Low-density parity check coding including punctured auxiliary bits

Abstract

A low-density parity check encoder is provided that encodes multiple information bits according to a low-density parity check matrix. The encoder generates auxiliary bits from the information bits, and the transmitter punctures the auxiliary bits while transmitting the information bits, thereby preserving the useful shape provided to the information bits by probabilistic amplitude shaping (PAS).

Description

[Technical Field]

[0001]

[0001] This application relates to a wireless communication system, and more specifically to a wireless communication system using low-density parity check coding including punctured auxiliary bits. [Background technology]

[0002]

[0002] New Radio (NR) 5th Generation (5 th Modern communication standards, such as 5G (Generation Generation) standards, utilize additional frequency bands compared to older standards, but communication is still bandwidth-limited. The resulting limitation on the bandwidth that must be transmitted limits the theoretically achievable data rate. To approach this theoretical minimum by increasing spectral efficiency, 5G systems can use higher-order modulation schemes where bits are encoded to form symbols. For example, in M-ary quadrature amplitude modulation (QAM), M bits are encoded, and 2 M A symbol is formed by selecting from a constellation of n possible QAM symbols, where M is a positive integer.

[0003]

[0003] If each symbol in the constellation has the same probability of being transmitted, a "shaping gap" occurs that reduces spectral efficiency by up to 1.53 dB. To reduce or eliminate this shaping gap, some higher-order modulation schemes can utilize probabilistic amplitude shaping (PAS). In PAS, the outer layer of amplitude shaping maps the input bits to amplitudes with a non-uniform distribution (ideally a Gaussian distribution). These amplitudes are then binary encoded to form corresponding streams of information bits, which are processed according to the inner layer of binary forward-error-correction (FEC) coding to provide parity bits for amplitude phase adjustment to generate the symbol constellation. It is advantageous to implement FEC coding using a low-density parity-check code (LDPC).

[0004]

[0004] In 5G, there are two base graph matrices for LDPC, namely base graph 1 (BG1) and base graph 2 (BG2). For each base graph matrix, the information bits corresponding to the first two columns of the matrix are punctured and therefore not transmitted. While this puncturing is advantageous in terms of improving coding performance, it can degrade the reduction of the shaping gap by probabilistic amplitude shaping. [Overview of the project]

[0005]

[0005] The following sections summarize some aspects of the present disclosure in order to provide a basic understanding of the technology discussed. The sole purpose of this is to present some concepts of one or more aspects of the present disclosure in outline form as an introduction to the more detailed explanations to be presented later.

[0006]

[0006] In one aspect of the present disclosure, a wireless device is configured to encode Z information bits into a (K b * + Y) b Z-bit codeword according to a low-density parity-check matrix, where K * is the amount of information bit strings in the base graph associated with the low-density parity-check matrix, the first Z bits of the codeword are parity bits, and the subsequent (K b + Y - 1) b Z bits include K * Z information bits and (Y - 1) b * Z additional parity bits, where Z is the lifting factor of the low-density parity-check matrix and Y is a positive integer. * Z個の追加のパリティビットを含み、Zが、低密度パリティ検査行列のリフティングファクタであり、Yが、正の整数である。

[0007]

[0007] In yet another aspect of the present disclosure, a wireless device is configured to encode Z information bits into a (K b * + Y) b Z-bit codeword according to a low-density parity-check matrix, where K * is the amount of information bit strings in the base graph associated with the low-density parity-check matrix, the first K b Z bits of the codeword are information bits, the subsequent (Y - 1) b * Z bits are parity bits, and further, the remaining Z bits of the codeword are parity bits, where Z is the lifting factor of the low-density parity-check matrix and Y is a positive integer. * Zビットが、パリティビットであり、更に、コードワードの残りのZビットが、補助ビットであり、Zが、低密度パリティ検査行列のリフティングファクタであり、Yが、正の整数である。

[0008]

[0008] In yet another aspect of the present disclosure, a computerized method includes selecting a matrix Q Z×Z that is equal to the sum of a set of ZXZ lifting matrices in the first column of a low-density parity-check matrix and is further invertible, and using the value of Z and the matrix Q Z×Z to generate a low-density parity-check matrix.Z×Z Lifting the base graph according to and according to the low-density parity check matrix, K b However, the amount of information bits in the base graph is the set of Z bits of the codeword, and the auxiliary bits are the (K) bits of the codeword. b +Y-1) * The set of Z bits is K b * Z information bits and (Y-1) * Multiple K, each containing Z parity bits, where Y is a positive integer. b * (K b +Y) * This includes encoding into a Z-bit codeword and transmitting one or more symbols that carry information based on the codeword.

[0009]

[0009] In yet another aspect of the present disclosure, the computerized method is a matrix Q equal to the sum of the set of ZXZ lifting matrices in the first column of the low-density parity check matrix. Z×Z Furthermore, the matrix Q is reversible. Z×Z Selecting and generating a low-density parity check matrix, the values ​​of Z and matrix Q Z×Z Lifting the base graph according to and according to the low-density parity check matrix, K b This is the amount of information bit sequences in the base graph, and the first K of the codeword. b * The Z bit is an information bit, and the (Y-1) bit that follows the codeword * A set of multiple K bits where Z is the parity bit, and the Z bits between the information bit and the parity bit are auxiliary bits, and Y is a positive integer. b * (K b +Y) * This includes encoding into a Z-bit codeword and transmitting one or more symbols that carry information based on the codeword.

[0010]

[0010] Other aspects, features, and embodiments of the present disclosure will become apparent to those skilled in the art upon consideration of the following description. [Brief explanation of the drawing]

[0011] [Figure 1]

[0011] An exemplary network of communication devices configured for systematic LDPC coding according to an aspect of the present disclosure is shown. [Figure 2]

[0012] The image shows a base graph 1 (BG1) according to an aspect of this disclosure, in which the first two columns are parity bit columns. [Figure 3]

[0013] Figure 3 is a diagram of an exemplary base graph according to an aspect of this disclosure. [Figure 4]

[0014] Figure 4 is a diagram of an exemplary parity check matrix according to an aspect of the present disclosure. [Figure 5]

[0015] This is an example of a base graph according to the aspects of this disclosure. [Figure 6]

[0016] This is a diagram of a transmitter with probabilistic amplitude shaping and systematic LDPC coding according to an aspect of the present disclosure. [Figure 7]

[0017] A systematic decoder according to one aspect of this disclosure is shown. [Figure 8]

[0018] This is a flowchart illustrating an exemplary method of systematic LDPC coding according to the embodiments of this disclosure.

[0012]

[0019] The implementations of this disclosure and their advantages are best understood by referring to the following “Modes for Carrying Out the Invention.” It should be understood that similar reference numerals are used to identify similar elements shown in one or more of the drawings. [Modes for carrying out the invention]

[0013]

[0020] Low-density parity-check codes are codecable, meaning the parity bit can be uniquely determined from the information bits according to the low-density parity-check matrix. There are many ways to implement the low-density parity-check matrix for low-density parity-check coding. While all of these various approaches can result in codecability, coding efficiency is also important. If the choice of low-density parity-check matrix results in an encoder that has to perform many operations to compute the parity bit, the resulting coding is unfavorable compared to another low-density parity-check matrix choice in which the parity bit can be computed using fewer operations. The same demands for efficiency also apply to LDPC decoders. Due to considerable effort and research into various methods for selecting the low-density parity-check matrix, the 5G protocol standardized on a pseudo-cyclic LDPC, where the protograph is shown as a base graph (either BG1 or BG2). Based on a lifting factor Z, each element in the base graph is replaced by a corresponding Z×Z permutation matrix to form the low-density parity-check matrix. Since 5G LDPC is pseudocyclic, various (non-zero) Z×Z permutation matrices are related to each other by cyclic shifts. This can be advantageous in reducing the memory requirements of encoders and decoders, as well as reducing computational complexity and the number of operations required.

[0014]

[0021] Therefore, it is desirable for user equipment or communication devices such as base stations to continue using either BG1 or BG2 for encoding and decoding. However, as mentioned above, this use of 5G LDPC comes at the cost of puncturing information bits (and thus the corresponding amplitudes), which increases the shaping gap that would otherwise be reduced by using techniques such as probabilistic amplitude shaping.

[0015]

[0022] As will be further described herein, in some cases, LDPC encoders and decoders are disclosed that may retain the use of a 5G base graph but puncture bits other than information bits. In another case, as will be described with reference to Figure 5, the 5G base graph may be modified, thereby also enabling the puncture of bits other than information bits. Since any suitable base graph may be used, the scope of this disclosure is not limited to the 5G base graph, and the scope of this disclosure may be adapted to further iterations of technology beyond 5G. Thus, communication systems may systematically use LDPC. A code is indicated herein as systematic if the information bits are not transformed or punctured, but instead retained within the transmitted codeword. The following implementations may be adopted in any application where systematic coding of LDPC is desired. The following description focuses on the use of systematic LDPC coding in the context of probabilistic amplitude shaping, but it will be understood that the LDPC coding and decoding described herein are applicable to any systematic forward error correction (FEC) application.

[0016]

[0023] Before describing systematic coding of LDPC in more detail, we first describe an exemplary communication system in which a communication device may implement systematic coding of 5G LDPC. Referring here to Figure 1, various aspects of the present disclosure are shown with reference to a wireless communication system 100. The wireless communication system 100 includes three interacting domains: a core network 102, a radio access network (RAN) 104, and an external data network 110. The RAN 104 includes a plurality of base stations 108 and a plurality of user equipment (UEs) 106. Each UE 106 or base station 108 is an embodiment of a network device configured to perform systematic coding of 5G LDPC, as will be further described herein.

[0017]

[0024] The wireless communication system 100 may enable each UE 106 to communicate data with an external data network 110, such as the Internet (but not limited to the Internet). RAN 104 may implement any suitable wireless communication technology(s) to provide wireless access to each UE 106. In one embodiment, RAN 104 may operate in accordance with the 3rd Generation Partnership Project (3GPP) New Radio (NR) specification, often referred to as 5G. As another example, RAN 104 may operate under a hybrid of 5G NR and the Evolutionary Universal Terrestrial Radio Access Network (eUTRAN) standard, often referred to as LTE. 3GPP refers to this hybrid RAN as Next Generation RAN or NG-RAN. Naturally, many other examples may be utilized within the scope of this disclosure.

[0018]

[0025] As shown in the figure, RAN104 includes a plurality of base stations 108. Generally, a base station is a network device in a radio access network that is responsible for radio transmission and radio reception in one or more cells with respect to UE106. In different technologies, standards, or contexts, a base station 108 may be referred to by those skilled in the art in various ways, such as a base transceiver station (BTS), radio base station, radio transceiver, transceiver function, basic service set (BSS), extended service set (ESS), access point (AP), node B (NB), eNode B (eNB), gNode B (gNB), or any other preferred technology.

[0019]

[0026] The base station 108 may conform to any suitable architecture, such as aggregated or non-aggregated. An aggregated base station may be configured to utilize a radio protocol stack that is physically or logically integrated within a single RAN node. A non-aggregated base station may be configured to utilize a protocol stack that is physically or logically distributed among two or more units (such as one or more centralized units (CUs), one or more distributed units (DUs), or one or more radio units (RUs)). In some embodiments, CUs may be implemented within a RAN node, and one or more DUs may be co-located with CUs or, alternatively, geographically or virtually distributed across one or more other RAN nodes. DUs may be implemented to communicate with one or more radio units. Each of the CU, DU, and radio unit may also be implemented as a virtual unit, namely a virtual central unit (VCU), a virtual distributed unit (VDU), or a virtual radio unit (VRU).

[0020]

[0027] A radio access network 104 supporting wireless communication for multiple mobile devices is further shown. Mobile devices may be referred to as user equipment (UE) in the 3GPP standard, but may also be referred to by those skilled in the art as mobile station (MS), subscriber station, mobile unit, subscriber unit, wireless unit, remote unit, mobile device, wireless device, wireless communication device, remote device, mobile subscriber station, access terminal (AT), mobile terminal, wireless terminal, remote terminal, handset, terminal, user agent, mobile client, client, or any other preferred term. UE 106 may include devices that provide a user with access to network services.

[0021]

[0028] UE106 may include several components configured for wireless communication. Such components may include antennas, antenna arrays, RF chains, amplifiers, one or more processors, etc., which are electrically coupled to one another. Some non-exclusive examples of mobile devices (mobile network devices) include cellular phones, smartphones, session initiation protocol (SIP) phones, laptops, personal computers (PCs), notebooks, netbooks, smartbooks, tablets, personal digital assistants (PDAs), and a wide range of embedded systems, such as those supporting the "Internet of Things" (IoT). In addition, network devices may include automobiles or other transport vehicles, remote sensors or actuators, robots or robotics devices, satellite radios, global positioning system (GPS) devices, object tracking devices, drones, multicopters, quadcopters, remote control devices, home and / or wearable devices such as eyewear, wearable cameras, virtual reality devices, smartwatches, health trackers or fitness trackers, digital audio players (e.g., MP3 players), cameras, game consoles, etc. Furthermore, network devices may include home audio, video, and / or multimedia devices, appliances, vending machines, intelligent lighting, home security systems, smart meters, and other digital home devices or smart home devices.

[0022]

[0029] Wireless communication between RAN104 and UE106 may be described as utilizing an air interface. Transmissions from base station 108 to one or more UE106 via the air interface may be referred to as downlink (DL) transmissions. According to some aspects of this disclosure, the term downlink may refer to point-to-multipoint transmissions originating from base station 108. Another way to describe this scheme may be to use the term broadcast channel multiplexing. Transmissions from UE106 to base station 108 may be referred to as uplink (UL) transmissions. According to further aspects of this disclosure, the term uplink may refer to point-to-point or point-to-multipoint transmissions originating from UE106.

[0023]

[0030] Therefore, base station 108 can broadcast downlink traffic 112 to one or more UEs 106. Generally, each base station 108 is a node or device responsible for scheduling traffic within the wireless communication network, including downlink traffic 112 and, in some embodiments, uplink traffic 116 and uplink control information 118 from one or more UEs 106. On the other hand, each UE 106 is a node or device that receives downlink control information 114 from another entity in the wireless communication network, such as base station 108, including, but not limited to, scheduling information (e.g., permission), synchronization or timing information, or other control information.

[0024]

[0031] Base station 108 may include a backhaul interface for communication with the backhaul portion 120 of the wireless communication system. The backhaul 120 may provide a link between base station 108 and the core network 102. Furthermore, in some examples, the backhaul network may provide interconnection between each base station 108. Various types of backhaul interfaces may be employed, such as direct physical connections and virtual networks, using any suitable transport network.

[0025]

[0032] The core network 102 may be part of the wireless communication system 100 and may be independent of the radio access technology used in RAN 104. In some embodiments, the core network 102 may be configured according to a 5G standard (e.g., 5GC). In other embodiments, the core network 102 may be configured according to a 4G evolved packet core (EPC) or any other preferred standard or configuration.

[0026]

[0033] In various implementations, air interfaces within a radio access network 104 may utilize licensed, unlicensed, or shared spectra. Licensed spectra generally provide exclusive use of a portion of the spectrum by mobile network operators purchasing licenses from government regulatory bodies. Unlicensed spectra provide shared use of a portion of the spectrum without requiring a government-licensed license. Generally, access to unlicensed spectra still requires compliance with some technical rules, but generally, any operator or device may gain access. Shared spectra may fall between licensed and unlicensed spectra, and while technical rules or restrictions may still be required to access them, they can still be shared by multiple operators and / or multiple RATs. For example, a license holder for a portion of a licensed spectrum may offer licensed shared access (LSA) to share that spectrum with other parties who have suitable licensing criteria for gaining access.

[0027]

[0034] The air interface in the wireless access network 104 may utilize one or more duplication algorithms. Duplex refers to a point-to-point communication link where both endpoints can communicate with each other in both directions. Full-duplex means that both endpoints can communicate with each other simultaneously. Half-duplex means that at any given time, only one endpoint can transmit information to the other. In wireless links, full-duplex channels generally rely on the physical separation of the transmitter and receiver, as well as appropriate interference cancellation techniques. Full-duplex emulation is often implemented for wireless links by utilizing frequency division duplex (FDD) or time division duplex (TDD). In FDD, transmissions in different directions operate on different carrier frequencies. In TDD, transmissions in different directions on a given channel are separated from each other using time division multiplexing. That is, at some time, the channel is dedicated to transmission in one direction, and at other times, the channel is dedicated to transmission in the other direction, and the direction can change very rapidly, for example, several times per slot. With this background information in mind, the systematic coding modes of 5G LDPC disclosed herein will be described in more detail.

[0028]

[0035] Systematic coding can utilize any suitable base graph, including the 5G LDPC base graph, or base graphs resulting from modifications of the 5G LDPC base graph or a new base graph. BG1 is shown as matrix 200 in Figure 2. Depending on the coding rate, the BG1 matrix 200 can be up to 46 rows × 68 columns. In normal (information bit punctured) coding using BG1, columns 1-22 are the information bit columns. Columns 23-68 are the parity bit columns. The first four rows and the first 26 columns form the core of the BG1 matrix. The parity bits encoded by columns 23-26 are therefore the core parity bits, and the parity bits encoded by columns 27-68 are shown as the extended parity bits. Note that the first four rows of the core parity bit columns 23-26 form a "double-diagonal" matrix pattern 210, which results in efficient calculation of the corresponding core parity bits. Using the core parity bits calculated during normal 5G operation, the desired number of extended parity bits can then be easily calculated using the "main diagonal" matrix pattern of the extended parity bit sequence.

[0029]

[0036] As described above, in the BG1 matrix, the core column indices are integers ranging from 1 to 26. In the BG2 matrix, the core is formed by the first 4 rows and the first 14 columns. Therefore, the set P of BG2 contains integers from 11 to 14. As will be explained in more detail below, a base graph (e.g., BG1, BG2, and thus any other base graph) can be lifted by a lifting factor Z. In this regard, the lifting factor Z is given by the function Z(a,k) = a * 2 k The formula is generated by where a is an integer multiplier selected from the set {2, 3, 5, 7, 9, 11, 13, 15} and k is an integer between 0 and 7. Lifting factors Z, all of which have the same integer multiplier, form what is referred to herein as the Z class.

[0030]

[0037] In some cases, determining the core parity bit may use only the core of the base graph. The lifting resulting from the lifting factor Z forms a lifted core parity check matrix. Each non-zero element in the core of the base graph is then replaced by a Z×Z permutation matrix. Zero elements are replaced by an all-zero Z×Z matrix. The identity element (equal to 1) is replaced by a cyclically shifted identity Z×Z matrix. As the elements increment from 1, the identity matrix is ​​cyclically shifted accordingly to form the corresponding Z×Z permutation matrix. Thus, as used herein, the term “permutation matrix” (also called the lifting matrix) refers only to the identity Z×Z matrix or the cyclic shift of the identity Z×Z matrix. Thus, the permutation matrix is ​​P i It can be expressed as P i This is a Z×Z permutation matrix, and as a result, for each column index j ∈ {0, 1, ..., Z-1}, the (j+i mod Z)th element of that column is 1. All remaining column elements are zero. If the elements to be replaced by the Z×Z permutation matrix are in an information bit sequence, the elements are multiplied by the Z corresponding information bits during LDPC encoding. Representing these Z information bits and the permutation matrix by the corresponding binary polynomial can be computationally efficient. Regarding the formation of binary polynomials, consider, for example, the binary word 1001. The binomial of such a word is the binary vector x 3 +0 * x 2 +0 * x+1. Binary polynomial and monomial x i It can be shown that modulo multiplication with is equivalent to a cyclic shift of a binary polynomial by i, where i is a positive integer.

[0031]

[0038] A pseudo-cyclic LDPC code with a lifting factor Z, or a cyclically lifted LDPC code, is x Z Ring of binary polynomials modulo +1

[0032]

number

[0033] It can be considered as code spanning. Keeping in mind the convention of binary polynomials, the core of BG1 or BG2 can be represented by a matrix H of size 4 x r, where r is 26 for BG1 and r is 14 for BG2. From matrix H, matrix H(x) is a ring

[0034]

number

[0035] It is a lifted matrix over H i,j If it is not equal to -1

[0036]

number

[0037] H i,j If it is equal to -1 then H i,j (x) = 0.

[0038]

[0039] Figure 3 is a diagram of an exemplary base graph 300, or at least the core of the base graph, which may be used in several embodiments. The base graph 300 has columns (also called “nodes”) 301 corresponding to information bits. Columns (or “nodes”) 302 corresponding to parity bits. In conventional LDPCs, column 303 is punctured. Naturally, the scope of this disclosure is not limited to base graph 300, as any suitable base graph may be used.

[0039]

[0040] Figure 4 shows an exemplary parity check matrix 400 associated with the BG1 matrix according to one embodiment. The parity check matrix 400 results from lifting the base graph, although in this embodiment, the lifted base graph does not correspond to the base graph 300, simply for the sake of illustration. Column 401 corresponds to the information bits, and column 402 corresponds to the parity bits. The parity check matrix 400 is merely one embodiment, and it should be understood that the scope of this disclosure may include any appropriate parity check matrix resulting from lifting any appropriate base graph.

[0040]

[0041] The diagram in Figure 4 shows a simplified representation of replacing the permutation matrix with a notation representing a specific cyclic shift. For example, the element in the upper left corner is 73, which represents a cyclic shift of 73 to the identity Z×Z matrix. Furthermore, in the embodiment of Figure 4, "-1" corresponds to "0" in the base graph. Both "0" and "1" correspond to the element "1" in the base graph (indicating that there is an edge connecting the corresponding variable column and parity column in the base graph). Furthermore, "0" indicates that the cyclic shift matrix is ​​the identity matrix (i.e., a 0 cyclic shift, or no cyclic shift), and "1" indicates that the cyclic shift matrix is ​​obtained by shifting the column of the identity matrix by 1 (to the right). Similarly, various embodiments may include any shift amount between 0 and Z-1.

[0041]

[0042] As mentioned above, the diagram in Figure 4 is a simplified representation, and the simplified format is such that the parity check matrix is ​​size 4. * This makes it possible to show it as 26. In contrast, if the parity check matrix 400 is written out in its entirety, it would have a size (4) due to Z×Z lifting. * Z) * (26 * This will result in having Z). Therefore, the leftmost column of the parity check matrix 400[73,303,68,220], when written out in detail, will be (4 *The format is Z rows × Z columns. The following example represents a parity check matrix generated by lifting the base graph by replacing each non-zero item in the base graph with a Z × Z cyclic lifting matrix (also called a permutation matrix) using H. In normal LDPC coding, the information bits

[0042]

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[0043] This is encoded according to formula (1).

[0044]

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[0045] In equation (1), each

[0046]

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[0047] This shows a vector of systematic bit lengths Z for encoding, and K b This indicates the quantity of the column in the base graph corresponding to the information variable column. Also, each vector

[0048]

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[0049] This is a vector of parity bits with length Z.

[0050]

[0043] In normal LDPC coding, the Z bit in s0 is punctured and replaced with a 4Z parity bit.

[0051]

number

[0052] However, it is generated from the LDPC code and transmitted. Of course, 4 is the number of rows in the core part of the graph and is just an example. In contrast, various embodiments of this disclosure replace s0 with some appropriately determined auxiliary vector a0 of length Z, and as a result, the first Z parity bit when encoded according to the LDPC code.

[0053]

number

[0054] The bit (corresponding to the terminal column of degree 3 in the cumulative chain of degree 2) is the same as the systematic bit s0. Therefore, the Z bit in s0 is "not punctured". In other words, some embodiments "reverse" the parity check matrix so that the systematic bit s0 appears as the first Z parity bit from the encoder after encoding.

[0055]

number

[0056] This corresponds to the start of the cumulative chain in the base graph, and the cumulative chain has a special structure that facilitates the encoding and "returning" the PCM. One embodiment of the cumulative chain is shown above as item 210 in Figure 2.

[0057]

[0044] One embodiment involves summing the matrices in the first Z column of the lifted parity check matrix to obtain equation (2).

[0058]

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[0059] matrix Q Z×Z This conforms to equation (3). Q Z×Z =P 00 +P 10 +P 20 +P30 Formula (3) Q represents the Z×Z matrix obtained by summing the matrices of the first column of the lifted PCM in the simplified representation in Figure 4. In equation (3), P 00 This refers to the lifting matrix in the first Z row and first Z column of the lifted parity check matrix H. In the embodiment of Figure 4, this corresponds to the lifting matrix having the simplified form 73. Lifting matrix P 10 These are located in the first Z column and second Z row of H, and the lifting matrix P 20 These are located in the first Z column and third Z row of H, and the lifting matrix P 30 These are located in the first Z column and the fourth Z row of H, and have a simplified form 220 in the embodiment of Figure 4.

[0060]

[0045] Furthermore, in equation (3), a0 is

[0061]

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[0062] and Q Z×Z Herein is a bit vector of length Z calculated from, where s0' represents a cyclically shifted version of the vector of length Z containing the formed informational bits s0. In this embodiment, the amount of shift is defined by a column of degree 3 corresponding to the first parity column (a column of degree 3 in the cumulative chain). In the embodiment of Figure 4, the first parity column is indicated by reference code 403 and may also be called the terminal column. The term "cumulative chain" may sometimes be used to refer to the entire parity column 402, or only a subsection of the parity column 402 that does not include the terminal column 403. Furthermore, in equation (3), b is another vector of length Z determined based on the parity check matrix of the LDPC code, and the remaining set of information bits is encoded together with s0. Note that in equation (3), other parity bits

[0063]

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[0064] These do not appear because they can be calculated by back substitution using a cumulative chain structure of degree 2.

[0065]

[0046] Continuing with this embodiment, a0 is Q Z×Z Once both and b are determined, the result can be calculated using formula (4).

[0066]

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[0067]

[0047] Note that bit a0 is not a parity bit, but is calculated using an information bit. For the purposes of this embodiment, bits in a vector a0 of length Z may be called auxiliary bits. In any case, auxiliary bits are punctured and therefore not transmitted.

[0068]

[0048] Encoding is performed on a vector of length Z.

[0069]

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[0070] Back substitution is used to calculate the remaining parity bits within the expression. For example,

[0071]

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[0072] This can be calculated from the first row of the parity check matrix using equation (5), and is a vector of length Z.

[0073]

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[0074] This can be calculated using equation (6) from the second row of the parity check matrix, and is a vector of length Z.

[0075]

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[0076] This can be calculated using equation (7), starting from the third row of the parity check matrix. A vector of length Z.

[0077]

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[0078] Once calculated, the codeword can be expressed as follows:

[0079]

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[0080]

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[0081]

[0049] In other words, according to this embodiment, the encoder has a0 and core parity bits such that equation (8) is satisfied.

[0082]

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[0083] Calculate the remainder. The bits in vector a0 are punctured and therefore not sent.

[0084]

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[0085]

[0050] The decoder decodes the codeword according to the parity check matrix H and systematic bits

[0086]

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[0087] You can obtain s0 by then re-encoding it, or by using message passing on the parity check matrix

[0088]

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[0089] It can be decrypted directly.

[0090]

[0051] In the above embodiments, the encoder may use an unmodified parity check matrix, such as a parity check matrix based on BG1 or BG2 or another suitable base graph. Different embodiments may instead redefine the base graph by substituting the punctured column and the first parity column of the original base graph. In the embodiment of Figure 5, the substitution involves swapping the locations of the terminal column 501 and the punctured column 502 such that the punctured column 502 is at the leftmost position of the parity column and the terminal column 501 is at the leftmost position of the information bit column. In other words, the punctured column 502 is at the leftmost position of the parity column, corresponds to the parity bit column, and is punctured. The terminal column 501 is at the leftmost position of the information bit column, corresponds to the information column, and is not punctured. The lifted parity check matrix resulting from this modified base graph is

[0091]

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[0092] It could be called that.

[0093]

[0052] In this embodiment,

[0094]

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[0095] Adopting this includes an auxiliary bit, which plays the same role as a0 in the previous embodiment. A vector of length Z.

[0096]

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[0097] This can be calculated using equation (9).

[0098]

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[0099]

[0053] The remaining parity bits can be calculated according to equation (10) and backward substitution, as shown in equations (5) to (7).

[0100]

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[0101] The bits inside are punctured and therefore not transmitted.

[0102]

number

[0103]

[0054] In the embodiments described above with respect to Figures 3 to 5, 1) the information bits are not punctured, 2) only one node is punctured, which is located within the set of parity sequences, 3) the terminal sequence terminating the cumulative chain of degree 2 corresponds to the information bit sequence, not the parity sequence as in legacy LDPC coding, and 4) the base graph includes an auxiliary bit sequence that is located between the information bit sequence and the parity bit sequence (as in Figure 3) or in the leftmost column (as in Figure 5). In an alternative way to represent the base graph, the punctured sequence may be located after the parity bit sequence, i.e., at the rightmost position of the base graph. A possible advantage of the embodiments described above is that all information bits are transmitted and none of the information bits are punctured. Such embodiments can preserve the beneficial shaping provided to the information bits by probabilistic amplitude shaping (PAS), thereby reducing the "shaping gap" and preserving spectral efficiency. However, the scope of this disclosure also includes applying the principles described above to uniform modulation (e.g., uniform QAM).

[0104]

[0055] Another possible advantage provided by the above embodiment is that by transmitting all information bits, the receiver may be able to make a hard decision to decode all information bits based on the channel log likelihood ratios (LLRs) without using conventional decoding tools. In other words, when the decoder detects that the channel signal-to-noise ratio (SNR) is higher than a threshold, the decoder may simply make a hard decision on the information bits instead of performing decoding. In contrast, in the case of the current NR BG1, the decoder must reconstruct the punctured information bits, so the receiver uses decoding techniques regardless of the SNR.

[0105]

[0056] Various aspects of the present disclosure include designing cyclic shift values ​​(also known as lifting values ​​for protograph LDPC codes) for LDPC codes to make encoding simpler and more efficient. According to equations (4) and (9), matrix Q Z×Z It should be reversible. Furthermore, various embodiments are Q Z×Z By making it computationally easier to invert x, the power usage efficiency and computational efficiency of the transmitter can be improved. As described above, a pseudo-cyclic LDPC code having a lifting factor Z, or a cyclically lifted LDPC code, is x Z Ring of binary polynomials modulo +1

[0106]

number

[0107] It can be considered as code spanning Q. In this case, Q Z×Z This can be written as follows:

[0108]

number

[0109] In the formula, each number k1,...,k d d corresponds to the cyclic shift value of each of the d edges connected to the punctured column. For example, in Figure 5, the punctured column is a vector of length 4 with values ​​1, 1, 1, 1. Summing these values ​​yields 4 edges, so d is equal to 4. The scope of this disclosure can be scaled to include any appropriate number of edges.

[0110]

[0057] In one embodiment, cyclic shift values ​​k1,...,k are connected to the punctured column. d Q Z×Z x Z Modulo +1

[0111]

number

[0112] is reversible over and

[0113]

Number

[0114] can be designed to have a simpler form. For example,

[0115]

Number

[0116] may contain smaller weights, may contain fewer non - zero values, or may be factored into simpler factors. Examples of simpler factors include (1 + x)(1 + x 2 ), etc.

[0117]

[0058] Generally, without a special structure, Q -1 (x) is assumed to be reversible and has about Z terms. One way to make the inversion computationally easier may involve requiring that k1,..., k d have a common divisor L (e.g., L = Z / 8, 8 > d). The common divisor L effectively reduces the amount of terms from Z to Z / L, and thus may make it computationally easier to invert Q(x).

[0118]

[0059] One example is x 0 + x 2L + x 3L + x 4L + x 5L + x 6L + x 7L and its inverse is x 7L ​​​​​​​​​​​8+1 This is equivalent to inverting it. In some examples, this principle can be used to design cyclic shift values ​​of Z that include factors of power 2. For example, 384 = 3 * 2 7 ;L in this case is 384 / 8. Therefore, the design of Z=8 is Z=L for any integer L * This can be easily generalized to 8.

[0119]

[0060] Generally, if there is a set of k1, ..., k7 for Z, for example,

[0120]

number

[0121] By setting this, it may be easy to extend the design to 2Z. In the above embodiment, once k1,...,k7 are determined for Z=8, it is also possible to determine all factors 8 * Applies to L.

[0122]

[0061] Another property of binary polynomials is that f(x) 2 =f(x 2 ) is true. As a result, the following is also true:

[0123]

number

[0124] Therefore, equation (12) is applied to Q(x), and equations (13) and (14) can be derived from it.

[0125]

number

[0126] Therefore, in a typical embodiment, the encoder Q such that the conditions described in equation (15) are met. Z×Z You can choose a value where k is an integer.

[0127] [Number]

[0128]

[0062] As a result, the matrix Q <00s0107>may be computationally easy to invert. In another more specific embodiment, the encoder may select Q Z×Z such that Equation (14) is satisfied, which may also be computationally easy to invert.

[0129]

[0063] In yet another embodiment, k1, k2, k3, k4 may be selected such that the terms of Equation (16) do not cancel. From Equation (16), Equations (17)-(18) may be derived. <00s0894>

[0130] [Number]

[0131] Thus, the encoder may select the matrix Q Z×Z such that Equation (18) is satisfied, thereby making the inversion relatively easy.

[0132]

[0064] An exemplary transmitter 600 including an LDPC encoder 605 is shown in FIG. 6. The LDPC encoder 605 may perform the encoding actions described with respect to FIGS. 2-5 and 8, including calculating a vector of length Z of parity bits and generating a codeword including the parity bits. <00009s07>

[0133]

[0065] A digital baseband source (not shown) provides k bits to a probabilistic amplitude shaping distribution matcher 610, where k is a plurality of positive integers. The distribution matcher 610 generates n amplitudes from the k bits, where n is a plurality of positive integers. In one embodiment, the distribution matcher 610 is 2 MValue-amplitude-shift-keyed (ASK) modulation can generate n amplitudes, where M is a positive integer related to the modulation order. The amplitude-bit mapper 615 maps each amplitude to M-1 amplitude bits. Thus, there are n(M-1) amplitude bits provided to the systematic LDPC encoder 605. These amplitude bits are information bits for the LDPC encoder 605. When BG1 is selected, the amount n(M-1) is 22 * It can be equal to Z, but this does not need to be exact so that it can be adapted by padding of information bits. Similarly, if BG2 is selected, the quantity n(M-1) is 10 * It may be equal to Z. The scope of this disclosure is not limited to BG1 and BG2, as any suitable base graph may be used.

[0134]

[0066] In transmitter 600, since there are n amplitudes, the ASK phase adjustment for each amplitude uses n parity bits. In this ASK phase adjustment, the binary zero parity bit may be mapped to a 0-degree (multiplied by 1) phase in mapper 620, and the binary 1 parity bit may be mapped to a 180-degree (multiplied by -1) phase. Mixer 625 mixes each amplitude with its phase to generate n constellation points. The information may be transmitted as one or more symbols.

[0135]

[0067] The systematic LDPC encoder 605 generates parity bits used for phase adjustment of the n amplitude. As described above, the LDPC encoder 605 calculates both auxiliary bits and parity bits, which are then combined with information bits to form a codeword. The transmitter 600 can puncture a vector of length Z containing the auxiliary bits.

[0136]

[0068] The transmitter 600 may be included in a communication device such as either the UE 106 or the base station 108 of the wireless communication system 100 that performs systematic coding of LDPC.

[0137]

[0069] An exemplary receiver 700 including an LDPC decoder 705 is shown in Figure 7. The LDPC decoder 705 is H and

[0138]

number

[0139] The codeword described above can be decoded using the above. The receiver 700 receives a signal containing one or more symbols, as described above with respect to Figure 6. The demodulator 725 and interleaver 720 generate a codeword containing parity bits and information bits. The decoder 705 receives the codeword and, in one embodiment, decodes the codeword according to the parity check matrix to obtain systematic bits

[0140]

number

[0141] It obtains and then re-encodes to obtain s0. In another embodiment, the decoder uses message passing on the parity check matrix to simply

[0142]

number

[0143] Direct decoding is possible. Direct decoding may be an option when there is acceptable signal quality, such as when the SNR is high. Decoder 705 also decodes the information bits.

[0144]

number

[0145] The amplitudes can be calculated therefrom, and those amplitudes can be demultiplexed (in demultiplexer 408) and reshaped in item 410 to generate information bits, which are multiplexed in multiplexer 409. Receiver 700 can be included in a communication device such as either UE 106 or base station 108 of wireless communication system 100 that performs LDPC decoding.

[0146]

[0070] When an appropriate base graph and an appropriate lifting factor Z are selected, transmitter 600 can proceed as summarized in the flowchart of FIG. 8.

[0147]

[0071] FIG. 8 is a diagram of an exemplary method 800 for encoding and transmitting information. The actions of FIG. 8 can be performed by a transmitter such as transmitter 600 of FIG. 6. More specifically, the functions associated with the actions of FIG. 8 can be implemented using hardware, firmware, and / or software. For example, the functions associated with the actions of FIG. 8 can be implemented on a computer-readable medium having computer-executable code, and when the computer-executable code is executed by one or more processors, the one or more processors can perform the actions of FIG. 8.

[0148]

[0072] In action 801, the transmitter selects a matrix Q equal to the sum of a set of ZXZ lifting matrices in the first column of the low-density parity-check matrix Z×Z The matrix Q Z×Z is invertible in this example. Selecting the matrix Q Z×Z can include any suitable technique for reducing the number of processing operations required for inversion of the matrix Q Z×Z In one example of selecting the matrix Q Z×Z the inverse Q -1 (x) has a simpler form, for example, contains fewer weights or a smaller amount of non-zero values, or can be factored into simpler factors such as (1 + x)(1 + x 2 ) and is selected such that it is either of these.

[0149]

[0073] In other embodiments, if action 801 is continued, matrix Q Z×Z Selecting may include satisfying conditions such as those described in equations (14) to (15) and (18).

[0150]

[0074] In action 802, the transmitter lifts the base graph according to the value of Z, and matrix Q Z×Z Select and generate a low-density parity check matrix. As described above, in some embodiments, matrix Q Z×Z This refers to the sum of the lifting matrices of the first column of the parity check matrix. Therefore, each of these lifting matrices can populate the first column of the parity check matrix. The base graph can be selected from BG1 or BG2, or from any other suitable base graph.

[0151]

[0075] In action 803, the transmitter performs a low-density parity check according to a plurality of K b * (K b +Y) * Encoded into a Z-bit codeword, K b This is the amount of information bit sequence in the base graph associated with the low-density parity check matrix. For example, in one embodiment using BG1, K b This is 22, and Y refers to the number of parity elements (4).

[0152]

[0076] In one embodiment, the first Z bit of the codeword is an auxiliary bit, and the subsequent (K) bits of the codeword b +Y-1) * Z bits are K b * Z information bits and (Y-1) * It includes Z additional parity bits, where Y is a positive integer. One embodiment of encoding using this method is described above with respect to equation (8) and Figures 3-4.

[0153]

[0077] In another example, the first K of the codewordb * The Z bit is an information bit, and is the (Y-1) bit following the codeword. * The Z bit is the parity bit, and furthermore, the Z bit between the information bit and the parity bit is the auxiliary bit. Y is a positive integer. Such embodiments are described above with respect to equation (10) and Figure 5.

[0154]

[0078] Once the information bits are encoded, they can be processed as described above with respect to Figure 6. Action 804 may include transmitting one or more symbols that carry the information based on the codeword.

[0155]

[0079] The scope of this disclosure is not limited to the specific actions shown in Figure 8. Rather, one or more actions may be added, omitted, rearranged, or modified. For example, actions 801-804 may be repeated as needed to transmit a desired amount of information. Further actions (not shown) may include receiving the transmitted constellation, performing demodulation and de-entering, and further performing decoding and de-shaping to generate binary bits representing the data.

[0156]

[0080] Hereinafter, this disclosure is summarized in a series of clauses.

[0157] Clause 1. Wireless communication device, According to the low-density parity check matrix, multiple K b * (K b +Y) * It has an encoder configured to encode into a Z-bit codeword, K b This is the amount of information bit sequence in the base graph associated with the low-density parity check matrix, where the first Z bits of the codeword are auxiliary bits, and the subsequent (K) bits of the codeword are auxiliary bits. b +Y-1) * Z bits, K b * Z information bits and (Y-1)* A wireless communication device that includes Z additional parity bits, where Z is the lifting factor of the low-density parity check matrix and Y is a positive integer.

[0158] Clause 2. The encoder punctures the first Z bit of the codeword and the subsequent (K) bits of the codeword. b +Y-1) * A wireless communications device as described in Clause 1, contained within a transmitter configured to transmit Z bits.

[0159] Clause 3. The low-density parity check matrix is ​​a lifted version of the base graph according to Z, and the first Z of the low-density parity check matrix * K b The column is the information bit column, followed by the low-density parity check matrix Z * (K b A wireless communication device as described in Clause 1 or 2, wherein the column is a parity bit column.

[0160] Clause 4. The low-density parity check matrix is ​​a lifted version of the base graph according to Z, and matrix Q Z×Z However, this is equal to the sum of the sets of ZXZ lifting matrices in the first Z columns of the low-density parity check matrix, and furthermore, matrix Q Z×Z However, a wireless communication device as described in any one of clauses 1 to 3, which is reversible.

[0161] Article 5. Matrix Q Z×Z However, polynomial

[0162]

number

[0163] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the order of the first column of the base graph, and Z(a,c)=a * 2 cA wireless communication device as described in Clause 4, wherein a is an integer from the set of integers that do not have a common divisor greater than 1, and c is an integer.

[0164] Clause 6. A wireless communication device as described in Clause 5, where L = Z / a.

[0165] Clause 7. The encoder has a common divisor L such that k1, ..., k d A wireless communications device as described in Clause 6, configured to select the appropriate option.

[0166] Article 8. Matrix Q Z×Z However, polynomial

[0167]

number

[0168] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the encoder is condition Q -1 (x) = Q(x)x k Q Z×Z A wireless communication device as described in Clause 4, configured to select such that k is an integer.

[0169] Article 9. Matrix Q Z×Z However, polynomial

[0170]

number

[0171] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the encoder is condition

[0172]

number

[0173] The matrix Q is satisfied such that Z×Z A wireless communications device as described in Clause 4, configured to select the appropriate option.

[0174] Clause 10. Matrix Q Z×Z However, polynomial

[0175]

number

[0176] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the encoder meets the following conditions: Q -1 (x) = Q(x) * x k , Q -1 (x) = Q(x) * Q(x 2 ) * x k , Q -1 (x) = Q(x) * Q(x 2 ) * Q(x 4 ) * x k , or Q -1 (x) = Q(x) * Q(x 2 ) * Q(x 4 ) * Q(x 8 ) * x k , In order to satisfy at least one of the following, matrix Q Z×Z A wireless communications device as described in Clause 4, configured to select the appropriate option.

[0177] Article 11. Matrix Q Z×Z However, polynomial

[0178]

number

[0179] It is equivalent to k1,...,k d Here, Q represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the encoder is Q -1 To reduce the number of terms in (x), Q -1 (x) is factorized, matrix Q Z×Z A wireless communications device as described in Clause 4, configured to select the appropriate option.

[0180] Clause 12. A wireless communication device is a wireless communication device as defined in any one of Clauses 1 to 11, including user equipment.

[0181] Clause 13. A wireless communication device is a wireless communication device as defined in any one of Clauses 1 to 11, including a base station.

[0182] Clause 14. Wireless communication devices, According to the low-density parity check matrix, multiple K b * (K b +Y) * It has an encoder configured to encode into a Z-bit codeword, K b However, this is the amount of information bit sequence in the base graph associated with the low-density parity check matrix, and is the first K of the codeword. b * The Z bit is an information bit, and the (Y-1) bit that follows the codeword * A wireless communication device in which Z bits are parity bits, the remaining Z bits of the codeword are auxiliary bits, Z is the lifting factor of the low-density parity check matrix, and Y is a positive integer.

[0183] Clause 15. The encoder punctures the auxiliary bits of the codeword, which are the first K bits of the codeword. b *The (Y-1) bit following the codeword, which consists of the Z bit and the parity bit. * A wireless communications device as described in Clause 14, contained within a transmitter configured to transmit Z bits.

[0184] Clause 16. The first column of the base graph is an unpunctured information bit sequence, and the subsequent (K) of the base graph b -1) The column is the information bit string, and the subsequent (Y) column of the base graph is the parity bit string. The auxiliary bit string is located between the information bit string and the parity bit string, or in the rightmost column. Wireless communication devices as described in Clause 14 or 15.

[0185] Article 17. Computerized methods, Matrix Q is equal to the sum of the sets of ZXZ lifting matrices in the punctured columns of the low-density parity check matrix. Z×Z Furthermore, the matrix Q is reversible. Z×Z Choosing and To generate a low-density parity check matrix, the values ​​of Z and matrix Q are used. Z×Z Lifting the base graph accordingly, According to the low-density parity check matrix, K b However, this is the amount of information bit sequence in the base graph, and the set of Z bits of the codeword is the auxiliary bits, and the (K) of the codeword. b +Y-1) * The set of Z bits is K b * Z information bits and (Y-1) * Multiple K, each containing Z parity bits, where Y is a positive integer. b * (K b +Y) * Encoding into a Z-bit codeword, Transmitting one or more symbols that carry information based on a codeword, Computerized methods, including those mentioned above.

[0186] Clause 18. The computerized method described in Clause 17, wherein the auxiliary bits are located in the codeword between the information bits and the parity bits, or in the rightmost column.

[0187] Clause 19. The first Z of the low-density parity check matrix. * K b The column is the information bit column, followed by the low-density parity check matrix Z * (K b The computerized method described in Clause 17 or 18, wherein the +Y) column is the parity bit column.

[0188] Article 20. Matrix Q Z×Z However, polynomial

[0189]

number

[0190] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the degree of the punctured column in the base graph, and Z(a,c)=a * 2 c The computerized method described in Clause 17 or 18, wherein a is an integer from the set of integers that do not have a common divisor greater than 1, and c is an integer.

[0191] The computerized method described in Clause 20, where L = Z / a.

[0192] Article 22. Matrix Q Z×Z The selection of k1, ..., k such that they have a common divisor L d A computerized method as described in Clause 21, including the selection of [the computerized method].

[0193] Article 23. Matrix Q Z×Z However, polynomial

[0194]

number

[0195] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the order of the punctured column in the base graph, and furthermore, matrix Q Z×Z Selecting this option is subject to the following conditions: Q -1 (x) = Q(x) * x k , Q -1 (x) = Q(x) * Q(x 2 ) * x k , Q -1 (x) = Q(x) * Q(x 2 ) * Q(x 4 ) * x k , or Q -1 (x) = Q(x) * Q(x 2 ) * Q(x 4 ) * Q(x 8 ) * x k , This includes satisfying at least one of the following conditions: The computerized method described in Article 17.

[0196] Article 24. Matrix Q Z×Z However, polynomial

[0197]

number

[0198] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, matrix Q Z×Z Selecting Q -1A computerized method as described in Clause 17, which includes performing factorization to reduce the number of terms in (x).

[0199] Article 25. Computerized methods, Matrix Q is equal to the sum of the sets of ZXZ lifting matrices in the first column of the low-density parity check matrix. Z×Z Furthermore, the matrix Q is reversible. Z×Z Choosing and To generate a low-density parity check matrix, the values ​​of Z and matrix Q are used. Z×Z Lifting the base graph accordingly, According to the low-density parity check matrix, K b This is the amount of information bit sequences in the base graph, and the first K of the codeword. b * The Z bit is an information bit, and the (Y-1) bit that follows the codeword * A set of multiple K bits where Z is the parity bit, and the Z bits between the information bit and the parity bit are auxiliary bits, and Y is a positive integer. b * (K b +Y) * Encoding into a Z-bit codeword, Transmitting one or more symbols that carry information based on a codeword, Computerized methods, including those mentioned above.

[0200] Clause 26. Transmitting one or more symbols punctures the auxiliary bits of the codeword and the first K of the codeword, which are information bits. b * The (Y-1) bit following the codeword, which consists of the Z bit and the parity bit. * A computerized method as described in Clause 25, including transporting information that matches Z bits.

[0201] Clause 27. The first Z column of the low-density parity check matrix is ​​an unpunctured information column, and the subsequent Z columns of the low-density parity check matrix are* (K b -1) The column is the information bit column, and the subsequent Z of the low-density parity check matrix * The computerized method according to clause 25 or 26, wherein column (Y) is a parity bit column, and Z auxiliary bit columns are located between the information bit column and the parity bit column.

[0202] Article 28. Matrix Q Z×Z However, polynomial

[0203]

number

[0204] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the order of the first column of the base graph, and Z(a,c)=a * 2 c Therefore, a is an integer from the set of integers that do not have a common divisor greater than 1, c is an integer, L = Z / a, and matrix Q Z×Z The selection of k1, ..., k such that they have a common divisor L d A computerized method as described in any one of clauses 25 to 27, including the selection of a computerized method.

[0205] Article 29. Matrix Q Z×Z However, polynomial

[0206]

number

[0207] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, matrix Q Z×Z Selecting this option is subject to the following conditions: Q -1 (x) = Q(x) * x k , Q -1 (x) = Q(x)* Q(x 2 ) * x k , Q -1 (x) = Q(x) * Q(x 2 ) * Q(x 4 ) * x k , or Q -1 (x) = Q(x) * Q(x 2 ) * Q(x 4 ) * Q(x 8 ) * x k , This includes satisfying at least one of the following conditions: The computerized method described in Article 25.

[0208] Article 30. Matrix Q Z×Z However, polynomial

[0209]

number

[0210] It is equivalent to k1,...,k d Here, represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, matrix Q Z×Z Selecting Q -1 A computerized method as described in Clause 25, which includes performing factorization to reduce the number of terms in (x).

[0211]

[0081] Herein, as will be understood by those skilled in the art, and depending on the specific applications present, many modifications, substitutions, and variations can be made to and from the materials, apparatus, configurations, and methods of use of the materials, apparatus, configurations, and devices of the Disclosure without departing from the spirit and scope of the Disclosure. In light of this, the specific embodiments illustrated and described herein are only a few examples, and the scope of the Disclosure should not be limited to the scope of such specific embodiments, but rather should be exactly the same as the scope of the claims and their functional equivalents appended below.

Claims

1. A wireless communication device, According to a low-density parity-check matrix, a plurality of K ｂ ＊ Z information bits are configured to be encoded into a codeword of (K ｂ +Y) ＊ Z bits, and an encoder is provided. K ｂ is the amount of an information bit string in a base graph associated with the low-density parity-check matrix. The first Z bits of the codeword are auxiliary bits. The subsequent (K ｂ +Y−1) ＊ Z bits of the codeword include the K ｂ ＊ Z information bits and (Y−1) ＊ Z additional parity bits. Z is the lifting factor of the low-density parity-check matrix, and Y is a positive integer. A wireless communication device.

2. The encoder punctures the first Z bit of the codeword and the subsequent (K) bits of the codeword. ｂ +Y-1) ＊ The wireless communication device according to claim 1, which is contained within a transmitter configured to transmit a Z bit.

3. The low-density parity check matrix is ​​a lifted version of the base graph according to Z, and the first Z of the low-density parity check matrix ＊ K ｂ The column is an information bit sequence, and the Z following the low-density parity check matrix ＊ The wireless communication device according to claim 1, wherein column (Y) is a parity bit column.

4. The low-density parity check matrix is ​​a lifted version of the base graph according to Z, and matrix Q Ｚ×Ｚ However, this is equal to the sum of the sets of ZXZ lifting matrices in the first Z column of the low-density parity check matrix, and furthermore, the matrix Q Ｚ×Ｚ However, the wireless communication device according to claim 1 is reversible.

5. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Math 1] It is equivalent to k １ , . . . ,k ｄ Here, represents the cyclic shift value, d is the order of the first column of the base graph, and Z(a, c) = a ＊ 2 ｃ The wireless communication device according to claim 4, wherein a is an integer from the set of integers that do not have a common divisor greater than 1, and c is an integer.

6. The wireless communication device according to claim 5, wherein L = Z / a.

7. The encoder has a common divisor L, １ , . . . ,k ｄ A wireless communication device according to claim 6, configured to select [a certain option].

8. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Math 2] It is equivalent to k １ , . . . ,k ｄ represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the encoder is condition Q －１ (x) = Q(x)x ｋ Q Ｚ×Ｚ The wireless communication device according to claim 4, configured to select such that k is an integer.

9. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Math 3] It is equivalent to k １ , . . . ,k ｄ Here, represents the cyclic shift value, d is the order of the first column of the base graph, and further, the encoder is condition [Math 4] The matrix Q such that the following conditions are met. Ｚ×Ｚ The wireless communication device according to claim 4, configured to select a.

10. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Math 5] It is equivalent to k １ , . . . ,k ｄ represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the encoder meets the following conditions: Q －１ (x)=Q(x) ＊ x ｋ 、 Q －１ (x)=Q(x) ＊ Q(x ２ ) ＊ x ｋ 、 Q －１ (x) = Q(x) ＊ Q(x) ２ ) ＊ Q(x) ４ ) ＊ x ｋ , or Q －１ (x) = Q(x) ＊ Q(x) ２ ) ＊ Q(x) ４ ) ＊ Q(x) ８ ) ＊ x ｋ In order to satisfy at least one of the following, the matrix Q Ｚ×Ｚ It is configured to select The wireless communication device according to claim 4.

11. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Math 6] It is equivalent to k １ , . . . ,k ｄ d represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the encoder is Q －１ To reduce the number of terms in (x), Q －１ The matrix Q is factorized as shown above. Ｚ×Ｚ The wireless communication device according to claim 4, configured to select a.

12. The wireless communication device according to claim 1, wherein the wireless communication device includes user equipment.

13. The wireless communication device according to claim 1, wherein the wireless communication device includes a base station.

14. A wireless communication device, According to the low-density parity check matrix, multiple K ｂ ＊ Z information bits (K ｂ +Y) ＊ It has an encoder configured to encode into a Z-bit codeword, K ｂ However, the amount of information bit sequence in the base graph associated with the low-density parity check matrix, and the first K of the codeword. ｂ ＊ The Z bit is an information bit, and the (Y-1) following the codeword ＊ A wireless communication device in which the Z bit is a parity bit, the remaining Z bits of the codeword are auxiliary bits, Z is the lifting factor of the low-density parity check matrix, and Y is a positive integer.

15. The encoder punctures the auxiliary bits of the codeword, and the first K of the codeword, which is the information bit. ｂ ＊ The Z bit and the parity bit of the codeword, which is the subsequent (Y-1) ＊ The wireless communication device according to claim 14, which is contained within a transmitter configured to transmit Z bits.

16. The first column of the base graph is an unpunctured information bit sequence, and the subsequent (K) of the base graph ｂ -1) The column is an information bit sequence, and the subsequent (Y) column of the base graph is a parity bit sequence. The auxiliary bit sequence is located between the information bit sequence and the parity bit sequence, or in the rightmost column. The wireless communication device according to claim 14.

17. A computerized method, Matrix Q is equal to the sum of the sets of ZXZ lifting matrices in the punctured columns of the low-density parity check matrix. Ｚ×Ｚ Furthermore, the matrix Q is reversible. Ｚ×Ｚ Choosing and To generate the low-density parity check matrix, the value of Z and the matrix Q Ｚ×Ｚ Lifting the base graph accordingly, According to the low-density parity-check matrix, K ｂ is the amount of information bit strings in the base graph, the set of Z bits of the codeword is the parity bits, and the (K ｂ + Y - 1) ＊ set of Z bits of the codeword is K ｂ ＊ Z information bits and (Y - 1) ＊ Z parity bits, where Y is a positive integer, and a plurality of the K ｂ ＊ Z information bits are encoded into the codeword of (K ｂ + Y) ＊ Z bits, and Transmitting one or more symbols that carry information based on the aforementioned codeword, Computerized methods, including those mentioned above.

18. The computerized method according to claim 17, wherein the auxiliary bit is located in the codeword between the information bit and the parity bit, or in the rightmost column.

19. The first Z ＊ K ｂ columns of the low-density parity-check matrix are information bit columns, and the subsequent Z ＊ (K ｂ + Y) columns of the low-density parity-check matrix are parity bit columns, the computerized method according to claim 17.

20. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Number 7] It is equivalent to k １ , . . . ,k ｄ Here, represents the cyclic shift value, d is the order of the punctured column in the base graph, and Z(a, c) = a ＊ 2 ｃ The computerized method according to claim 17, wherein a is an integer from the set of integers that do not have a common divisor greater than 1, and c is an integer.

21. The computerized method according to claim 20, wherein L = Z / a.

22. The aforementioned matrix Q Ｚ×Ｚ Selecting such that the k has a common divisor L １ , . . . ,k ｄ The computerized method according to claim 21, which includes selecting

23. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Number 8] It is equivalent to k １ , . . . ,k ｄ represents the cyclic shift value, d is the order of the punctured column in the base graph, and furthermore, the matrix Q Ｚ×Ｚ Selecting this option is subject to the following conditions: Q －１ (x)=Q(x) ＊ x ｋ 、 Q －１ (x)=Q(x) ＊ Q(x ２ ) ＊ x ｋ 、 Q －１ (x) = Q(x) ＊ Q(x) ２ ) ＊ Q(x) ４ ) ＊ x ｋ , or Q －１ (x)=Q(x) ＊ Q(x ２ ) ＊ Q(x ４ ) ＊ Q(x ８ ) ＊ x ｋ 、 This includes satisfying at least one of the following conditions: The computerized method according to claim 17.

24. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Number 9] It is equivalent to k １ , . . . ,k ｄ represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the matrix Q Ｚ×Ｚ Selecting Q －１ The computerized method according to claim 17, comprising performing factorization to reduce the number of terms in (x).

25. A computerized method, Matrix Q is equal to the sum of the sets of ZXZ lifting matrices in the first column of the low-density parity check matrix. Ｚ×Ｚ Furthermore, the matrix Q is reversible. Ｚ×Ｚ Choosing and To generate the low-density parity check matrix, the value of Z and the matrix Q Ｚ×Ｚ Lifting the base graph accordingly, According to the low-density parity check matrix, K ｂ However, this is the amount of information bit sequence in the base graph, and the first K of the codeword. ｂ ＊ The Z bit is an information bit, and the (Y-1) following the codeword ＊ A plurality of K, where Z is a parity bit, and the Z bit between the information bit and the parity bit is an auxiliary bit, and Y is a positive integer. ｂ ＊ Z information bits (K ｂ +Y) ＊ Encoding the Z-bit codeword, Transmitting one or more symbols that carry information based on the aforementioned codeword, Computerized methods, including those mentioned above.

26. Transmitting one or more of the above symbols punctures the auxiliary bits of the codeword and the first K of the codeword which is the information bit. ｂ ＊ The Z bit and the parity bit of the codeword, which is the subsequent (Y-1) ＊ The computerized method according to claim 25, comprising transporting information that matches the Z bit.

27. The first Z column of the low-density parity check matrix is ​​an unpunctured information column, and the subsequent Z column of the low-density parity check matrix is ＊ (K ｂ -1) The column is an information bit sequence, and the Z of the low-density parity check matrix is ​​further subsequent ＊ The computerized method according to claim 25, wherein column (Y) is a parity bit column, and Z auxiliary bit columns are located between the information bit column and the parity bit column.

28. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Number 10] It is equivalent to k １ , . . . ,k ｄ Here, represents the cyclic shift value, d is the order of the first column of the base graph, and Z(a, c) = a ＊ 2 ｃ The matrix Q is such that a is an integer from the set of integers that do not have a common divisor greater than 1, c is an integer, L = Z / a, and the matrix Q is such that Ｚ×Ｚ Selecting such that the k has a common divisor L １ , . . . ,k ｄ A computerized method according to claim 25, comprising selecting

29. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Math 11] It is equivalent to k １ , . . . ,k ｄ represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the matrix Q Ｚ×Ｚ Selecting this option is subject to the following conditions: Q －１ (x)=Q(x) ＊ x ｋ 、 Q －１ (x)=Q(x) ＊ Q(x ２ ) ＊ x ｋ 、 Q －１ (x) = Q(x) ＊ Q(x) ２ ) ＊ Q(x) ４ ) ＊ x ｋ , or Q －１ (x)=Q(x) ＊ Q(x ２ ) ＊ Q(x ４ ) ＊ Q(x ８ ) ＊ x ｋ 、 This includes satisfying at least one of the following conditions: The computerized method according to claim 25.

30. The aforementioned matrix Q Ｚ×Ｚ However, polynomial [Math 12] It is equivalent to k １ , . . . ,k ｄ represents the cyclic shift value, d is the order of the first column of the base graph, and furthermore, the matrix Q Ｚ×Ｚ Selecting Q －１ The computerized method according to claim 25, comprising performing factorization to reduce the number of terms in (x).

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