BP decoder-oriented high-performance polarization code construction method

Abstract

The invention relates to the technical field of communication channel coding, and discloses a high-performance polarization code construction method for a BP decoder. According to the method, firstly, n + 1 polarization channel groups and the reliability sequence of the polarization channel groups are obtained through a noise-free BP decoding analysis method or a binary expansion grouping reliability sorting algorithm, the code length N of polarization codes is equal to 2n, and n is a positive integer; secondly, a reliability sequence of different polarization channels in each group is obtained by using a sprite-assisted noise-free BP decoding analysis method, so that a reliability sequence of N polarization channels is determined; and finally, selecting the indexes of NR polarization channels with high reliability as information bits according to the specific code rate R, and taking the indexes of the remaining N-NR polarization channels as frozen bits to finish the construction of the polarization code with the code length N and the code rate R. The construction method is independent of an actual channel, can effectively reduce the complexity of the polarization code construction oriented to the BP decoder, and can improve the error correction performance of a low frame error rate region.

Description

Technical Field

[0001] The present invention relates to the technical field of communication channel coding, and in particular to a high-performance polar code construction method for a BP decoder. Background Art

[0002] The purpose of communication is to effectively and reliably transmit the information generated by the source to the destination. However, the information transmission process is inevitably interfered by various noises. Channel coding, as a key technology of the communication system, ensures the reliability of communication by adding check codes. Polar codes, proposed in 2008, are the first type of channel coding method that has been theoretically proven to reach the Shannon capacity limit. Polar codes have the characteristics of low coding algorithm complexity, error-free flattening, and achievable capacity, making polar codes a research hotspot in the field of channel coding once proposed. They are now used in 5G enhanced mobile broadband (eMBB) communication scenarios as a channel coding scheme for control information. When the code length of the polar code tends to infinity, the channel can be fully polarized and the performance reaches the Shannon capacity limit. However, for actual communication systems, the performance of polar codes with medium and short code lengths under the serial cancellation (SC) decoding algorithm is not ideal. The introduction of the belief propagation (BP) decoding algorithm solves the disadvantage of high latency of the SC decoding algorithm.

[0003] Polarization code is based on the concept of channel polarization. According to the principle of channel polarization, N = 2 n Independent binary channels W (actual physical channels) can be combined and split to obtain N interdependent polarization channels, where n is a positive integer. Although the total channel capacity of the N polarization channels remains unchanged, the capacity of each polarization channel shows a polarization phenomenon. Especially when N tends to infinity, the polarization channels can be divided into two categories, one is a pure noise channel with a channel capacity of 0, and the other is a noiseless channel with a channel capacity of 1, and the proportions of these two types of channels are 1-I(W) and I(W), respectively, where I(W) is the symmetric channel capacity of the physical channel W. Therefore, when frozen bits (known at the receiving end) are transmitted on a pure noise channel and information bits are transmitted on a noiseless channel, the channel capacity can be reached. However, when N is a finite value, the channel polarization is incomplete, and the channel capacity of some polarization channels is between 0 and 1. Therefore, for any code length N=2 n Given a code rate R, how to measure the reliability of each polarization channel and how to select the most reliable NR polarization channels to transmit information bits will determine the error correction capability of the polar code. This problem is also called the polar code construction problem.

[0004] However, so far, the existing construction methods are mainly designed for SC decoding algorithms, such as the Density Evolution (DE) algorithm, the Gaussian Approximation (GA) algorithm, the Polarization Weight (PW) algorithm, etc., and these algorithms all rely on actual channel conditions. Since the BP decoding algorithm and the SC decoding algorithm use different mechanisms for decoding, these construction algorithms are not suitable for the BP decoder. The existing construction methods for BP decoders are generally designed based on Monte Carlo simulation, such as the LLR-based bit exchange algorithm and the simulation-based bit exchange algorithm, which have extremely high complexity. The LLR-based bit exchange algorithm first uses the construction method for the SC decoder to give the initial information set and frozen set; then uses Monte Carlo simulation to calculate the mean of the log likelihood ratio (LLR) of each information bit, generally counting the mean of the LLR of 5000 frames; finally, the N frames with the smallest mean are selected. s The index of the information bits is the most reliable N s The indices of the frozen bits are exchanged, usually N s =12. The simulation-based bit exchange algorithm first uses the construction method for SC decoder to give the initial information set and frozen set; then, Monte Carlo simulation is used to calculate the LLR value of each information bit in BP decoding exceeding the LLR th The average number of iterations required to determine the worst polarization channel for transmitting information bits is generally counted for 5000 frames. Finally, the index of this information bit is exchanged with the index of the most reliable frozen bit. Repeat the previous steps to exchange the information bit index and the frozen bit index one by one until N information bits are exchanged. s In addition, these construction methods also depend on the specific channel conditions. Summary of the invention

[0005] The present invention aims at the defects in polar code construction for BP decoders and provides a high-performance polar code construction method for BP decoders. Compared with some common construction methods, this method first uses a noise-free BP decoding analysis method or a binary expansion group reliability sorting algorithm to group and sort all N polarized channels, and then uses a spirit-assisted noise-free BP decoding analysis method to obtain the reliability sorting of each group, thereby obtaining the reliability sorting of all polarized channels. This construction method has low complexity, is independent of actual channel conditions, and has good error correction performance.

[0006] In a first aspect, the present invention provides a high-performance polar code construction method for a BP decoder, comprising:

[0007] First, for any code length N=2 n , using the noise-free BP decoding analysis method or the binary expansion group reliability sorting algorithm, all n+1 polarization channel groups {WH d ,d∈Z,0≤d≤n} and its reliability ranking o=(WH n ,WH n-1 ,…,WH1,WH0), the reliability of polarized channel groups is arranged from high to low from left to right, and the reliability of different polarized channels in the same group is the same, where N = 2 n , n is a positive integer. The reliability of the polarization channel is characterized by the LLR output by the noise-free BP decoder. The larger the LLR value, the higher the reliability.

[0008] Secondly, the elf-assisted noiseless BP decoding analysis method is used to rank the reliability of different polarization channels in each group. The reliability is characterized by the LLR output by the elf-assisted noiseless BP decoder. The larger the LLR value, the higher the reliability of the corresponding polarization channel in this group.

[0009] Then, the reliability ranking o=(o1, o2, …, o N )=(N,o n-1 ,o n-2 ,…,o 1 ,1),The reliability of polarized channels is arranged from high to low from left to right, where o d Group WH for polarized channels d Reliability ranking of different polarization channels in , d∈Z, 1≤d≤n-1;

[0010] Finally, according to the code rate R, the reliability ranking of the N polarized channels is o = (o1, o2, ..., o N ), select the indexes of the most reliable NR polarized channels as information bits, and the indexes of the remaining N-NR polarized channels as frozen bits, to complete the construction of the polar code with code length N and code rate R;

[0011] When polarized channels are grouped and the reliability ranking of n+1 polarized channel groups is determined, the complexity of the binary expansion group reliability ranking algorithm is lower than that of the noise-free BP decoding analysis method, and there is no computer calculation overflow or out-of-precision problem.

[0012] In the second aspect, the present invention uses the noise-free BP decoding analysis method to group all N polarized channels, and the obtained n+1 groups are {WH d,d∈Z,0≤d≤n}, and sort the reliability of all packets. The reliability of the polarized channel is characterized by the LLR output by the noiseless BP decoder. The larger the LLR value, the higher the reliability of the corresponding polarized channel group. The reliability of different polarized channels in the same group is the same. The noiseless BP decoding analysis method first sets the initial left information L n+1,j =a, initial right information R 1,j =0, j = 1, 2, ..., N, a is a positive real number greater than 0, and then perform a BP iterative decoding, and output the result L 1,j As the jth polarization channel The LLR value of .

[0013] In a third aspect, a generation algorithm for grouping polarized channels and ranking them for reliability is provided, which is less complex than the noise-free BP decoding analysis method, namely, a binary expansion grouping reliability ranking algorithm, including:

[0014] First, for each polarization channel W N (j) , calculate the binary expansion of j-1 (j n ,j n-1 ,…,j1),j n is the most significant bit, that is And find (j n ,j n-1 ,…,j1) weight d, where j = 1,2,…,N, d = 0,1,…,n;

[0015] Then, all polarized channels are grouped according to the weight of the binary expansion of the polarized channel index minus 1. The group of all polarized channels is {WH d ,d∈Z,0≤d≤n}, if Then n ,l n-1 ,…,l1) and (j n ,j n-1 ,…,j1) have a weight of d, where WH0 and WH n Only polarization channels are included and

[0016] Finally, since the reliability of the polarized channel group with a larger weight is higher, the reliability ranking of the n+1 polarized channel groups is o=(WH n ,WH n-1 ,…,WH1,WH0);

[0017] Because it is only necessary to compare the number of element 1s in the binary expansion of the polarized channel index minus 1 to group and sort all N polarized channels, the complexity of the binary expansion grouping reliability sorting algorithm is less than the noise-free BP decoding analysis method adopted in the second aspect.

[0018] In the fourth aspect, a method for analyzing the noise-free BP decoding assisted by a wizard is provided for analyzing the noise-free BP decoding assisted by a wizard ... d Different polarization channels in (d=1,2,…,n-1,n≥2) Perform reliability ranking, including:

[0019] The first step is to let the input sequence of the polar code encoder be BPSK modulation (0→1, 1→-1), each channel outputs symbol y j The LLR value is (i.e. the initial left information of the noise-free BP decoding assisted by the elf), b n,d Greater than 0. The specific value range depends on the values ​​of n and d. d=1,2,…,n-1, n≥2, N=2 n , j = 1, 2, ..., N;

[0020] The second step is to set the initial right information of the noise-free BP decoding assisted by the elf

[0021] The third step is to perform BP iterative decoding, that is, in the tth iteration, the left information of the node (i, j) in the factor graph is updated to Right information updated to Where i is the index of the stage in the polar code factor map, i = 1, 2, ..., n, j is the index of the row in the polar code factor map, j = 1, 2, ..., N, t is the number of iterations,

[0022] Step 4: If this condition is met for three consecutive iterations, it is considered that the noise-free BP iterative decoding assisted by the elf is effective in computing The LLR value converges when Polarization Channel LLR values ​​in the Genie-assisted noiseless BP decoding analysis method, where T l is the final number of iterations;

[0023] Step 5: Repeat steps 2 to 4 until WH d The LLR values ​​of all polarization channels in are determined;

[0024] Step 6: WH d The LLR values ​​of all polarized channels in are sorted from large to small, and the order of the corresponding polarized channel indexes is WHd The reliability ranking of all polarized channels in d , that is, if Then in o d k is in front of l, where

[0025] Step 7: Repeat steps 1 to 6 until each group WH d The reliability rankings of different polarization channels in (d=1,2,…,n-1,n≥2) are obtained;

[0026] Finally, the reliability ranking of the N polarized channels is o = (o1, o2, …, o N )=(N,o n-1 ,o n-2 ,…,o 1 ,1);

[0027] The initial value b of the left information n,d Need to be set appropriately, so that all The result of the operation is not much different from the value of x or y, that is, the LLR values ​​of all nodes on the factor graph are relatively large, but cannot exceed the calculation accuracy and range. When 2≤n≤10, b n,d The value range is shown in Table 1.

[0028] Table 1 When 2≤n≤10, b n,d The value range of

[0029]

[0030] Compared with the prior art, the advantages of the present invention are:

[0031] 1. The present invention provides a high-performance polar code construction method for a BP decoder, wherein the reliability ranking of the determined polarized channels is independent of the channels actually used;

[0032] 2. The complexity of the high-performance polar code construction method for BP decoder provided by the present invention is lower than that of the common construction methods for BP decoder, such as the LLR-based bit exchange algorithm and the simulation-based bit exchange algorithm;

[0033] 3. The high-performance polar code construction method for BP decoder provided by the present invention has better error correction performance compared with the LLR-based bit exchange algorithm, the simulation-based bit exchange algorithm and the polarization weight algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The present invention provides a flowchart of a high-performance polar code construction method for a BP decoder.

[0035] Figure 2 The performance comparison diagram of a high-performance polar code construction method for BP decoder provided by the present invention and other construction methods when the code length N is 128 and the code rates are different.

[0036] Figure 3 A performance comparison diagram of a high-performance polar code construction method for BP decoder provided by the present invention and other construction methods when the code length N is 256 and the code rates are different.

[0037] Figure 4 The performance comparison diagram of a high-performance polar code construction method for BP decoder provided by the present invention and other construction methods when the code length N is 512 and the code rates are different. DETAILED DESCRIPTION

[0038] The specific implementation of the present invention is further described in detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0039] Example 1

[0040] The first embodiment of the present invention uses a noise-free BP decoding analysis method to divide all polarization channels with a code length of N into n+1 groups and sort them by reliability, where N=2 n , the specific steps are as follows:

[0041] Step 101. Let the input sequence of the polar code encoder be BPSK modulation (0→1, 1→-1), the initial left information L of the noiseless BP decoder n+1,j =a, initial right information R 1,j =0, j=1,2,…,N, a is a positive real number greater than 0;

[0042] Step 102: Input all the initial information into the BP decoder. After the factor graph of the polar code updates the left information from left to right for the first time, each bit u is obtained. j Or each polarization channel W N (j) Left information L 1,j As its final LLR value, that is, using the recursive equation Calculate L 1,j , where i = 1, 2, ..., n, j = 1, 2, ..., N,

[0043] Step 103. Group the polarized channels according to their LLR values. Polarized channels with the same LLR values ​​belong to the same group. There are n+1 groups in total, namely {WH d ,d∈Z,0≤d≤n};

[0044] Step 104: Sort the LLR values ​​of each polarized channel group from large to small to obtain the reliability ranking of n+1 polarized channels o=(WH n ,WH n-1 ,…,WH1,WH0)=(N,WH n-1 ,…,WH1,1).

[0045] As shown in Table 2, the noise-free BP decoding analysis method is used to divide the polarization channels with a code length of 8 into 4 groups, and their reliability ranking is o=(WH3, WH2, WH1, WH0), where a=2.

[0046] Table 2 Reliability ranking of 4 polarized channel groups with code length 8

[0047]

[0048] Example 2

[0049] This embodiment provides a method with lower complexity than the noise-free BP decoding analysis method to group N polarized channels and sort their reliability, namely, a binary expansion grouping reliability sorting algorithm. The specific steps are as follows:

[0050] Step 201. For each polarized channel Calculate the binary expansion of j-1 (j n ,j n-1 ,…,j1),j n is the most significant bit, that is And find (j n ,j n-1 ,…,j1) weight d, where j = 1,2,…,N, d = 0,1,…,n;

[0051] Step 202: Group all polarized channels according to the weight of the binary expansion of the polarized channel index minus 1. All polarized channel groups are {WH d ,d∈Z,0≤d≤n}, if Then n ,l n-1 ,…,l1) and (j n ,j n-1 ,…,j1) have a weight of d, where WH0 and WH n Only polarization channels are included and

[0052] Step 203. Since the reliability of the polarized channel group with a larger weight is higher, the reliability ranking of the n+1 polarized channel groups is o=(WH n ,WHn-1 ,…,WH1,WH0)=(N,WH n-1 ,…,WH1,1).

[0053] Because it is only necessary to compare the number of elements 1 in the binary expansion of the polarized channel index minus 1 to group all N polarized channels and perform reliability sorting, the complexity of the binary expansion grouping reliability sorting algorithm in the second embodiment of the present invention is much smaller than the noise-free BP decoding analysis method in the first embodiment of the present invention, but the polarized channel groups and their reliability sorting obtained by the two methods are exactly the same.

[0054] Example 3

[0055] Based on the reliability ranking of polarized channel groups obtained in the first and second embodiments of the present invention, this embodiment provides a genie-assisted noise-free BP decoding analysis method for determining the reliability of each group of WH d Different polarization channels in (d=1,2,…,n-1,n≥2) The reliability ranking of all N polarized channels is obtained by performing the following steps:

[0056] Step 301. Let the input sequence of the polar code encoder be BPSK modulation (0→1, 1→-1), each channel outputs symbol y j The LLR value is (i.e. the initial left information of the noiseless BP decoding assisted by the elf), where b n,d Greater than 0. The specific value range depends on the values ​​of n and d. d=1,2,…,n-1, n≥2, N=2 n , j = 1, 2, ..., N;

[0057] Step 302. Let the initial right information of the elf-assisted noise-free BP decoding be

[0058] Step 303. Perform BP iterative decoding, that is, in the tth iteration, the left information of the node (i, j) in the factor graph is updated to Right information updated to Where i is the index of the stage in the polar code factor map, i = 1, 2, ..., n, j is the index of the row in the polar code factor map, j = 1, 2, ..., N, t is the number of iterations,

[0059] Step 304. When If this condition is met for three consecutive iterations, it is considered that the noise-free BP iterative decoding assisted by the elf is effective in computing The LLR value converges when Polarization Channel LLR values ​​in the Genie-assisted noiseless BP decoding analysis method, where T l To calculate the polarization channel The final number of iterations of the LLR value;

[0060] Step 305. Repeat steps 302 to 304 until WH d The LLR values ​​of all polarization channels in are determined;

[0061] Step 306. WH d The LLR values ​​of all polarized channels in are sorted from large to small, and the order of the corresponding polarized channel indexes is WH d The reliability ranking of all polarized channels in d , that is, if and Then in o d In , k comes before l;

[0062] Step 307. Repeat steps 301 to 306 until each group WH d The reliability rankings of different polarization channels in (d=1,2,…,n-1,n≥2) are obtained.

[0063] In the third embodiment of the present invention, the initial value b of the left information n,d Need to be set appropriately, so that all The result of the operation is not much different from the value of x or y, that is, the LLR values ​​of all nodes on the factor graph are relatively large, but cannot exceed the calculation accuracy and range. When 2≤n≤10, b n,d The value range is shown in Table 1.

[0064] Combining the third embodiment of the present invention with the second embodiment or the first embodiment, an arbitrary code length N=2 can be obtained. n The reliability ranking of all polarized channels is o=(o1, o2, …, o N )=(N,o n-1 ,o n-2 ,…,o 1 ,1).

[0065] Example 4

[0066] This embodiment provides a high-performance polar code construction method for BP decoder, which is used to construct an arbitrary code length N=2 n (n is a positive integer) and a polar code with an arbitrary code rate R (R=K / N, 0≤R≤1, K is the number of information bits), the specific steps are as follows:

[0067] Step 401. For any code length N, use the noise-free BP decoding analysis method in the first embodiment or the binary expansion group reliability ranking algorithm in the second embodiment to obtain all n+1 polarized channel groups and their reliability rankings o=(WH n ,WH n-1 ,…,WH1,WH0)=(N,WH n-1 ,…,WH1,1), the reliability of polarized channel groups is arranged from high to low from left to right, and the reliability of different polarized channels in the same group is the same;

[0068] Step 402: using the elf-assisted noiseless BP decoding analysis method in the third embodiment, the reliabilities of different polarized channels in each group are sorted. The reliability of polarized channels in the same group is characterized by the LLR output by the elf-assisted noiseless BP decoder. The larger the LLR value, the higher the reliability of the corresponding polarized channel in the group.

[0069] Step 403: Determine the reliability ranking o=(o1, o2, ..., o N )=(N,o n-1 ,o n -2 ,…,o 1 ,1),The reliability of polarized channels is arranged from high to low from left to right, where o d Group WH for polarized channels d Reliability ranking of different polarization channels in , d∈Z, 0≤d≤n;

[0070] Step 404. According to the code rate R, the reliability of the N polarized channels is ranked o = (o1, o2, ..., o N ), the indexes of the most reliable NR polarization channels are selected as information bits to transmit information bits, and the indexes of the remaining N-NR polarization channels are used as frozen bits to complete the construction of the polarization code with code length N and code rate R.

[0071] In the fourth embodiment, only one left information update from left to right is performed on the factor graph or the number of element 1s in the binary expansion of the polarized channel index minus 1 is compared, so that all N polarized channels can be grouped and their reliability rankings can be obtained; then, when determining the reliability of each polarized channel in the same group, only one frame of Monte Carlo simulation is performed on each polarized channel; therefore, the complexity of the high-performance polar code construction method for BP decoders provided by the present invention is less than that of other common construction methods for BP decoders, such as an LLR-based bit exchange algorithm and a simulation-based bit exchange algorithm.

[0072] In the fourth embodiment of the present invention, a specific example of high-performance polar code construction for BP decoder is as follows:

[0073] When the code length N of the polar code is 8, the polarized channel grouping obtained in the first embodiment or the second embodiment of the present invention is WH3={W8 (8)},WH2={W8 (4) ,W8 (6) ,W8 (7)},WH1={W8 (2) ,W8 (3) ,W8 (5)}, WH0={W8 (1)}, and their reliability ranking is o=(WH3, WH2, WH1, WH0);

[0074] Using the elf-assisted noise-free BP decoding analysis method in the third embodiment of the present invention, the LLR value of each polarized channel in WH2 is determined to be Sort 2 =(7,6,4), determine the LLR value of each polarization channel in WH1 as Sort 1 =(5,3,2), where b 3,1 =2, b 3,2 =2;

[0075] The reliability ranking of the 8 polarized channels is o=(8,7,6,4,5,3,2,1);

[0076] A polar code with a code rate of 1 / 2 is constructed, and the selected information bits are 8, 7, 6, 4, and the frozen bits are 5, 3, 2, 1.

[0077] In summary, the first embodiment of the present invention utilizes the noiseless BP decoding analysis method to divide all N polarized channels into n+1 groups, and performs reliability sorting of different polarized channel groups. The larger the LLR value output by the noiseless BP decoder, the higher the reliability of the corresponding polarized channel group. The second embodiment of the present invention provides a polarized channel grouping and reliability sorting generation algorithm with lower complexity, that is, a binary expansion grouping reliability sorting algorithm, which performs grouping and sorting by comparing the number of elements 1 of the binary expansion of the polarized channel index minus 1. Then, the third embodiment of the present invention provides a wizard-assisted noiseless BP decoding analysis method, which performs reliability sorting of different polarized channels in the same group, utilizing The LLR output by the noise-free BP decoder assisted by the elf is used to characterize the reliability of the corresponding polarized channel. The larger the LLR value, the higher the reliability of the corresponding polarized channel, thereby obtaining the reliability ranking of all polarized channels; finally, in the fourth embodiment of the present invention, polar codes with arbitrary code lengths and code rates are constructed according to the reliability ranking of the polarized channels; numerical results show that the error correction performance of a high-performance polar code construction method for BP decoders provided by the present invention is better than that of an LLR-based bit exchange algorithm, a simulation-based bit exchange algorithm, and a polarization weight algorithm, and its complexity is much smaller than that of common construction methods for BP decoding, such as an LLR-based bit exchange algorithm and a simulation-based bit exchange algorithm.

[0078] The entire process of the polar code construction method for BP decoder provided by the present invention is as follows: Figure 1 As shown, firstly, the noise-free BP decoding analysis method or the binary expansion group reliability ranking algorithm is used to obtain n+1 polarized channel groups and their reliability rankings. Secondly, the wizard-assisted noise-free BP decoding analysis method is used to obtain the reliability rankings of different polarized channels in each group, thereby determining the reliability rankings of N polarized channels. Finally, according to the specific code rate R, the indexes of NR polarized channels with high reliability are selected as information bits, and the indexes of the remaining N-NR polarized channels are used as frozen bits to complete the construction.

[0079] In order to verify the effectiveness of the present invention, numerical simulation experiments were carried out, and the error correction performance was compared with that of the LLR-based bit exchange algorithm, the simulation-based bit exchange algorithm and the polarization weight algorithm under the same conditions.

[0080] In the numerical simulation, the channel is an AWGN channel, BPSK modulation (0→1, 1→-1), BP decoding and the maximum number of iterations is 50, and the design-SNR of the LLR-based bit exchange algorithm and the simulation-based bit exchange algorithm is 2.5dB. In all simulation figures, the signal-to-noise ratio of the AWGN channel is calculated using E b / N0 is used to represent the error correction performance, and the block error rate (BLER) is used to represent the error correction performance. The proposed high-performance polar code construction method for BP decoder, the LLR-based bit-swapping algorithm, the simulation-based bit-swapping algorithm, and the polarization weight algorithm provided by the present invention are represented by Proposed construction, LLR-based bit-swapping, Simulation-based bit-swapping, and PW simplification, respectively. In order to ensure the accuracy of the simulation results, each E b The calculation of BLER under / N0 counts at least 100 error frames.

[0081] Figure 2 , Figure 3 and Figure 4 The frame error rate performance of different code rates under the conditions of code length N = 128, N = 256 and N = 512 is shown respectively. Under different code lengths and code rates, the error correction performance of a high-performance polar code construction method for BP decoder provided by the present invention is better than that of the LLR-based bit exchange algorithm, the simulation-based bit exchange algorithm and the polarization weight algorithm, especially in the medium and high signal-to-noise ratio area, and the performance gain increases with the decrease of the frame error rate. For example, when N = 256 and R = 0.226, at BLER = 10 -5 Compared with the LLR-based bit exchange algorithm, the simulation-based bit exchange algorithm and the polarization weight algorithm, the high-performance polar code construction method for the BP decoder provided by the present invention has a performance gain of more than 0.5 dB.

[0082] The specific embodiments described above further illustrate the purpose, technical solutions and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. It is particularly pointed out that for those skilled in the art, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A high-performance polar code construction method for BP decoder, characterized in that: The following steps are involved: Step 101. For any code length N, use the noise-free BP decoding analysis method or the binary expansion group reliability sorting algorithm to obtain all n+1 polarized channel groups {WH d ,d∈Z,0≤d≤n} and its reliability ranking o=(WH n ,WH n-1 ,…,WH1,WH0)=(N,WH n-1 ,…,WH1,1), the reliability of polarization channel groups is arranged from high to low from left to right, and the reliability of different polarization channels in the same group is the same, where the code length of the polarization code is N = 2 n , n is a positive integer. The reliability of the polarization channel is characterized by the LLR output by the noise-free BP decoder. The larger the LLR value, the higher the reliability. Step 102: Use the Spirit-assisted noise-free BP decoding analysis method to group each polarized channel WH d The reliability of different polarization channels in the group is ranked. The reliability of the polarization channel is characterized by the LLR output by the elf-assisted noiseless BP decoder. The larger the LLR value, the higher the reliability of the corresponding polarization channel in this group, where d=1,2,…,n-1, n≥2; Step 103: Determine the reliability ranking o=(o1, o2, ..., o N )=(N,o n-1 ,o n-2 ,…,o 1 ,1),The reliability of polarized channels is arranged from high to low from left to right, where o d Group WH for polarized channels d Reliability ranking of different polarization channels in , where d=1,2,…,n-1, n≥2; Step 104. According to the code rate R, in the reliability sorting of the N polarized channels, the indexes of the most reliable NR polarized channels are selected as information bits to transmit information bits, and the indexes of the remaining N-NR polarized channels are used as frozen bits, thereby completing the construction of the polar code with a code length of N and a code rate of R.

2. A method for determining N polarized channel groups and ranking them for reliability with lower complexity than the noise-free BP decoding analysis method, namely, a binary expansion grouping reliability ranking algorithm, characterized in that: The following steps are involved: Step 201. For each polarized channel Calculate the binary expansion of j-1 (j n ,j n-1 ,…,j1),j n is the most significant bit, that is And find (j n ,j n-1 ,…,j1) weight d, where j = 1, 2,…, N, d = 0, 1,…, n, N = 2 n , n is a positive integer; Step 202: Group all polarized channels according to the weight of the binary expansion of the polarized channel index minus 1. All polarized channel groups are {WH d ,d∈Z,0≤d≤n}, if Then n ,l n-1 ,…,l1) and (j n ,j n-1 ,…,j1) have a weight of d, where WH0 and WH n Only polarization channels are included and Step 203. Since the reliability of the polarized channel group with a larger weight is higher, the reliability ranking of the n+1 polarized channel groups is o=(WH n ,WH n-1 ,…,WH1,WH0)=(N,WH n-1 ,…,WH1,1).

3. A Genie-assisted noise-free BP decoding analysis method for determining the WH of each polarized channel group d (d=1,2,…,n-1,n≥2,n is a positive integer) The reliability ranking is characterized by: The following steps are involved: Step 301. Let the input sequence of the polar code encoder be BPSK modulation (0→1, 1→-1), each channel outputs symbol y j The LLR value is (i.e., the initial left information of the noiseless BP decoding assisted by the elf), where b n,d >0, d=1,2,…,n-1, n≥2, N=2 n , j = 1, 2, ..., N; Step 302. Let the initial right information of the elf-assisted noise-free BP decoding be Step 303. Perform BP iterative decoding, that is, in the tth iteration, the left information of the node (i, j) in the factor graph is updated to Right information updated to Where i is the index of the stage in the polar code factor map, i = 1, 2, ..., n, j is the index of the row in the polar code factor map, j = 1, 2, ..., N, t is the number of iterations, Step 304. When If this condition is met for three consecutive iterations, it is considered that the noise-free BP iterative decoding assisted by the elf is effective in computing The LLR value converges when Polarized Channel LLR values ​​in the Genie-assisted noiseless BP decoding analysis method, where T l To calculate the polarization channel The final number of iterations of the LLR value; Step 305. Repeat steps 302 to 304 until WH d The LLR values ​​of all polarization channels in are determined; Step 306. WH d The LLR values ​​of all polarized channels in are sorted from large to small, and the order of the corresponding polarized channel indexes is WH d The reliability ranking of all polarized channels in d , that is, if and Then in o d In , k comes before l; Step 307. Repeat steps 301 to 306 until each group WH d The reliability rankings of different polarization channels in (d=1,2,…,n-1,n≥2) are obtained.

4. The method for analyzing the noise-free BP decoding assisted by a spirit according to claim 3, characterized in that: The initial left information b in step 301 n,d The value range depends on the size of n and d, 0.5≤d 2,1 ≤170, 1.1≤d 3,1 ≤110,1.1≤d 3,2 ≤110, 1.7≤d 4,1 ≤71,1.7≤d 4,2 ≤71,1.7≤d 4,3 ≤71,2.4≤d 5,1 ≤25.4, 2.4≤d 5,2 ≤25.4, 2.4≤d 5,3 ≤25.4, 2.4≤d 5,4 ≤25.4,3.1≤d 6,1 ≤15.6,3.1≤d 6,2 ≤15.6,3.1≤d 6,3 ≤15.6,3.1≤d 6,4 ≤15.6,3.1≤d 6,5 ≤15.6,4.4≤d 7,1 ≤5.3,4.4≤d 7,2 ≤5.3,4.4≤d 7,3 ≤5.3,4.4≤d 7,4 ≤5.3,4.4≤d 7,5 ≤5.3,4.4≤d 7,6 ≤5.3,5.6≤d 8,1 ≤13.4,5.6≤d 8,2 ≤13.4,5.6≤d 8,3 ≤13.4,5.6≤d 8,4 ≤13.4,5.6≤d 8,5 ≤13.4,2.5≤d 8,6 ≤4.5, 2.5≤d 8,7 ≤4.5,7.0≤d 9,1 ≤11.8,7.0≤d 9,2 ≤11.8,7.0≤d 9,3 ≤11.8,7.0≤d 9,4 ≤11.8,7.0≤d 9,5 ≤11.8,3.8≤d 9,6 ≤4.7,3.8≤d 9,7 ≤4.7, 0.5≤d 9,8 ≤3.1,8.2≤d 10,1 ≤9.1,8.2≤d 10,2 ≤9.1,8.2≤d 10,3 ≤9.1,8.2≤d 10,4 ≤9.1,8.2≤d 10,5 ≤9.1,4.51≤d 10,6 ≤4.65,4.51≤d 10,7 ≤4.65,1.5≤d 10,8 ≤3.1,1.3≤d 10,9 ≤2.6, where d=1,2,…,n-1,n≥2,n=log2N, N is the code length.

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