A high-performance polar code construction method for BP decoder

Abstract

The application relates to the technical field of communication channel coding, and discloses a high-performance polar code construction method for a BP decoder. The method first uses a noiseless BP decoding analysis method or a binary expansion grouping reliability sorting algorithm to obtain n+1 polar channel groups and reliability sorting, wherein the polar code length N=2 n , n is a positive integer; secondly, a noiseless BP decoding analysis method assisted by a wizard is used to obtain the reliability sorting of different polar channels in each group, so that the reliability sorting of N polar channels is determined; finally, according to a specific code rate R, the indexes of NR polar channels with high reliability are selected as information bits, and the indexes of the remaining N-NR polar channels are selected as frozen bits, so that the construction of the polar code with the code length N and the code rate R is completed. The construction method is independent of an actual channel, can effectively reduce the complexity of the polar code construction for the BP decoder, and can improve the error correction performance in a low frame error rate region.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of communication channel coding, and particularly relates to a high-performance polar code construction method for a BP decoder. BACKGROUND

[0002] The purpose of communication is to effectively and reliably transmit information generated by a signal source to a signal sink. However, in the process of information transmission, various noises inevitably interfere. As a key technology of a communication system, channel coding guarantees the reliability of communication by adding a check code. Polar code proposed in 2008 is the first type of channel coding method that is theoretically proved to be able to reach the Shannon capacity limit. Polar code has the characteristics of low encoding and decoding algorithm complexity, no error flat layer and capacity reach, so that polar code has become a research hotspot in the field of channel coding since it is proposed. Polar code is used in the 5G enhanced mobile broadband (eMBB) communication scenario as a channel coding scheme for control information. When the code length 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 code with medium and short code length under the successive cancellation (SC) decoding algorithm is not ideal. The introduction of the belief propagation (BP) decoding algorithm solves the high delay defect of the SC decoding algorithm.

[0003] Polar code is established on the basis of the concept of channel polarization. According to the channel polarization principle, N=2 n independent binary channels W (actual physical channels) can be obtained through channel merging and splitting operations, where n is a positive integer. Although the total channel capacity of the N polarized channels does not change, the capacity of each polarized channel shows a two-polarization phenomenon. Especially when N tends to infinity, the polarized 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 proportion of the two types of channels is 1-I(W) and I(W) respectively, where I(W) is the symmetric channel capacity of the physical channel W. Therefore, when transmitting frozen bits (known at the receiving end) on the pure noise channel and transmitting information bits on the noiseless channel, the channel capacity can be reached. However, when N is a finite value, the channel polarization is not complete, and the channel capacity of some polarized channels is between 0 and 1. Therefore, for any code length N=2 n and a given code rate R, how to measure the reliability of each polarized channel and how to select the most reliable NR polarized channels to transmit information bits will determine the error correction capability of polar code, which is also called the construction problem of polar code.

[0004] However, so far, the existing construction methods are mainly designed for SC decoding algorithm, such as Density Evolution (DE) algorithm, Gaussian Approximation (GA) algorithm, Polarization Weight (PW) algorithm, etc., and these algorithms all depend on the actual channel condition. Since the BP decoding algorithm and the SC decoding algorithm use different mechanisms for decoding, these construction algorithms are not applicable to the BP decoder. The existing construction methods for the BP decoder 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 value of the Log Likelihood Ratio (LLR) of each information bit, generally the mean value of the LLR of 5000 frames is calculated; finally, the index of the N s information bits with the smallest mean value is exchanged with the index of the N s most reliable frozen bits, generally N s equals 12. The simulation-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 average number of iterations required for the LLR value of each information bit in the BP decoding to exceed the LLR th threshold, thereby determining the worst polarization channel for transmitting the information bit, generally the number of iterations of 5000 frames is calculated; 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 index of each information bit and the index of the frozen bit until the index of N s information bits is exchanged. In addition, these construction methods also depend on the specific channel condition. SUMMARY

[0005] The present application provides a high-performance polar code construction method for the BP decoder to solve the defects of the polar code construction method for the BP decoder. Compared with some common construction methods, the method first groups and sorts all N polarization channels using the noiseless BP decoding analysis method or the binary expansion grouping reliability sorting algorithm, then obtains the reliability sorting of each grouping using the precision spirit assisted noiseless BP decoding analysis method, thereby obtaining the reliability sorting of all polarization channels, the construction method has low complexity, does not depend on the actual channel condition, and has good error correction performance.

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

[0007] First, for any code length N = 2 n , using a noiseless BP decoding analysis method or a binary expansion grouping reliability sorting algorithm, all n+1 polar channel groups {WH d , d∈Z, 0≤d≤n} and their reliability sorting o = (WH n , WH n-1 , …, WH1, WH0) are obtained, from left to right, the reliability of the polar channel groups is arranged from high to low in turn, and the reliability of different polar channels in the same group is the same, wherein N = 2 n , n is a positive integer, and the reliability of the polar channel is represented by the LLR output by the noiseless BP decoder, and the larger the LLR value, the higher the reliability;

[0008] Second, a noiseless BP decoding analysis method assisted by a genie is used to sort the reliability of different polar channels in each group, wherein the reliability is represented by the LLR output by the noiseless BP decoder assisted by the genie, and the larger the LLR value, the higher the reliability of the polar channel in the group;

[0009] Then, the reliability sorting o = (o1, o2, …, o N ) = (N, o n-1 , o n-2 , …, o 1 , 1) of all N polar channels is determined, from left to right, the reliability of the polar channels is arranged from high to low in turn, wherein o d is the reliability sorting of different polar channels in the polar channel group WH d , d∈Z, 1≤d≤n-1;

[0010] Finally, according to the code rate R, in the reliability sorting o = (o1, o2, …, o N ) of the N polar channels, the indices of the most reliable NR polar channels are selected as information bits, and the indices of the remaining N-NR polar channels are selected as frozen bits, thereby completing the construction of the polar code with the code length N and the code rate R.

[0011] When the polar channels are grouped and the reliability sorting of the n+1 polar channel groups is determined, the complexity of the binary expansion grouping reliability sorting algorithm is lower than that of the noiseless BP decoding analysis method, and there is no problem of computer calculation overflow or precision exceeding.

[0012] In a second aspect, the application uses a noiseless BP decoding analysis method to group all N polar channels, and the obtained n+1 groups are {WH d, and all the groups are sorted by reliability, the reliability of a polar channel is characterized by the LLR output by a noiseless BP decoder, the larger the LLR value, the higher the reliability of the polar channel group corresponding to the LLR value, and the reliabilities of different polar channels in the same group are the same, wherein the noiseless BP decoding analysis method first sets the initial left information L n+1,j = a, and the initial right information R 1,j = 0, j = 1, 2, …, N, a is a positive real number greater than 0, then performs one BP iteration decoding, and takes the output result L 1,j as the LLR value of the jth polar channel.

[0013] In a third aspect, a generation algorithm for grouping and sorting the reliabilities of polar channels with lower complexity than the noiseless BP decoding analysis method, i.e., a binary expansion grouping reliability sorting algorithm, is provided, comprising:

[0014] First, for each polar channel , the binary expansion of j-1 (j n ,j n-1 ,…, j1) is calculated, j n is the most significant bit, i.e. , and the weight D of (j n ,j n-1 ,…, j1) is obtained, wherein j = 1, 2, …, N, and D = 0, 1, …, n.

[0015] Then, all the polar channels are grouped according to the weights of the binary expansions of the polar channel indexes minus 1, and all the polar channel groups are {WH d , d e Z, 0 < d < n}, if , then the weights of (l n ,l n-1 ,…, l1) and (j n ,j n-1 ,…, j1) are both equal to d, wherein WH0 and WH n only contain the polar channels and

[0016] Finally, since the polar channel group with a larger weight has a higher reliability, the reliabilities of the n+1 polar channel groups are sorted as o = (WH n , WH n-1 ,…, WH1, WH0).

[0017] ​Because only the number of 1s in the binary expansion of the polar channel index minus 1 needs to be compared, all N polar channels can be grouped and sorted, so the complexity of the binary expansion grouping reliability sorting algorithm is less than the noiseless BP decoding analysis method adopted in the second aspect.

[0018] In a fourth aspect, a genie-aided noiseless BP decoding analysis method is provided for reliability sorting of each group WH d (d = 1, 2, …, n-1, n≥2) of different polar channels , comprising:

[0019] In a first step, the input sequence of the polar code encoder is BPSK modulated (0→1, 1→-1), and the LLR value of each channel output symbol y j is (i.e., the initial left information of the genie-aided noiseless BP decoding), b n,d is greater than 0, and the specific value range is related to the values of n and d, d = 1, 2, …, n-1, n≥2, and N = 2 n , j = 1, 2, …, N.

[0020] In a second step, the initial right information of the genie-aided noiseless BP decoding is set to

[0021] In a third step, BP iterative decoding is performed, i.e., in the tth iteration, the left information of the node (i, j) in the factor graph is updated to and the right information is updated to where i is the index of the stage in the polar code factor graph, i = 1, 2, …, n, j is the index of the row in the polar code factor graph, j = 1, 2, …, N, t is the iteration number,

[0022] In a fourth step, when and this condition is satisfied for three consecutive iterations, it is considered that the genie-aided noiseless BP iterative decoding converges when calculating the LLR value of , is the LLR value of the polar channel in the genie-aided noiseless BP decoding analysis method, where T l is the final iteration number.

[0023] In a fifth step, the second step to the fourth step are repeated until the LLR values of all polar channels in WH d are determined.

[0024] In a sixth step, the LLR values of all polar channels in WH d are sorted from large to small, and the order of the corresponding polar channel indices is WHd reliability ordering of all polarized channels in o d , i.e. if then in o d k precedes l, where

[0025] In the seventh step, the first to sixth steps are repeated until the reliability ordering of different polarized channels in (d=1, 2, …, n-1, n≥2) is obtained. d

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

[0027] The initial value b n,d of the left information needs to be set properly, which should make the results of the operations on all x or y, i.e. the LLR values of all nodes on the factor graph are relatively large, but cannot exceed the calculation precision and range. When 2≤n≤10, the value range of b n,d is shown in Table 1.

[0028] Table 1 Value range of b n,d when 2≤n≤10, d=1, 2, …, n-1

[0029]

[0030] Compared with the prior art, the present application has the following advantages:

[0031] 1. The high-performance polar code construction method for a BP decoder provided by the present application determines the reliability ordering of polarized channels independently of the actual used channel.

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

[0033] 3. The high-performance polar code construction method for a BP decoder provided by the present application has better error correction performance than the LLR-based bit swapping algorithm, the simulation-based bit swapping algorithm and the polar weight algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a flowchart of the high-performance polar code construction method for a BP decoder provided by the present application.​

[0035] Figure 2 For code length N = 128, the performance comparison chart of the high-performance polar code construction method for the BP decoder provided by the application and other construction methods at different code rates.

[0036] Figure 3 For code length N = 256, the performance comparison chart of the high-performance polar code construction method for the BP decoder provided by the application and other construction methods at different code rates.

[0037] Figure 4 For code length N = 512, the performance comparison chart of the high-performance polar code construction method for the BP decoder provided by the application and other construction methods at different code rates. DETAILED DESCRIPTION

[0038] The specific embodiments of the application will be further described in detail below with reference to the accompanying drawings and examples. The following examples are used to illustrate the application, but are not used to limit the scope of the application.

[0039] Example 1

[0040] The first embodiment of the application uses a noiseless BP decoding analysis method to divide all polar channels with code length N into n+1 groups and perform reliability sorting, where N = 2 n , and 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 n+1,j of the noiseless BP decoder 1,j = a, the initial right information R j = 0, j = 1, 2, …, N, and a is a positive real number greater than 0;

[0042] Step 102. Input all initial information to the BP decoder, and after the factor graph of the polar code is updated from left to right for the first time, the left information L 1,j of each bit u j or each polar channel is obtained as its final LLR value, that is, L 1,j is calculated using the recursive equation , where i = 1, 2, …, n, j = 1, 2, …, N,

[0043] Step 103. Grouping according to the LLR value of each polar channel, the polar channels with the same LLR value belong to the same group, and there are n+1 groups in total, that is, {WH d , d ∈ Z, 0 ≤ d ≤ n};

[0044] Step 104. Sort the polarization channel packets from largest to smallest according to their LLR values ​​to obtain the reliability ranking of the n+1 polarization channel packets o = (WH n WH n-1 ,…,WH1,WH0)=(N,WH n-1 ,…,WH1,1).

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

[0046] Table 2. Reliability ranking of the four polarization channel packets with a code length of 8.

[0047]

[0048] Example 2

[0049] This embodiment provides a method with lower complexity than the noiseless BP decoding analysis method to group N polarization channels and perform reliability ranking, namely the binary expansion group reliability ranking algorithm, the specific steps of which are as follows:

[0050] Step 201. For each polarization channel Calculate the binary expansion of j-1 (j n ,j n-1 ,…,j1),j n The most significant bit, i.e. And obtain (j) n ,j n-1 The weights D of j, ..., j1), where j = 1, 2, ..., N, and D = 0, 1, ..., n;

[0051] Step 202. Group all polarization channels according to the weight of the binary expansion of the polarization channel index minus 1. All polarization channel groups are {WH}. d If ,d∈Z,0≤d≤n}, Then (l) n ,l n-1 ,…,l1) and (j n ,j n-1 The weights of all (j1, ...,j2) are equal to d, where WH0 and WH2 are equal to d. n Each contains only polarization channels and

[0052] Step 203. Since the greater the weight of the polarization channel group, the higher its reliability, the reliability ranking of the n+1 polarization channel groups is o = (WH n WH n-1WH0) = (N, WH n-1 WH1,1).

[0053] Because only the number of elements 1 in the binary expansion of the polar channel index minus 1 needs to be compared, all N polar channels can be grouped and sorted in reliability, so the complexity of the binary expansion grouping and reliability sorting algorithm in the second embodiment of the present application is much smaller than the noiseless BP decoding analysis method in the first embodiment of the present application, but the polar channel grouping and its reliability sorting obtained by the two methods are exactly the same.

[0054] Embodiment 3

[0055] Based on the reliability sorting of the polar channel grouping obtained by the first and second embodiments of the present application, this embodiment provides a genie-aided noiseless BP decoding analysis method for determining the reliability sorting of different polar channels in each group WH d (d = 1, 2, …, n-1, n≥2) so as to obtain the reliability sorting of all N polar channels, and the specific steps are as follows:

[0056] Step 301. Let the input sequence of the polar code encoder be BPSK modulation (0→1, 1→-1), and the LLR value of each channel output symbol y j is (i.e. the initial left information of the genie-aided noiseless BP decoding), where b n,d is greater than 0, and the specific value range is related to the values of n and d, d = 1, 2, …, n-1, n≥2, and N = 2 n , j = 1, 2, …, N.

[0057] Step 302. Let the initial right information of the genie-aided noiseless BP decoding be

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

[0059] Step 304. When and this condition is satisfied for three consecutive iterations, it is considered that the genie-aided noiseless BP iterative decoding converges when calculating the LLR value of , and the reliability sorting of the polar channel ​LLR value in the method of noise-free BP decoding analysis assisted by a genie, wherein T l is the final iteration number for calculating the LLR value of the polar channel ;

[0060] Step 305. Repeat steps 302 to 304 until the LLR values of all polar channels in WH d are determined.

[0061] Step 306. Sort the LLR values of all polar channels in WH d from large to small, and the order of the corresponding polar channel indexes is the reliability order o d of all polar channels in WH d , that is, if and then k is in front of l in o d .

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

[0063] In the third embodiment of the present application, the initial value b n,d of the left information needs to be set properly, so that the results of all operations on the factor graph are not much different from the values of x or y, that is, the LLR values of all nodes on the factor graph are relatively large, but cannot exceed the calculation precision and range. When 2≤n≤10 and d=1,2,…,n-1, the value range of b n,d is shown in Table 1.

[0064] In combination with the third embodiment and the second embodiment or the first embodiment of the present application, the reliability order of all polar channels with an arbitrary code length N=2 n can be obtained as o=(o1,o2,…,o N )=(N,o n-1 ,o n-2 ,…,o 1 ,1).

[0065] Embodiment 4

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

[0067] Step 401. For any code length N, the all n+1 polar channel groups and their reliability order o = (WH n ,WH n-1 ,…,WH1,WH0) = (N,WH n-1 ,…,WH1,1) are obtained by using the noiseless BP decoding analysis method in the first embodiment or the binary expansion grouping reliability ordering algorithm in the second embodiment, and the reliability of the polar channel groups from left to right is arranged in turn from high to low, and the reliability of different polar channels in the same group is the same.

[0068] Step 402. The reliabilities of different polar channels in each group are ordered by using the genie-aided noiseless BP decoding analysis method in the third embodiment, and the reliabilities of polar channels in the same group are represented by the LLR output by the genie-aided noiseless BP decoder, and the larger the LLR value is, the higher the reliability of the corresponding polar channel in the group is.

[0069] Step 403. The reliability order o = (o1, o2, …, o N ) = (N, o n-1 ,o n -2 ,…,o 1 ,1) of all N polar channels is determined, and the reliability of the polar channels from left to right is arranged in turn from high to low, wherein o d is the reliability order of different polar channels in the polar channel group WH d , and d∈Z, 0≤d≤n.

[0070] Step 404. According to the code rate R, the indices of the most reliable NR polar channels in the reliability order o = (o1, o2, …, o N ) of the N polar channels are selected as the information bits to transmit information bits, and the indices of the remaining N-NR polar channels are selected as the frozen bits, and the construction of the polar code with the code length N and the code rate R is completed.

[0071] In the fourth embodiment, only one left information update from left to right on the factor graph or the number of elements 1 in the binary expansion of the polar channel index minus 1 is needed to group all N polar channels and obtain their reliability order; then, when determining the reliability of each polar channel in the same group, only one frame of Monte Carlo simulation is needed for each polar channel; therefore, the complexity of the high-performance polar code construction method for the BP decoder provided in the application is less than that of other common construction methods for the BP decoder, such as the bit swapping algorithm based on LLR and the bit swapping algorithm based on simulation.

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

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

[0074] Using the noiseless BP decoding analysis method assisted by the genie in the third embodiment of the present application, the LLR value of each polar channel in WH2 is determined as The order o 2 =(7, 6, 4), the LLR value of each polar channel in WH1 is determined as The order o 1 =(5, 3, 2), where b 3,1 =2, b 3,2 =2;

[0075] The reliability order of the 8 polar 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, and 4, and the frozen bits are 5, 3, 2, and 1.

[0077] In summary, the first embodiment of the present application uses a noiseless BP decoding analysis method to divide all N polarized channels into n+1 groups, and to perform reliability sorting of different polarized channel groups, wherein the greater 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 application provides a polarized channel grouping and reliability sorting generation algorithm with lower complexity, i.e., a binary expansion grouping reliability sorting algorithm, which performs grouping and sorting by comparing the number of elements 1 in the binary expansion of the polarized channel index minus 1; then, the third embodiment of the present application provides a noiseless BP decoding analysis method assisted by a genie, which performs reliability sorting of different polarized channels in the same group, uses the LLR output by the noiseless BP decoder assisted by the genie to represent the reliability of the corresponding polarized channel, and the greater the LLR value, the higher the reliability of the corresponding polarized channel, so as to obtain the reliability sorting of all polarized channels; finally, the fourth embodiment of the present application constructs a polar code with an arbitrary code length and code rate according to the reliability sorting of the polarized channels; numerical results show that the error correction performance of the high-performance polar code construction method for a BP decoder provided by the present application is better than that of the LLR-based bit swapping algorithm, the simulation-based bit swapping algorithm and the polar weight algorithm, and the complexity of the method is far less than that of common BP decoding-oriented construction methods, such as the LLR-based bit swapping algorithm and the simulation-based bit swapping algorithm.

[0078] The entire process of the polar code construction method for a BP decoder provided by the present application is shown in Figure 1 First, n+1 polarized channel groups and their reliability sorting are obtained by using a noiseless BP decoding analysis method or a binary expansion grouping reliability sorting algorithm, then the reliability sorting of different polarized channels in each group is obtained by using a noiseless BP decoding analysis method assisted by a genie, so as to determine the reliability sorting of N polarized channels, and finally, NR polarized channels with high reliability are selected according to a specific code rate R, and the indexes of the N-NR polarized channels are used as frozen bits, to complete the construction.

[0079] To verify the effectiveness of the present application, numerical simulation experiments are performed, and the error correction performance is compared with that of the LLR-based bit swapping algorithm, the simulation-based bit swapping algorithm and the polar 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. The design-SNR of the LLR-based bit swapping algorithm and the simulation-based bit swapping algorithm is 2.5 dB. In all simulation graphs, the signal-to-noise ratio of the AWGN channel is represented by E bBLER under N0, the proposed construction method of high performance polar code for BP decoder, the LLR-based bit-swapping algorithm, the simulation-based bit-swapping algorithm and the polar weight algorithm are denoted as Proposed construction, LLR-based bit-swapping, Simulation-based bit-swapping and PW respectively. In order to ensure the accuracy of simulation results, at least 100 error frames are counted for the calculation of BLER under N0. b BLER under N0, the proposed construction method of high performance polar code for BP decoder, the LLR-based bit-swapping algorithm, the simulation-based bit-swapping algorithm and the polar weight algorithm are denoted as Proposed construction, LLR-based bit-swapping, Simulation-based bit-swapping and PW respectively. In order to ensure the accuracy of simulation results, at least 100 error frames are counted for the calculation of BLER under N0.

[0081] Figure 2 、 Figure 3 and Figure 4 respectively show the error frame rate performance of different code rates under the conditions of code length N = 128, N = 256 and N = 512. Under the conditions of different code length and code rate, the error correction performance of the proposed construction method of high performance polar code for BP decoder is better than that of the LLR-based bit-swapping algorithm, the simulation-based bit-swapping algorithm and the polar weight algorithm, especially in the medium and high SNR region, and the performance gain is greater and greater as the error frame rate decreases. For example, when N = 256, R = 0.226, at BLER = 10 -5 -4, the proposed construction method of high performance polar code for BP decoder has a performance gain of more than 0.5 dB compared with the LLR-based bit-swapping algorithm, the simulation-based bit-swapping algorithm and the polar weight algorithm.

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

Claims

1. A high performance polar code construction method for BP decoder, characterized in that, The method comprises the following steps: Step 1. For any code length N, using a binary expansion grouping reliability ordering algorithm, obtain all n+1 polar channel groupings and their reliability ordering, where the code length N of the polar code = 2 n , n is a positive integer, and the binary expansion grouping reliability ordering algorithm comprises: Step 101. For each polarized channel Compute the binary expansion of j - 1 (j n ,j n-1 ,…,j1), j n is the most significant bit, i.e. and find the weight D of (j n ,j n-1 ,…,j1), where j = 1, 2, …, N, D = 0, 1, …, n. Step 102. Group all polarized channels according to the weight of their binary expansion with the index of the polarized channel reduced by 1, all polarized channel groups being {WH d , d e Z, 0 < d < n}, if then (l n , l n-1 ,..., l1) and (j n , j n-1 ,..., j1) have both weight d, where WH0and WH n contain only polarized channels and Step 103. Since the greater the weight of the polarization channel packet, the higher its reliability, the reliability ranking of the n+1 polarization channel packets is o = (WH n WH n-1 ,…,WH1,WH0)=(N,WH n-1 ,…,WH1,1); Step 2. Sorting the reliabilities of different polar channels in each polar channel group WH d , where d = 1, 2, …, n-1, n≥2, by using a genie-aided noiseless BP decoding analysis method, the reliabilities of polar channels are represented by the LLRs output by the genie-aided noiseless BP decoder, the larger the LLR value, the higher the reliability of the corresponding polar channel in the group, wherein the genie-aided noiseless BP decoding analysis method comprises: Step 201. Let the input sequence to the polar code encoder be BPSK modulation, the initial left information for the genie-aided noiseless BP decoding is where b n,d > 0, j = 1, 2,..., N; Step 202. Let the initial right information of the sprite-assisted noise-free BP decoding be Step 203. Perform BP iterative decoding, i.e., the left information of the node (i, j) in the factor graph is updated as the right information of the node (i, j) is updated as where i is the index of the stage in the polar code factor graph, i = 1, 2, …, n, j is the index of the row in the polar code factor graph, j = 1, 2, …, N, t is the iteration number, Step 204. When and this condition is satisfied for three consecutive iterations, then the genie-aided noiseless BP iterative decoding is considered to converge in computing the LLR values, for the polar channel LLR values in the genie-aided noiseless BP decoding analysis method, where T l is the final iteration number for computing the LLR values for the polar channel ​​ Step 205. Repeat steps 202 to 204 until the LLR values for all polarized channels in WH d are determined. Step 206. Sort the LLR values of all the polarized channels in WH d in descending order, and the order of the corresponding polarized channel indices is WH d . d That is, if and then k is in front of l in o d . Step 207. Repeat steps 201 to 206 until the reliability ordering of each packet WH d over different polarized channels is obtained. Step 3. Determine the reliability ranking of all N polarization channels o = (o1, o2, ..., o N )=(N,o n-1 ,o n-2 ,…,o 1 ,1), the reliability of polarization channels is arranged from high to low from left to right, where o d For polarized channel packets WH d The reliability ranking of different polarization channels, d = 1, 2, ..., n-1, n ≥ 2; Step 4. According to the code rate R, in the reliability ordering of the N polar channels, the indexes of the most reliable NR polar channels are selected as the information bits to transmit information bits, and the indexes of the remaining N-NR polar channels are selected as frozen bits, so as to complete the construction of the polar code with the code length N and the code rate R.

2. The method of claim 1, wherein the method is a method of constructing a high performance polar code for a BP decoder. Initial information b for the sprite-assisted noise-free BP decoding analysis method in step 2 n,d The value range of d 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 = log2 N, N is the code length.

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