicators.

27. The method of claim 26, wherein at least one of the following conditions exists: One or more reference points of the plurality of reference points correspond to binary numbers; One or more left subinterval boundaries of the plurality of subintervals of the interval correspond to binary numbers; One or more reference points of the plurality of reference points coincide with one or more corresponding left subinterval boundaries of the plurality of left subinterval boundaries; or A total number of reference points in the plurality of reference points is less than a total number of left subinterval boundaries of the plurality of subintervals of the interval.

28. The method of claim 26, wherein: The plurality of left subinterval boundaries are stored as a binary tree structure having a root node, a plurality of internal nodes, and a plurality of leaf nodes; Each of the plurality of internal nodes stores a key corresponding to a corresponding left subinterval boundary; and Each leaf node of the plurality of leaf nodes stores a subinterval index corresponding to a corresponding subinterval of the plurality of subintervals of the interval.

29. The method of claim 28, wherein obtaining the subinterval of the interval further comprises: performing a binary search by traversing a path of the binary tree structure from the root node to a leaf node of the plurality of leaf nodes, wherein the leaf node of the plurality of leaf nodes stores a subinterval index corresponding to the subinterval of the interval; identifying the subinterval of the interval based at least in part on the subinterval index; determining an approximate region index based at least in part on the first sequence length and the identification of the subinterval of the interval; identifying one or more polynomial coefficient indices, the one or more polynomial coefficient indices being associated with the approximation region index; identifying a corresponding multiplication index for each of the one or more polynomial coefficient indices; as well as A respective type indicator is identified for each of the one or more polynomial coefficient indices.

30. The method of claim 29, wherein performing the binary search further comprises: determining a difference between the normalized energy and a reference point corresponding to the subinterval of the interval; or A difference is determined between a centered and scaled energy and a reference point corresponding to the subinterval of the interval, wherein the centered and scaled energy corresponds to a square root of the first sequence length multiplied by a difference between: the normalized energy and the uniform energy.

31. The method of claim 30, wherein utilizing the subinterval of the interval and the normalized energy further comprises: calculating one or more polynomial values, each polynomial value of the one or more polynomial values ​​corresponding to a respective polynomial coefficient index of the one or more polynomial coefficient indices; determining one or more multiplication factors, each multiplication factor of the one or more multiplication factors being associated with a corresponding polynomial coefficient index of the one or more polynomial coefficient indices based at least in part on a multiplication index; as well as One or more approximations are determined, each of the one or more approximations being based at least in part on a product of a corresponding polynomial value of the one or more polynomial values ​​and a corresponding multiplication factor of the one or more multiplication factors.

32. The method of claim 23, wherein each respective polynomial approximation is based at least in part on a plurality of polynomial coefficients and a polynomial degree, the plurality of polynomial coefficients and the polynomial degree being stored in a memory of the transmitter device.

33. The method of claim 32, wherein the plurality of polynomial coefficients are stored in a lookup table.

34. The method of claim 23, wherein forming the polynomial approximation of the plurality of approximation factors comprises: determining an approximate region based at least in part on the first sequence length and the first sequence energy, the approximate region being associated with the first alphabet; as well as An approximation form corresponding to the approximation region is identified, wherein the polynomial approximation forming the plurality of approximation factors is based at least in part on the identification of the approximation form.

35. A method according to claim 23, wherein the cumulative number of sequences defines a cardinality of a set of all sequences within the first alphabet, each sequence in the set of all sequences within the first alphabet having a corresponding length equal to the length of the first sequence and a corresponding energy less than or equal to the energy of the first sequence.

36. The method of claim 23, wherein obtaining the approximation of the logarithm of the cumulative number of sequences further comprises: multiplying each polynomial approximation of the plurality of approximation factors by a corresponding multiplication factor, the corresponding multiplication factor being based at least in part on the first sequence length; obtaining a plurality of approximations based at least in part on the multiplying, each approximation in the plurality of approximations corresponding to a respective polynomial approximation in the polynomial approximations of the plurality of approximation factors; and The plurality of approximations are summed to obtain the approximation of the logarithm of the cumulative sequence quantity.

37. The method of claim 23, wherein the polynomial approximation of the plurality of approximation factors comprises at least one of: a first piecewise polynomial approximation of a saturated entropy function of the normalized energy, the saturated entropy function corresponding to a first approximation factor of the plurality of approximation factors, and the saturated entropy function being associated with the first alphabet; or A respective piecewise polynomial approximation corresponds to each of one or more additional functions, each of the one or more additional functions being a function of the normalized energy or the lumped and scaled energy.

38. The method of claim 23, wherein forming the polynomial approximation of the plurality of approximation factors further comprises: Singularities are removed from at least one polynomial approximation of the polynomial approximations of the plurality of approximation factors.

39. The method of claim 23, wherein the logarithm of the cumulative sequence quantity is base 2 and the performing of the exponential operation is base 2.

40. The method of claim 23, wherein at least one of the following conditions exists: the probabilistic shaping scheme is associated with the second alphabet and the second sequence length; The second alphabet size is greater than 1; or The second alphabet includes a plurality of magnitude symbols.

41. The method of claim 23, wherein: the first alphabet is a subset of or equal to the second alphabet; The first sequence length is less than or equal to the second sequence length; and The first sequence energy is less than or equal to the energy threshold.

42. The method of claim 23, wherein at least one of the following conditions exists: The second sequence length is a power of 2; or The first sequence length is a power of 2.

43. The method of claim 23, wherein the probabilistic shaping scheme and the transmitting are performed by a user equipment (UE).

44. The method of claim 23, wherein the probabilistic shaping scheme and the transmitting are performed by a network node.

45. A non-transitory computer-readable medium storing an instruction set for wireless communication, the instruction set comprising: One or more instructions that, when executed by one or more processors of a sender device, cause the sender device to: obtaining a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; forming a polynomial approximation of a plurality of approximation factors as part of the probabilistic shaping scheme; obtaining an approximation of a logarithm of a cumulative number of sequences using the polynomial approximation of the plurality of approximation factors, the logarithm of the cumulative number of sequences associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; performing an exponential operation on the approximation of the logarithm of the cumulative sequence quantity, thereby obtaining an approximation of the cumulative sequence quantity; encoding the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a sequence of symbols, the sequence of symbols having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the sequence of symbols belongs to a second alphabet having a second alphabet size; as well as A message is sent to one or more receiver devices based at least in part on the sequence of symbols.

46. ​​An apparatus for wireless communication, the apparatus comprising: means for obtaining a plurality of information bits for a probabilistic shaping scheme, the probabilistic shaping scheme being associated with an energy threshold; means for forming a polynomial approximation of a plurality of approximation factors as part of said probabilistic shaping scheme; means for obtaining an approximation of a logarithm of a cumulative number of sequences using the polynomial approximation of the plurality of approximation factors, the logarithm of the cumulative number of sequences being associated with a first alphabet having a first alphabet size, a first sequence length, and a first sequence energy; means for performing an exponential operation on said approximation of said logarithm of said cumulative sequence quantity thereby obtaining an approximation of said cumulative sequence quantity; means for encoding the plurality of information bits based at least in part on the approximation of the cumulative number of sequences as part of the probabilistic shaping scheme to obtain a sequence of symbols, the sequence of symbols having a length equal to a second sequence length and an energy less than or equal to the energy threshold, wherein each symbol in the sequence of symbols belongs to a second alphabet having a second alphabet size; and Means for sending a message to one or more receiver devices based at least in part on the sequence of symbols.

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