Polarization adjustment based finite field multiple access system, power allocation method and decoding method

Abstract

The application discloses a polar adjustment-based finite field multiple access system, a power distribution method and a decoding method, and belongs to the technical field of 6G communication.The application is used for solving the problem of low-rate channel coding in a communication scene and the problem of obtaining coding gain through multi-user channel coding in a multi-user transmission scene in an uplink.The application is used for distributing power to a diagonal form FFMA system to form a corresponding finite field multiple access system.In the process of power distribution, the power is distributed to different symbols for modulating and sending useful information parts by using elements in a polar adjustment vector or polar coefficients.For the case of distributing power by using the polar coefficients, a binary minimum distance decoding algorithm is used for decoding, information bit parts are preliminarily screened in an information bit detection stage, and each information part screened in the information bit detection stage is combined in a joint decoding stage, so that the code word is reconstructed, and the parity check part is decoded after the combination.

Description

Technical Field

[0001] This invention belongs to the field of 6G communication technology and relates to transmitter design and branch minimum distance decoding method for finite field multiple access. Background Technology

[0002] In modern wireless communication systems, channel coding is a crucial component for ensuring data transmission reliability. With the increasing number of wireless network users and the growing demand for higher data rates, effectively managing multiple users sharing the same spectrum resources has become a key research focus. Particularly for uplink communication, since users in different locations need to send information to the base station through the same channel, designing efficient coding schemes that can simultaneously support multiple users is of paramount importance. Furthermore, when users communicate with short data packets, data transmission relies on a low-rate codeword scheme, and the problem of low-rate coding must be solved to guarantee reliability. The following outlines the specific challenges faced by low-rate channel coding and multiuser channel coding in multiple access scenarios.

[0003] Firstly, low-rate code design: In coding theory, designing low-rate channel codewords is an extremely challenging problem. In some communication scenarios involving short data packet transmission, each user transmits a short data packet, for example... bits / user, using The total number of degrees of freedom (DoF) represented is usually very large, for example... This means that channel coding must be designed as The rate, where the subscript "SU" indicates a single user, is such that there is currently no established method for designing such low-rate channel codewords, making this an open problem in the field.

[0004] Secondly, multi-user channel coding: Currently, there are few schemes focusing on uplink multi-user channel coding because different users are located in different locations, and their information sequences are independent. This leads to a lack of cooperation among users, preventing them from obtaining coding gains. In such cases, high reliability is typically required for multi-user transmission. Although there has been work on multiple access codes, this research mainly focuses on multi-user detection rather than achieving coding gains through multi-user channel coding. Multi-user channel coding is a very attractive problem because it has the potential to simultaneously provide coding gains and user separation. Clearly, the design of multi-user channel coding remains a challenging research problem.

[0005] Low-rate coding and multi-user channel coding play crucial roles in modern wireless communication systems. Low-rate coding improves the reliability of short data packet transmission by adding redundancy, ensuring accurate data reception in noisy and interference environments, which is particularly important for applications such as IoT devices and emergency message transmission. Multi-user channel coding significantly improves system performance and reliability when multiple users share the same channel by providing additional coding gain and effective user signal separation, supporting large-scale connections and reducing mutual interference. These two technologies not only solve key challenges in current communications but also lay the foundation for the development of future wireless communication technologies, driving improvements in spectral efficiency and the realization of emerging applications. Summary of the Invention

[0006] This invention aims to solve the problem of low-rate channel coding in communication scenarios, and to address the issue of obtaining coding gain in multi-user channel coding under multi-user transmission scenarios in the uplink.

[0007] A power allocation method for finite-domain multiple access systems based on polarization regulation, which performs power allocation based on a DF-FFMA system;

[0008] DF-FFMA system refers to a diagonal FFMA system, i.e., codeword matrix. Includes an information array used to carry user information. and parity array And the vector corresponding to the user bit sequence Located in the information array The FFMA system on the main diagonal; the FFMA system is a finite-domain multiple access system.

[0009] For codeword matrix diagonal code words , No. Information sequence of a user , of which Each user of The bit sequence is located in The Item 1, all other items are 0;

[0010] DF-FFMA modulates only the part of the data that is useful for transmission. , express The useful information part, namely , The subscript "S" indicates shortening;

[0011] DF-FFMA performs power distribution in either of the following two ways:

[0012] Method 1: The parity check block length is , The codeword length is Power is distributed The different symbols, the total transmit power of each user is The polarization adjustment vector is ,in, The subscript "pav" indicates the polarization adjustment vector. These are elements in the polarization adjustment vector. , ; The power of each symbol is determined by the following formula:

[0013]

[0014] in, This represents the average transmit power of each symbol;

[0015] Method 2: The parity check block length is , The codeword length is Power is distributed The different symbols, the total transmit power of each user is ;against The information part and the parity part, the power allocated to the information part of each symbol is The power allocated to the parity check portion of each symbol is , The polarization coefficient is given; the power distribution condition is...

[0016]

[0017] in, This is the polarization scaling factor; the subscript "pas" indicates polarization adjustment.

[0018] According to the conditions of power allocation and Determine the power allocation method and implement power allocation.

[0019] Furthermore, in Method 2, the maximum power allocated to the information portion of each symbol is... .

[0020] A finite-domain multiple access system based on polarization regulation, wherein the system is an irregular PA-DF-FFMA, that is, a polarization-regulated DF-FFMA capable of irregular power distribution;

[0021] DF-FFMA system refers to a diagonal FFMA system, i.e., codeword matrix. Includes an information array used to carry user information. and parity array And the vector corresponding to the user bit sequence Located in the information array The FFMA system on the main diagonal; the FFMA system is a finite-domain multiple access system.

[0022] For codeword matrix diagonal code words , No. Information sequence of a user , of which Each user of The bit sequence is located in The Item 1, all other items are 0;

[0023] DF-FFMA modulates only the part of the data that is useful for transmission. , express The useful information part, namely , The subscript "S" indicates shortening;

[0024] The polarization-regulated DF-FFMA, capable of achieving irregular power distribution, performs power distribution in the following manner:

[0025] The parity check block length is , The codeword length is Power is distributed The different symbols, the total transmit power of each user is The polarization adjustment vector is ,in, The subscript "pav" indicates the polarization adjustment vector. These are elements in the polarization adjustment vector. , ; The power of each symbol is determined by the following formula:

[0026]

[0027] in, This represents the average transmit power of each symbol.

[0028] A finite-domain multiple access system based on polarization regulation, wherein the system is a regular PA-DF-FFMA, that is, a polarization-regulated DF-FFMA capable of regular power allocation;

[0029] DF-FFMA system refers to a diagonal FFMA system, i.e., codeword matrix. Includes an information array used to carry user information. and parity array And the vector corresponding to the user bit sequence Located in the information array The FFMA system on the main diagonal; the FFMA system is a finite-domain multiple access system.

[0030] For codeword matrix diagonal code words , No. Information sequence of a user , of which Each user of The bit sequence is located in The Item 1, all other items are 0;

[0031] DF-FFMA modulates only the part of the data that is useful for transmission. , express The useful information part, namely , The subscript "S" indicates shortening;

[0032] The polarization-regulated DF-FFMA, which enables regular power distribution, performs power distribution in the following manner:

[0033] The parity check block length is , The codeword length is Power is distributed The different symbols, the total transmit power of each user is ;against The information part and the parity part, the power allocated to the information part of each symbol is The power allocated to the parity check portion of each symbol is , The polarization coefficient is given; the power distribution condition is...

[0034]

[0035] in, This is the polarization scaling factor; the subscript "pas" indicates polarization adjustment.

[0036] According to the conditions of power allocation and Determine the power allocation method and implement power allocation.

[0037] Furthermore, the maximum power allocated to the information portion of each symbol is .

[0038] A decoding method for a finite-field multiple access system based on polarization adjustment, the method comprising the following steps:

[0039] Received signal sequence It is divided into an information part and a parity check part, namely ,in The information section includes The data block, for the first data block There are data blocks, The block length of each block is ;

[0040] (1) Information bit detection stage:

[0041] First, the information is divided into blocks for detection, based on decision thresholds. right Preliminary judgment:

[0042] Regarding the first Information sub-blocks The judgment process is as follows:

[0043]

[0044] in, Indicates the first estimated value based on the received signal. The k-th bit in a sub-block of information; It is the log-likelihood value calculated based on the received signal;

[0045] After this judgment process, the number of unknown information bits within the sub-block... , and They represent the estimated received signals, respectively. and Distance to the received signal:

[0046]

[0047]

[0048] All estimated signals of the sub-block Combined, they correspond to the estimated sequence of the user. ,get Distance from the received signal ;right distance Sort in ascending order and select the top few. The distance values ​​constitute the distance set of this information segment, denoted as . ,in , , , ;

[0049] For each distance value Through decimal to binary conversion function The distance value corresponding to Transform into an estimated binary vector ; Each element in the binary vector set corresponds to a unique vector; for each information sub-block, a binary vector set is obtained. ,Right now ;

[0050] (2) Joint decoding stage:

[0051] After the information bit detection stage, we obtain A binary set, namely The sub-blocks and their corresponding binary sets are joined sequentially. The joining process begins with... and Take one element from each pair and combine them, concatenate the sequences corresponding to the two elements, and then sum the corresponding distance values. and When combined, it can produce A combination of elements, assuming that after each combination, the elements are filtered according to their distance values. One as a candidate set for the next coalition, After combining the sub-blocks, we get A set of candidate information sequences, denoted as , for The candidate estimation information sequence obtained by jointly connecting the sub-blocks has a length of [number]. Each candidate information sequence in the set corresponds to a calculated distance value, therefore the corresponding distance sorting list is: ;

[0052] Regarding the first One candidate estimation information sequence It is made of A length of Composed of binary sequences, represented as , Using channel coding System form of generator matrix The transmission codeword is reconstructed for each sub-block according to the DF-FFMA encoding method, and the parity block obtained again is... The parity check block is transformed from the finite field to the complex field by the function. Modulation to obtain signal ,get Modulated signal with parity bits: Then, the modulated signal is summed to obtain ;

[0053] Calculate the parity check part and Distance:

[0054]

[0055] in, Alternative information sequence The corresponding total distance is sorted in ascending order Sort, corresponding to The binary sequence of minimum distances is given by the following formula:

[0056]

[0057] Received That is, the multi-user information sequence obtained by decoding.

[0058] Furthermore, the log-likelihood value calculated based on the received signal. as follows:

[0059]

[0060] in, It is the estimated noise variance. and It is the posterior probability calculated based on the received signal.

[0061] Furthermore, the estimated binary vector .

[0062] Furthermore, the aforementioned The corresponding parity check part and distance .

[0063] Furthermore, the aforementioned Distance from the received signal as follows:

[0064]

[0065] in, express The decimal number, that is , The subscript "B2D" indicates the conversion from binary to decimal.

[0066] The present invention has the following beneficial effects:

[0067] This invention provides a polarization-adjusted finite-field multiple access scheme designed specifically for multi-user transmission, along with a corresponding bifurcated minimum distance (BMD) decoding method that approximates the maximum a posteriori probability. Simultaneously, this scheme overcomes the difficulties of low-rate channel coding and solves the problem of obtaining coding gain in multi-user channel coding in the uplink. Attached Figure Description

[0068] Figure 1 This is a block diagram of the FFMA uplink system architecture in GMAC.

[0069] Figure 2 This is a schematic diagram of the BMD algorithm.

[0070] Figure 3 The BER performance of the low-rate channel code constructed based on PA-DF-FFMA is given.

[0071] Figure 4 The BER performance of the low-rate channel code constructed based on PA-DF-FFMA is given.

[0072] Figure 5 The BER performance of PA-DF-FFMA and IDMA systems in GMAC.

[0073] Figure 6 The BER performance of PA-DF-FFMA and IDMA systems in GMAC. Detailed Implementation

[0074] This invention is widely applicable to various application areas such as the Internet of Things (IoT), ultra-large-scale machine-type communications (uMTC), enhanced mobile broadband (eMBB), ultra-reliable low-latency communications (URLLC), and vehicle-to-everything (V2X). By optimizing the multiple access mechanism and decoding method, this invention can significantly improve the system's access efficiency and data transmission reliability, meeting the diverse and demanding communication application requirements of the future.

[0075] This invention provides a corresponding polarization-modulated finite-field multiple access (DF-FFMA) scheme based on the diagonal form finite-field multiple access (DF-FFMA) scheme. This improves power utilization efficiency, achieves better bit error rate (BER) performance in low-speed channel coding, and can obtain coding gain in multi-user transmission scenarios.

[0076] The PA-DF-FFMA scheme utilizes the entire channel's resources through polarization, fully leveraging the channel's degrees of freedom (DoF). In multi-user scenarios, this scheme can coordinate power allocation and channel coding in multi-user transmission, ensuring efficient use of channel resources. However, in single-user scenarios, it essentially becomes a low-rate channel codeword. When using LDPC coding as the multi-user transmission codeword, polarization can convert LDPC codes designed for high data rates into LDPC codes suitable for lower data rates. Experimental comparisons show that this scheme maintains good BER performance even at low rates, representing a significant breakthrough in addressing the challenges of low-rate coding.

[0077] Furthermore, this scheme allows the receiver to perform channel decoding before multi-user separation, enabling the system to simultaneously obtain coding gain from multiple concurrent user transmissions. By comparing the PA-DF-FFMA scheme with the classic IDMA scheme, it is found that the PA-DF-FFMA scheme achieves coding gain while maintaining good reliability even with a large number of users. Specific implementation method one:

[0079] This embodiment is a finite-domain multiple access system based on polarization regulation, and its power allocation method.

[0080] For finite-domain multiple access schemes for uplink multi-user transmission, when LDPC coding is used as the transmitting codeword, the performance of MSA as the iterative decoding algorithm at the receiving end cannot be reflected. This is because the decoding performance of MSA is difficult to reach the optimal level at low data rates, and the potential advantages of the system cannot be fully reflected.

[0081] This invention introduces a polarization-adjusted transmission method based on the existing FFMA scheme, which can optimize the allocation of channel resources during the modulation and transmission stage, and maximize the performance of the PA-DF-FFMA system by using a binary minimum distance decoding algorithm at the receiving end.

[0082] The concept of EP code encoding:

[0083] The EP code is based on the binary-to-finite-field GF(q) transform function (denoted as ). This is achieved through [the following]. Let the [number] [become] [the] [number]. The sequence of messages sent by each user is as follows Where K is a positive integer representing the number of messages sent by the user. The EP encoder will process each bit sequence Transformation function from binary to finite field GF(q) Uniquely mapped to a sequence of elements ,Right now Similarly, EP codes can be decoded using a finite field to binary conversion function. To achieve this, that is .

[0084] Assuming each user is assigned an EP, for example, the first... One EP, i.e. Assigned to the One user, , and The subscript "j" indicates the first... Each EP, with subscripts "0" and "1" representing the input information bits. and At this time, you can The Each component Represented as:

[0085]

[0086] in, Defined as a switch function, if the input information is Then the transformed element components are Conversely, it is .set up The first user input bit information A bit block consisting of 10 components is , Then its corresponding EP codeword for The user The output element block component corresponding to each bit is represented as follows: .

[0087] The concept of AIEP codes over finite fields:

[0088] For binary source transmission systems, the transmitted information is only... , Two situations, using To represent a pair of elements, where and , and The subscript j in the text indicates that the element pair is the j-th element pair, where 0 and 1 represent the information being sent. still The following will use the same characters. and These represent EP and EP code, respectively.

[0089] of A non-zero element is denoted as Divide it into Each of the three mutually exclusive EPs consists of... A non-zero element and its additive inverse Composition, pairing such elements This is called an additive inverse pair (AIEP). The set that is divided into AIEP is denoted as This partition is called the AIEP partition. When hour, There is only one EP, that is The subscript "B" indicates a binary or The situation.

[0090] set up for In AIEP, of which It is not greater than Positive integers, i.e. The superscript "s" indicates a single symbol. This makes AIEP a ,Right now ,definition Reverse order AIEP (R-AIEP) for .

[0091] this AIEP constitute One of the middle The partitioning of element subsets is Sub-partitioning, let . of R-AIEP constitute The inversion set, denoted as or .

[0092] set up For definition in one above tuple, where the first Each component From ,and ,Should Tuples are Cartesian product of AIEPs One of the elements, each Seen as one of the User AIEP typing, due to This constitutes the definition in of User AIEP code words, and has Each code character.

[0093] Will On tuple Sum all elements and then modulo Calculation, expressed as This calculation method is called Finite-fieldsum pattern (FFSP). Assume... and yes any two tuple, if Then the FFSP result With the corresponding One-to-one mapping of tuples. Given If it is possible to uniquely restored A tuple is called a It possesses the structural properties of unique sum-pattern mapping (USPM). If we consider a structure with USPM structural properties... In As a User typing, then... Called in On User-uniquely decodable AIEP code (UD-AIEP).

[0094] The concept of orthogonal uniquely decodable AIEP codes:

[0095] Assumption yes The fundamental element, then Able to represent All elements on, Each element on All can be represented as Linear combination:

[0096] ,

[0097] in, And coefficient yes The elements above can be seen from the above formula. It can be by The upper length is vector Unique representation.

[0098] Finite field Able to form On 3D vector space , Each vector in is one above tuple, for It can be known that It is The longest tuple, it is only in the first... The value of one position is 1, and the rest are 0, therefore this can be called... Long tuples It constitutes Orthogonal basis.

[0099] Given two elements and Their sum can be expressed as:

[0100] ,

[0101] The tuple representation of the above results is as follows ,for ,if yes An additive inverse pair or a pair of zero elements. ,but , ,Right now and They are the inverses of each other's addition. It constitutes AIEP.

[0102] if yes The AIEP on the top, then yes AIEP on the top, using express On A set of AIEPs, in which , ,for :

[0103] ,

[0104] yes The structure with USPM features A set of AIEPs, where the subscript "o" indicates orthogonality, therefore, the Cartesian product... of AIEP in A group was formed in the middle User UD-AIEP codeword, this codeword is in The definition above includes Each codeword is composed of... In It consists of non-zero elements. When At that time, we can form indivual The user's UD-AIEP code is as follows: These codewords are mutually exclusive, that is... , , .

[0105] Each codeword in the code is composed of A definition in On Composed of tuples, and each There is only one source in the corresponding position of the tuple. Non-zero elements, set exist The above constitutes a The user's orthogonal UD-AIEP code is obtained by concatenating this... indivual User UD-AIEP code Formed.

[0106] Now, consider orthogonal UD-AIEP codes. A special case for commonly used finite fields It has only one base EP, defined as And not AIEP, therefore for The orthogonal UD-EP code, let For definition in Orthogonal UD-EP codes on.

[0107] This implementation method is based on extended domain The orthogonal unique decodable code constructed on top This paper uses an example to introduce the diagonal form and corresponding polarization form of the uplink FFMA system in a Gaussian multiple-access channel (GMAC), and provides a corresponding multi-user decoding algorithm. This implementation method is used in... In the case of orthogonal UD-AIEP codes, it can also be directly extended. It can be a prime number or a power of a prime number. However, in the case of a multi-base system, the polarization adjustment method becomes more complicated, and the BMD decoding algorithm also becomes more complicated. Of course, this implementation method is also applicable to fading channels.

[0108] FFMA systems suitable for uplink multi-user communication scenarios:

[0109] The uplink FFMA system in GMAC is based on an extended domain of GF(2). orthogonal UD-EP codes constructed above in , , It is the unique EP code on GF(2). Parameter The number of time slots representing a finite domain can be viewed as virtual resource blocks (VRBs), thus determining the number of users the system can accommodate. It can be equal to or less than The FFMA uplink system architecture block diagram is as follows: Figure 1 As shown, where and This represents the transformation from binary to the finite field GF(q) and from the finite field GF(q) to binary; and It is the transformation from finite field GF(q) to finite field GF(Q) and the transformation from finite field GF(Q) to finite field GF(q); and This represents the transformation from a finite field to the complex field and the transformation from the complex field to a finite field. The transmitting end first performs EP coding and channel coding on the information sequence sent by the user, then modulates the coded sequence, and finally sends the modulated sequence to the GMAC channel.

[0110] 1. Diagonal FFMA system:

[0111] No. The bit sequence output by each user is represented as follows: The transmitter will send the bit sequence Uniquely mapped to the sequence of elements This is due to the EP code. It was decided. Regarding... , The Each component Due to its corresponding value on GF(2) Represented by tuples, that is ,in .So of The tuple representation is

[0112]

[0113] The Bit representation is

[0114]

[0115] It has only one element. Long sparse vector.

[0116] Next, the sequence obtained after EP encoding It will pass through a linear block codes, It is the length of the block code. The information bit length is used to perform global channel coding to obtain the transmitted codeword. ,Right now

[0117]

[0118] The generator matrix for global channel coding has dimensions of . ,in , The entire coding can be viewed as a two-level concatenated coding system, where EP coding serves as the inner coding and channel coding... As an external code, this code is called coding.

[0119] Each codeword formed by encoding The signal mapped onto the complex domain after BPSK modulation ,Right now ,for , The element Represented as:

[0120]

[0121] in, This kind of from Mapped to The method is called the transformation from the finite field to the complex field, denoted as: ,after Send to GMAC.

[0122] Received signal at the receiving end for The superposition of the signal and noise signals of each user is expressed as:

[0123]

[0124] in, It is a distribution of AWGN vector, The sum in the sequence is called the Complex Domain Sum Pattern (CFSP) signal sequence. ;

[0125]

[0126] Generally, the generating matrix can be in systematic form. Non-system form Two forms All of these can be used in the FFMA system; however, the system form... It can provide greater flexibility when designing FFMA systems.

[0127] Suppose that the dimension defined on GF(2) is The generating matrix is ​​of systematic form. It is the maximum number of users that can be accommodated. It is the number of bits of user information. This is the codeword length; the encoded codeword at this point. It has the following forms:

[0128]

[0129] in, It is a sparse vector. This refers to the added redundancy in the check block; the subscript "red" indicates redundancy. (System configuration) Each user's code can be used as one codeword matrix To indicate, , Codeword matrix It can be divided into two parts: the information part. Checksum section As shown in the following formula:

[0130]

[0131] Information section It is an array, i.e. ,in, It is The matrix, when hour, users one information bit lie in On the main diagonal, when hour, Information Still located On the main diagonal, and All other rows or columns are 0. Parity check section It is The matrix consists of all parity checks formed based on the generating matrix.

[0132] In multi-user transmission scenarios, It could be very large, in this case, It is a sparse matrix, for of Information array , Each item It is matrix, Information bits lie in On the main diagonal, all off-diagonal elements are 0, among which , .Will After rearranging the columns, we can obtain a... array ,in lie in On the main diagonal, all other entries are 0, as shown below:

[0133]

[0134] in, yes The vector, with the subscript "D" indicating diagonal, is let... Indicates the first A sequence of information from users, with a length of . , , of which individual users of The bit sequence is located in The One item, and all other items are 0.

[0135] Then, through the generation matrix in systematic form right Encode to obtain The code ,in yes The parity check block is a The tuples, together with the codewords of each user, form a diagonal codeword matrix. :

[0136]

[0137] Depend on Information array and Parity array composition, .

[0138] From the code It can be observed that the useful vector is... and Only located in The Items and parity check items At this point, all other terms are 0. Therefore, for diagonal codewords... It is possible to modulate and transmit only the useful information portion. The subscript "S" indicates shortening. This is a shortened block length structure, which saves transmission power, a desirable feature for short data packet transmission. The FFMA system is called the diagonal FFMA system (DF-FFMA).

[0139] Please note that permutation and rearrangement operations do not affect the properties of the FFMA system. For the DF-FFMA system, Each user's bit sequence is transmitted in orthogonal mode, and appended The parity check sequence significantly saves transmission power.

[0140] 2. Polarization-tuned DF-FFMA system:

[0141] Users in DF-FFMA systems benefit from shorter block lengths and reduced power consumption. This represents the average transmit power of each symbol, for Channel code The code length is The information bit length is The length of the check bit is The total transmit power for each user is The DF-FFMA system, considering the need to save transmission power, only utilizes... If the power is insufficient to fully utilize the performance of the entire system, then the remaining power needs to be considered. Power utilization.

[0142] PA-DF-FFMA, based on DF-FFMA, redistributes unused power. By optimizing power allocation, it adjusts channel capacity according to the allocated power, thus forming a polarization pattern. Note that when using LDPC codes as channel codes, and when there is only one user, i.e. PA-DF-FFMA actually becomes a polarization-modulated LDPC (PA-LDPC) code. PA-DF-FFMA has two polarization modulation modes: regular and irregular.

[0143] The regular and irregular PA-DF-FFMA power allocation schemes are shown below:

[0144] (1) Irregular PA-DF-FFMA:

[0145] Further analysis of the shortened codewords Since the parity check block length is ,therefore The codeword length is Or, equivalently, the number of symbols is In the irregular PA-DF-FFMA scheme, different power is allocated... Different notations define the polarization-adjusted vector (PAV) as follows: ,in The subscript "pav" indicates the polarization adjustment vector. The power of each symbol is given by the following formula:

[0146]

[0147] in, This ensures that the total transmission power of the PA-DF-FFMA remains at [value missing]. .

[0148] Clearly, irregular PA-DF-FFMA offers significant flexibility because the power of each bit can be customized; however, this flexibility introduces design complexity due to the large number of parameters involved. The following section primarily discusses the regular PA-DF-FFMA system, which is easier to implement compared to the irregular version.

[0149] (2) PA-DF-FFMA of the rule:

[0150] Examining the structure of DF-FFMA reveals two distinct parts: an information section and a parity section (or block). Assume the power allocated to the information section for each symbol is... The power allocated to the parity check portion of each symbol is Then, the conditions for power allocation (or polarization regulation) are:

[0151]

[0152] in, Defined as the polarization scaling factor, the subscript "pas" indicates polarization adjustment. Conditions ensure that the total transmission power remains constant; The condition specifies that the information section receives more power than the parity section. Ideally, the goal is to maximize the reliability of the information section by allocating as much power as possible to it. Additionally, considering the unused power... The maximum power that can be allocated to the information portion of each symbol is This is equivalent to repeating the information portion of each symbol. Therefore, the power allocation method of PA-DF-FFMA can be determined by the above power allocation conditions. Specific Implementation Method Two:

[0154] This embodiment presents a decoding method for a finite-field multiple access system (power allocation) based on polarization adjustment. This embodiment uses a binary minimum distance decoding algorithm for decoding.

[0155] As the power of the information portion is gradually increased, its reliability also gradually increases, resulting in a high level of reliability. Based on this characteristic, this invention proposes a bifurcated minimum distance (BMD) decoding algorithm for PA-DF-FFMA. This algorithm consists of two distinct stages: the detection of information bits and the joint decoding of information bits and parity bits.

[0156] (1) Information bit detection stage: This stage focuses on the initial screening of information bits. This process identifies a narrow detection range, thereby reducing the complexity of subsequent joint decoding;

[0157] (2) Joint Decoding Stage: This stage focuses on combining the information parts obtained from the information bit detection stage, reconstructing the codeword, and then decoding it by combining the parity check part. The purpose of this stage is to combine the information bit and parity bit parts to find the optimal solution that is closest to the multi-user information sequence;

[0158] The BMD algorithm proposed in this invention aims to progressively improve efficiency and accuracy, and it approximates maximum a posteriori (MAP) detection. The process of the BMD algorithm is as follows: Figure 2 As shown, the processing procedure is as follows:

[0159] Considering the DF-FFMA structure, the received signal sequence It can be divided into an information part and a parity check part, that is... , The information section includes The data block, for the first data block There are data blocks, The length of each block is .

[0160] In the first stage of the BMD algorithm, the information bits are detected in blocks. The input signal is the information part, and since it is in diagonal form, the... A received data block can be represented as

[0161]

[0162] in, It is a distribution of The AWGN vector. Clearly, the polarization adjustment process enhances the information bits. and The Euclidean distance is used to improve reliability.

[0163] To reduce detection complexity, a decision threshold is given. right A preliminary judgment was made, based on the first... Information sub-blocks The first stage of the detection process is illustrated using an example. Since the information bits undergoing polarization adjustment improve reliability, this decision process does not significantly affect the final decoding result. The decision process is as follows:

[0164] ,

[0165] ,

[0166] in, Indicates the first estimated value based on the received signal. The first information sub-block (the first The k-th bit in the sequence of information sent by each user; It is the estimated noise variance. It is the log-likelihood ratio (LLR) calculated based on the received signal. and It is the posterior probability calculated based on the received signal;

[0167] Following this decision-making process, the number of unknown information bits within this sub-block... , and They represent the estimated received signals, respectively. and The distance to the received signal can be calculated using the following formula:

[0168]

[0169]

[0170] For DF-FFMA, all estimated signals for this sub-block Combined, they correspond to the estimated sequence of the user. , From collection After the judgment process, the elements of the set are determined by... Reduce to This improves detection efficiency, therefore... The distance to the received signal is calculated as follows:

[0171]

[0172] in, express The decimal number, that is , The subscript "B2D" indicates the conversion from binary to decimal.

[0173] right distance Sort in ascending order and select the top few. The distance values ​​constitute the distance set of this information segment, denoted as . ,in , , , .

[0174] For each distance value By transforming the function The distance value corresponding to Transform into an estimated binary vector This yields the corresponding possible information sequence, where It is a decimal to binary conversion function, that is...

[0175]

[0176] Each element in the set corresponds to a unique vector. Therefore, a binary vector set can be obtained for each information sub-block. ,Right now Then, the set of each information sub-block and They are used as inputs to the second stage of the BMD algorithm, which helps in the subsequent decoding process.

[0177] In the second stage of the BMD algorithm, multiple information sub-blocks need to be combined and the codeword reconstructed before decoding using the parity check component. To illustrate this, we need to consider the set of each information sub-block. As mentioned above, Divided into Each sub-block, obtained after the first stage. A binary set, namely First, the sub-block sets are joined sequentially. This joining process includes concatenating candidate sequences and joining distance values. For example, the first sub-block... and the second sub-block When performing a union, assume that the two sub-blocks each have and Each element carries two pieces of information: one is the possible estimated sequence corresponding to that element, and the other is the distance between the modulated estimated sequence and the received signal; sub-block and When combined, it can produce The process involves combining elements and performing two tasks: concatenating the corresponding sequences of elements and superimposing the distance values. Assume that after each combination, the elements are filtered according to their distance values ​​beforehand. One as a candidate set for the next coalition, After combining the sub-blocks, we get A set of candidate information sequences, denoted as , for The candidate estimation information sequence obtained by jointly connecting the sub-blocks has a length of [number]. Each candidate information sequence in the set corresponds to a calculated distance value, therefore the corresponding distance sorting list is: .

[0178] With the first One candidate estimation information sequence For example, it consists of A length of Composed of binary sequences, represented as , Using channel coding System form of generator matrix The codeword is reconstructed for each sub-block according to the DF-FFMA encoding method. The resulting parity block is then... The parity check block is transformed from the finite field to the complex field by the function. Modulation to obtain signal Therefore, it is possible to obtain Modulated signal with parity bits: Then sum these modulated signals:

[0179]

[0180] This represents the sum of the parity bits in the reconstructed transmitted signal. It is used to calculate the distance between the parity bits, given the input parity part. It and The distance is:

[0181]

[0182] in, Alternative information sequence The corresponding total distance is sorted in ascending order Sort, corresponding to The binary sequence of minimum distances is given by the following formula:

[0183]

[0184] therefore, It is the sequence of multi-user information obtained through decoding.

[0185] The error performance and complexity of the BMD algorithm proposed in this invention are mainly affected by the threshold. and cut-off length and The impact, increase , and A value of usually improves error performance, but also increases complexity. For , and Choosing an appropriate value to balance error performance and complexity is crucial; the BMD algorithm described above is based on user information. It can be used directly when it is small, but for larger ones... The BMD algorithm can be used directly by simply performing block processing; similarly, it is also applicable to non-binary cases, but at the cost of high complexity.

[0186] Example: PA-DF-FFMA Uplink System

[0187] Only channel coding with a rate greater than or equal to 0.5 is considered. This is because the BMD algorithm heavily relies on the reliability of the information portion. Therefore, the analysis is restricted to satisfying... Channel coding. The following uses... and Taking two QC-LDPC codes with different code rates as examples of channel coding in a PA-DF-FFMA system, this paper analyzes the BER performance of low-rate channel codes based on PA-DF-FFMA and compares the performance of IDMA and FFMA systems.

[0188] (1) BER performance of low-rate channel codes based on PA-DF-FFMA

[0189] At that time, the BER performance of the PA-DF-FFMA system is mainly determined by Channel code Decision. Consider two cases: In the first case, the channel code... It is binary. LDPC encoding The rate is 0.5; in the second case, the channel code... It is binary. LDPC encoding The rate is 0.84.

[0190] In both of the above cases, the PA-DF-FFMA system proposed in this invention is considered a low-rate LDPC code. In this case, due to the small number of information bits (e.g., ) and larger block lengths (e.g., ), The PA-DF-FFMA system has essentially become a low-rate channel code (e.g., The BER performance of the PA-DF-FFMA system in the above two cases is shown in [reference needed]. Figures 3-4 .

[0191] Figure 3 BER performance of low-rate channel codes constructed based on PA-DF-FFMA ( (Rc=0.5), set and Compare bits / user. For example... Figure 3 As shown, with the number of information bits The increase, The BER performance of the PA-DF-FFMA system is arrive The performance will improve, and then arrive It begins to degenerate at that time, that is, at arrive Local extrema occur within a certain range. However, the exact value at which this extremum is reached is unknown. The value is unknown because all results are based on computer simulations; however, it is well known that typical traffic for a single user is approximately [amount missing]. arrive Therefore, we can conclude that, with compared to, It achieved better BER performance. Specifically, when At that time, compared to the uncoded case, The BER of the PA-DF-FFMA system showed a gain of approximately 3.2 dB. In contrast, this is relative to the original LDPC encoding. The performance still has a gap of about 4.4 dB.

[0192] Figure 4 BER performance of low-rate channel codes constructed based on PA-DF-FFMA ( (Rc=0.584), set and Compare bits / user. For example... Figure 4 As shown, with The BER of PA-DF-FFMA is the opposite, and the channel coding is as follows: ( The BER performance of the PA-DF-FFMA system increased with... The increase is monotonically greater than the uncoded case. The BER of the PA-DF-FFMA system showed a gain of approximately 3.2 dB. In contrast, this is relative to the original LDPC encoding. The performance still has a gap of about 3.2 dB.

[0193] (2) Comparison between FFMA and IDMA systems

[0194] LDPC encoding based on two different rates and The BER performance of the PA-DF-FFMA proposed in this invention is compared with that of the IDMA system. Relevant performance simulations are shown below. Figures 5-6 .

[0195] The number of users is Polarization scaling factor To ensure a fair comparison, the total resource utilization of the IDMA system was also... The transmitter of an IDMA system consists of convolutional codes, repetition codes, and an interleaver. The information bits, after being encoded using a 1 / 2 rate convolutional code, generate a codeword of length 20. The number of repetitions in the repeating code... That is, each symbol of the codeword is repeated 300 times. Therefore, the frame length for each user remains the same. The receiver uses Turbo iteration to recover the transmitted symbol sequence.

[0196] Figure 5 Set the BER performance (Rc=0.5) of PA-DF-FFMA and IDMA systems in GMAC. Compare bits / user with J=1, 4, 10, 100, such as Figure 5 As shown, when At that time, the PA-DF-FFMA system proposed in this invention is superior to the IDMA system. Due to the parameters... The capabilities of the PA-DF-FFMA system are comparable to those of the repetition codes used in the IDMA system. Therefore, the difference in BER is primarily attributed to the length of the channel codeword, which is crucial for maintaining the same frame length between FFMA and IDMA systems (e.g., ...). In the IDMA system, the parity block length is 10 because channel coding must be performed before the multiplexing of complex domain resources. In contrast, the proposed PA-DF-FFMA system performs channel coding after the multiplexing of finite domain resources, enabling it to use a parity block length of 3000. According to Shannon's theory, longer channel coding can provide better coding gain; therefore, the BER performance of the proposed PA-DF-FFMA system is superior to that of the IDMA system. However, when the number of users is... At that time, the error performance of the PA-DF-FFMA system was not as good as that of the IDMA system.

[0197] Similarly, channel coding will be used. The PA-DF-FFMA system for error control has a total resource consumption of The above comparison of IDMA systems is fair. At this point, the IDMA system... , The information bits are generated into a codeword sequence through convolutional coding at a rate of 0.84, with a codeword length of 12. Since such a short channel codeword cannot provide effective error correction, therefore... The BER performance of the IDMA system is the same as that of the uncoded BPSK, as shown in [see figure]. Figure 6 . Figure 6 Set the BER performance (Rc=0.5 and 0.84) for PA-DF-FFMA and IDMA systems in GMAC. Compare bits / user and J=100; from Figure 6 It can be observed that, compared to the IDMA system (or the uncoded case), The proposed PA-DF-FFMA system provides approximately 2.1 dB of coding gain. This finding demonstrates that even with a large number of users, the proposed PA-DF-FFMA system can still achieve coding gain and maintain good transmission reliability, thus proving the effectiveness of the proposed FFMA system.

[0198] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A decoding method for a finite field multiple access system based on polarization adjustment, characterized in that, The system is a regular PA-DF-FFMA, that is, a polarization-regulated DF-FFMA that can achieve regular power distribution; DF-FFMA system refers to a diagonal FFMA system, i.e., codeword matrix. Includes an information array used to carry user information. and parity array And the vector corresponding to the user bit sequence Located in the information array The FFMA system on the main diagonal; the FFMA system is a finite-domain multiple access system. For codeword matrix diagonal code words , No. Information sequence of a user , of which Each user of The bit sequence is located in The Item 1, all other items are 0; yes Parity check block; DF-FFMA modulates only the part of the data that is useful for transmission. , express The useful information part, namely , The subscript S indicates shortening; The polarization-regulated DF-FFMA, which enables regular power distribution, performs power distribution in the following manner: The parity check block length is , It is the length of the block code. It is the length of the information bits; It is the maximum number of users that can be accommodated. It is the number of bits of user information; The codeword length is Power is distributed The different symbols, the total transmit power of each user is ;against The information part and the parity part, the power allocated to the information part of each symbol is The power allocated to the parity check portion of each symbol is , The polarization coefficient is given; the power distribution condition is... in, This is the polarization scaling factor, with the subscript pas indicating polarization adjustment; According to the conditions of power allocation and Determine the power allocation method and implement power allocation; The method includes the following steps: Received signal sequence It is divided into an information part and a parity check part, namely ,in The information section includes The data block, for the first... There are data blocks, The block length of each block is ; This indicates the parity check section; (1) Information bit detection stage: First, the information is divided into blocks for detection, based on decision thresholds. right Preliminary judgment: Regarding the first Information sub-blocks The judgment process is as follows: in, Indicates the first estimated value based on the received signal. The k-th bit in a sub-block of information; It is the log-likelihood value calculated based on the received signal; After this judgment process, the number of unknown information bits within the sub-block... , and They represent the estimated received signals, respectively. and Distance to the received signal: All estimated signals of the sub-block Combined, they correspond to the estimated sequence of the user. ,get Distance from the received signal ;right distance Sort in ascending order and select the top few. The distance values ​​constitute the distance set of this information segment, denoted as . ,in , , , ; For each distance value Through decimal to binary conversion function The distance value corresponding to Transform into an estimated binary vector ; Each element in the binary vector set corresponds to a unique vector; for each information sub-block, a binary vector set is obtained. ,Right now ; (2) Joint decoding stage: After the information bit detection stage, we obtain A binary set, namely The sub-blocks and their corresponding binary sets are joined sequentially. The joining process begins with... and Take one element from each pair and combine them, concatenate the sequences corresponding to the two elements, and then sum the corresponding distance values. and When combined, it can produce A combination of elements, assuming that after each combination, the elements are filtered according to their distance values. One as a candidate set for the next coalition, After combining the sub-blocks, we get A set of candidate information sequences, denoted as... , for The candidate estimation information sequence obtained by jointly connecting the sub-blocks has a length of [number]. Each candidate information sequence in the set corresponds to a calculated distance value, therefore the corresponding distance sorting list is: ; Regarding the first One candidate estimation information sequence It is made of A length of The binary sequence is composed of, and is represented as , Using channel coding System form of generator matrix The transmission codeword is reconstructed for each sub-block according to the DF-FFMA encoding method, and the parity block obtained again is... The parity check block is transformed from the finite field to the complex field by the function. Modulation to obtain signal ,get Modulated signal with parity bits: Then, the modulated signal is summed to obtain ; Calculate the parity check part and Distance: in, Alternative information sequence The corresponding total distance is sorted in ascending order Sort, corresponding to The binary sequence of minimum distances is given by the following formula: Received That is, the multi-user information sequence obtained by decoding.

2. The decoding method for a finite field multiple access system based on polarization adjustment according to claim 1, characterized in that, Log-likelihood value calculated from the received signal as follows: in, It is the estimated noise variance. and It is the posterior probability calculated based on the received signal.

3. The decoding method for a finite field multiple access system based on polarization adjustment according to claim 1, characterized in that, Estimated binary vector .

4. The decoding method for a finite field multiple access system based on polarization adjustment according to claim 1, characterized in that, The The corresponding parity check part and distance .

5. A decoding method for a finite field multiple access system based on polarization adjustment according to any one of claims 1 to 4, characterized in that, The Distance from the received signal as follows: in, express The decimal number, that is , The subscript B2D indicates the conversion from binary to decimal.

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