A low-complexity polar code construction method

Abstract

The application relates to the technical field of communication channel coding, and discloses a low-complexity polar code construction method. The method uses the log-likelihood ratio (LLR) output by noiseless SC decoding to represent the reliability of each polar channel, first uses a binary expansion reliability sorting generation algorithm to obtain the reliability sorting of all N polar channels, then according to a code rate R, selects the indexes of the most reliable NR polar channels in the reliability sorting of the N polar channels as information bits, and uses the indexes of the remaining N-NR polar channels as frozen bits, and finally completes the construction of a polar code with a code length N and a code rate R. The method is independent of an actual channel, can effectively reduce the complexity of polar code construction, and improves the performance in a medium-high signal-to-noise ratio (SNR) region.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of communication channel coding, and particularly relates to a low-complexity polar code construction method. BACKGROUND

[0002] The purpose of communication is to effectively and reliably transmit information generated by a signal source to a signal sink. However, the information is inevitably disturbed by various noises in the process of transmission. Channel coding technology, as a key technology of a communication system, 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. Moreover, the polar code also has the characteristics of explicit structure, low complexity of encoding and decoding algorithm, and error-free flat layer. The encoding complexity is O(NlogN), and if the Successive Cancellation (SC) decoding algorithm is used, the decoding complexity is also O(NlogN), N=2 n code length, and n is a non-negative integer. Therefore, since the polar code is proposed, it has become a research hotspot in the field of channel coding. It is now used in the 5G enhanced mobile broadband (eMBB) communication scenario as a channel coding scheme for control information.

[0003] The core idea of the polar code is channel polarization. According to the channel polarization principle, N=2 n binary channels (actual physical channels) that are independent of each other can be obtained through channel merging and channel splitting operations. Although the total capacity of the N polar channels is unchanged, the capacity of each polar channel presents a polarization phenomenon. Especially when N tends to infinity, the polar 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. 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 takes a finite value, the channel polarization is not sufficient, and the channel capacity of some polar channels is between 0 and 1. Therefore, for any code length N=2 nand how to select the most reliable NR polarized channels to transmit information bits, will determine the error correction capability of the polar code, which is also called the construction problem of the polar code. However, so far, there is no certain construction method for an additive white Gaussian noise (AWGN) channel. Common suboptimal construction algorithms, such as a Monte Carlo simulation construction method, a density evolution (DE) algorithm and a Gaussian approximation (GA) algorithm, all depend on actual channel conditions and have high complexity. Although a polarization weight (PW) algorithm can calculate the reliability of a polarized channel by using an index of the polarized channel, the value of the parameter β is set according to the reliability ranking obtained by the Gaussian approximation algorithm, so the error correction capability is slightly weak.

[0004] The Monte Carlo simulation construction method is suitable for various different types of channels, but has a complexity of O (MNlogN), where M is the number of Monte Carlo simulations. The density evolution algorithm determines the error probability of each polarized channel by calculating a probability density function of a log-likelihood ratio (LLR) of the polarized channel, and then selects polarized channels with low error probability to transmit information bits. However, the density evolution algorithm also has high complexity, and has a complexity of O (Nξlogξ), where ξ is the number of samples used, and a typical value is 10 5 . In order to reduce the complexity of the density evolution algorithm, the Gaussian approximation algorithm estimates the reliability of each polarized channel by tracking the mean value of the LLR of the polarized channel, and this method has similar error correction performance to the density evolution algorithm. SUMMARY

[0005] The present application provides a low-complexity polar code construction method to overcome the defects of the existing polar code construction methods. Compared with other common construction methods, this method uses binary expansion of the index of the polarized channel to obtain the reliability ranking of all polarized channels, has low construction complexity, does not depend on actual channel conditions, and has better error correction performance in the medium and high signal-to-noise ratio regions.

[0006] In a first aspect, the present application provides a low-complexity polar code construction method, comprising:

[0007] First, for any code length N = 2 n , the reliability ranking o = (o0, o1, …, o N-1), the reliabilities of the polar channels from left to right are arranged in descending order, the reliability of the polar channel is represented by the LLR output by the noiseless SC decoding, the greater the LLR value is, the higher the reliability of the corresponding polar channel is;

[0008] Then, according to the code rate R, in the reliability sorting of the N polar channels, the indexes of the most reliable NR polar channels are selected as information bits, and the indexes of the remaining N-NR polar channels are used as frozen bits, so that the construction of the polar code with the code length N and the code rate R is completed;

[0009] If it is required to design polar codes with multiple code lengths, since the reliability sorting of the polar channels has nesting, only the reliability sorting of the polar channels with the longest code length N needs to be stored, and the polar codes with lengths less than or equal to N can be constructed according to the reliability sorting of the polar channels with the code length N, which can further reduce the complexity of construction and storage space;

[0010] The generation of the reliability sorting of the polar channels can adopt a noiseless SC decoding analysis method, or a binary expansion reliability sorting generation algorithm, the complexity of the binary expansion reliability sorting generation algorithm is lower than that of the noiseless SC decoding analysis method, and there is no problem of computer calculation overflow or exceeding the precision.

[0011] In a second aspect, in order to generate the reliability sorting of all polar channels with an arbitrary code length N=2 n , the present application provides a noiseless SC decoding analysis method, comprising:

[0012] First, let the input sequence of the polar code encoder be BPSK modulation (0→1, 1→-1), the LLR of each channel output symbol y i is (the initial LLR of the noiseless SC decoding), wherein N=2 n , i=0, 1, …, N-1, if 0≤n≤2, the threshold value is otherwise, the threshold value is

[0013] Then, input all channel information into the SC decoder to obtain the LLR value of each bit u i or each polar channel . The LLR value can comprehensively reflect all structural characteristics of the polar channel , and represent the reliability thereof, wherein i=0, 1, …, N-1.

[0014] Finally, sort all from large to small, and sort the corresponding indexes o=(o0, o1, …, o N-1) is the reliability of all N polarized channels, the reliability decreases from left to right, i.e.,

[0015] Under the condition of satisfying , the value of a cannot be too large or too small, otherwise it may cause computer overflow or precision problems;

[0016] Since it is assumed that BPSK modulation (0→1, 1→-1), and Then The calculation of Where i=0,1,…N-1, (i n-1 ,i n-2 ,…,i0) is the binary expansion of the index i of the polarized channel , i.e. If i k =1 (k=0,1,…,n-1), then Otherwise z is the input of the current function;

[0017] If the input sequence is a random 0-1 sequence, the initial LLR value represents the reliability of the polarized channel , and the obtained polarized channel reliability ranking is the same as that of the all-zero sequence, and of the same polarized channel are equal, where i=0,1,…N-1;

[0018] The complexity of the noiseless SC decoding analysis method is less than that of the commonly used construction methods, such as Monte Carlo simulation construction method, density evolution algorithm, Gaussian approximation algorithm and polarization weight algorithm, etc.

[0019] In the third aspect, the structural characteristics of the polarized channel reliability ranking determined by the noiseless SC decoding analysis method are obtained, including:

[0020] According to the Hamming weight of the binary expansion of the index of the polarized channel, all polarized channels are grouped, and all polarized channel groups are {WH d ,0≤d≤n}, if Then the Hamming weight of (i n-1 ,i n-2 ,…,i0) and (j n-1 ,j n-2 ,…,j0) is d, WH0 and WH n respectively only contain polarized channels and

[0021] Feature one, if the polarization channel has a larger Hamming weight of the n-bit binary expansion of its index i (i n-1 ,i n-2 ,…,i0), then is larger, the polarization channel is more reliable, i.e., d is larger, all polarization channels in the polarization channel group WH d are more reliable;

[0022] Feature two, in the polarization channel group WH d , if and β i is smaller, then is larger, the polarization channel is more reliable in WH d , wherein, represents the Hamming weight of the sub-vector (i k-1 ,…,i0), and d=1,…,n-1, n≥2;

[0023] Feature three, when and β i =β j , if the zero elements in (i n-1 ,i n-2 ,…,i0) are in higher significant bits than the zero elements in (j n-1 ,j n-2 ,…,j0) in the dictionary order, then the reliability of the polarization channel is higher than that of the polarization channel

[0024] Feature four, the reliability ranking determined by the noiseless SC decoding analysis method has nestedness, and the reliability ranking of a polarization channel with a code length of N remains unchanged in the reliability ranking of a polarization channel with a code length of 2N.

[0025] In the fourth aspect, according to the structural features of the polarization channel reliability ranking in the third aspect, a lower complexity polarization channel reliability ranking generation algorithm, i.e., a binary expansion reliability ranking generation algorithm, is provided, comprising:

[0026] First, for each polarization channel , calculate the binary expansion of its index i (i n-1 ,i n-2 ,…,i0), i.e., and obtain the Hamming weight d of (i n-1 ,i n-2 ,…,i0), wherein i=0,1,…,N-1, d=0,1,…,n;

[0027] Then, all polarized channels are grouped according to the Hamming weight of the binary expansion of the polarized channel index. The group of all polarized channels is {WH d ,0≤d≤n}, if Then (i n-1 ,i n-2 ,…,i0) and (j n-1 ,j n-2 ,…,j0) all have a Hamming weight of d, and the polarized channel group with a larger Hamming weight has a higher reliability, so o(0) = N-1, o(N-1) = 0;

[0028] Secondly, when the Hamming weight d decreases from n-1 to 1, the polarization channel group WH is determined d Reliability ranking of different polarization channels in d ,if And β i The smaller the WH d Medium polarization channel The more reliable, Represents a subvector (i k-1 ,…,i0), and n≥2;

[0029] Next, when And β i =β j When i and j are further determined at o d In the order, if we follow the dictionary order, (i n-1 ,i n-2 ,…,i0) has a zero element ratio (j n-1 ,j n-2 ,…,j0) are in the more significant position, then the polarization channel The reliability is higher than that of polarized channels In o d In the example, i is placed before j;

[0030] Finally, the reliability ranking of all polarized channels is o=(o n ,o n-1 ,o n-2 ,…,o 1 ,o 0 )=(N-1,o n-1 ,o n -2 ,…,o 1 ,0);

[0031] Because the number and position of 0 and 1 in the binary expansion of the polar channel index are compared to obtain the reliability order of all polar channels, the complexity of the binary expansion reliability order generation algorithm is less than the noiseless SC decoding analysis method in the second aspect.

[0032] Compared with the prior art, the application has the advantages that:

[0033] 1. The polar channel reliability order determined by the noiseless SC decoding analysis method and the binary expansion reliability order generation algorithm provided by the application is independent of the actual used channel.

[0034] 2. The complexity of the polar code construction method provided by the application is less than that of the commonly used construction methods, such as the Monte Carlo simulation construction method, the density evolution algorithm, the Gaussian approximation algorithm and the polar weight algorithm, because the number and position of 0 and 1 in the binary expansion of the polar channel index are compared to obtain the reliability order of all polar channels.

[0035] 3. Because the polar channel reliability order has the nested property, in the scene where multiple code lengths need to be constructed, the low-complexity polar code construction method provided by the application can further reduce the complexity and storage space of construction.

[0036] 4. Because the polar channel reliability order determined by the application can reflect the key structural factors affecting the performance of the polar code at medium and high signal-to-noise ratios, the low-complexity polar code construction method provided by the application has better error correction performance in the low frame error rate region compared with the Monte Carlo simulation construction method, the Gaussian approximation algorithm and the polar weight algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 The flowchart of the low-complexity polar code construction method provided by the application;

[0038] Figure 2 The performance comparison chart of the low-complexity polar code construction method provided by the application and other construction methods when the code length N = 64 and the code rate is different;

[0039] Figure 3 The performance comparison chart of the low-complexity polar code construction method provided by the application and other construction methods when the code length N = 256 and the code rate is different;

[0040] Figure 4 The performance comparison chart of the low-complexity polar code construction method provided by the application and other construction methods when the code length N = 512 and the code rate is different. DETAILED DESCRIPTION

[0041] The specific embodiments of the present application are described in further detail below in conjunction with the accompanying drawings and examples. The following examples are used to illustrate the present application but are not intended to limit the scope of the present application.

[0042] The present application uses the absolute value of the LLR output by the SC decoding to represent the reliability of each polar channel, and the greater the absolute value of the LLR, the more reliable the corresponding polar channel. In order to avoid the influence of random noise on the LLR value of each polar channel, so that the absolute value of the LLR can comprehensively reflect all the structural characteristics of the polar channel, the present application uses the absolute value of the LLR output by the noiseless SC decoding to represent the reliability of each polar channel. If the input sequence Then the absolute value of the LLR is equal to the LLR itself.

[0043] Embodiment 1

[0044] The first embodiment of the present application provides a noiseless SC decoding analysis method for determining the reliability ranking of all polar channels with a code length of N, and the specific steps are as follows:

[0045] Step 101. Let the input sequence of the polar code encoder be BPSK modulation (0→1, 1→-1), and the output symbol y of each channel i The LLR of (initial LLR of noiseless SC decoding), where i=0, 1, …, N-1, If 0≤n≤2, the threshold value is Otherwise, the threshold value is

[0046] Step 102. Input all channel information into the SC decoder to obtain the LLR value of each bit u i or each polar channel which can comprehensively reflect all the structural characteristics of the polar channel , indicating its reliability, where i=0, 1, …, N-1;

[0047] Step 103. Sort all from large to small, and the corresponding index sorting o=(o0, o1, …, o N-1 ) is the reliability ranking of all N polar channels, and the reliability decreases from left to right, i.e.

[0048] In the first embodiment of the present application, since it is assumed that BPSK modulation (0→1, 1→-1), and Then the calculation of can be further simplified as​ where i = 0, 1, …, N-1, (i n-1 ,i n-2 ,…,i0) is the polarization channel binary expansion of index i, i.e. if i k = 1 (k = 0, 1, …, n-1), then otherwise z is the input of the current function.

[0049] In the first embodiment of the present application, the value of a cannot be too large or too small under the condition that otherwise, it may cause the computer to overflow or exceed the precision problem.

[0050] In the first embodiment of the present application, the complexity of generating the reliability ordering of the polarization channel is less than that of the common construction method, such as the Monte Carlo simulation construction method, the density evolution algorithm, the Gaussian approximation algorithm and the polarization weight algorithm.

[0051] In the first embodiment of the present application, the input sequence may also be a random 0-1 sequence, at this time, the initial LLR value represents the reliability of the polarization channel , the reliability ordering of the polarization channel obtained is consistent with the all-zero sequence, and of the same polarization channel are equal, where i = 0, 1, …, N-1. As shown in Table 1, the reliability ordering of the polarization channel with a code length of 8 is consistent when the all-zero input sequence and the random input sequence are used respectively, where a = 2.

[0052] Table 1 Reliability ordering of polarization channel with code length of 8

[0053]

[0054] According to the Hamming weight d of the binary expansion of the index of the polarization channel, the present application divides all polarization channels into n+1 groups {WH d , 0≤d≤n}, where WH0and WH n only contain polarization channels and The reliability ordering of the polarization channel obtained in the first embodiment of the present application also has the following structural characteristics:

[0055] Characteristic one. If the Hamming weight of the n-bit binary expansion (i n-1 ,i n-2 ,…,i0) of the index i of the polarization channel is larger, then is larger, and the polarization channel The more reliable, i.e., the larger d, the more reliable all the polar channels in the polar channel group WH d .

[0056] Feature Two. In the polar channel group WH d , if and β i is smaller, then is larger, the polar channel in WH d is more reliable, wherein, denotes the Hamming weight of the sub-vector (i k-1 ,…,i0), and d = 1,…,n-1, n≥2.

[0057] Feature Three. When and β i = β j , if the zero elements in (i n-1 ,i n-2 ,…,i0) are in higher significant bits than the zero elements in (j n-1 ,j n-2 ,…,j0) in the dictionary order, then the reliability of the polar channel is higher than that of the polar channel

[0058] Feature Four. The reliability ordering has a nested property, the reliability ordering of polar channels with code length N remains unchanged in the reliability ordering of polar channels with code length 2N.

[0059] Embodiment 2

[0060] Based on the structural features of the reliability ordering of polar channels obtained in the first embodiment of the present application, this embodiment provides a method with lower complexity to generate the reliability ordering of all polar channels, i.e., a binary expansion reliability ordering generation algorithm, the specific steps are as follows:

[0061] Step 201. For each polar channel , calculate the binary expansion of its index i (i n-1 ,i n-2 ,…,i0), i.e. and obtain the Hamming weight d of (i n-1 ,i n-2 ,…,i0), wherein i = 0,1,…,N-1, d = 0,1,…,n.

[0062] Step 202. Group all polar channels according to the Hamming weight of the binary expansion of the polar channel index, all polar channel groups are {WH d ,0≤d≤n}, if​ Then (i n-1 ,i n-2 ,…,i0) and (j n-1 ,j n-2 ,…,j0) are all equal to d, and the polarized channel group with a larger Hamming weight has a higher reliability, so o(0) = N-1, o(N-1) = 0;

[0063] Step 203: When the Hamming weight d decreases from n-1 to 1, determine the polarization channel group WH d Reliability ranking of different polarization channels in d ,if And β i The smaller the WH d Medium polarization channel The more reliable, Represents a subvector (i k-1 ,…,i0), and n≥2;

[0064] Step 204. When And β i =β j When i and j are further determined at o d In the order, if we follow the dictionary order, (i n-1 ,i n-2 ,…,i0) has a zero element ratio (j n-1 ,j n-2 ,…,j0) are in the more significant position, then the polarization channel The reliability is higher than that of polarized channels In o d In the example, i is placed before j;

[0065] Step 205. The code length is N=2 n When the reliability ranking of all polarized channels of the polar code is o=(o n ,o n-1 ,o n -2 ,…,o 1 ,o 0 )=(N-1,o n-1 ,o n-2 ,…,o 1 ,0).

[0066] In the second embodiment of the present application, because only the number and position of 0 and 1 in the binary expansion of the polar channel index need to be compared to obtain the reliability order of all polar channels, the complexity of the binary expansion reliability order generation algorithm is much lower than that of the noiseless SC decoding analysis method in the first embodiment of the present application, but the reliability orders obtained by the two methods are exactly the same.

[0067] Embodiment 3

[0068] Based on the polar channel reliability order obtained in the second embodiment of the present application, the embodiment provides a low-complexity polar code construction method, and the specific steps are as follows:

[0069] Step 301. For any code length N = 2 n , the binary expansion reliability order generation algorithm is used to obtain the reliability order of all polar channels;

[0070] Step 302. According to the code rate R, in the reliability order 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 used as frozen bits, to complete the construction of the polar code with the code length N and the code rate R.

[0071] If polar codes with multiple code lengths need to be designed, the nested nature of the polar channel reliability order can be used to further reduce the construction complexity and storage space, and the specific construction steps are as follows:

[0072] Step 401. Determine the longest code length N;

[0073] Step 402. Generate the polar channel reliability order of the longest code length N according to step 301, and store it;

[0074] Step 403. According to the nested nature of the polar channel reliability order, obtain the reliability order of the polar channel with the required code length (less than or equal to N);

[0075] Step 404. According to the requirements of the code length and the code rate, complete the construction of the corresponding polar code according to step 302.

[0076] In the third embodiment of the present application, the reliability order of the polar channel can also be generated by the noiseless SC decoding analysis method in the first embodiment, but the construction complexity is slightly higher.

[0077] In the third embodiment of the present application, a specific polar code construction example is as follows:

[0078] When the code length N of the polar code is 8, the polar channel reliability order o = (7, 6, 5, 3, 4, 2, 1, 0) obtained by the binary expansion reliability order generation algorithm in the second embodiment of the present application;

[0079] Construct a polar code with code rate 1 / 2, and select information bits as 7, 6, 5, 3, and frozen bits as 4, 2, 1, 0.

[0080] In summary, the first embodiment of the present application provides a noiseless SC analysis method, the LLR value output by the noiseless SC decoding is used to represent the reliability of the corresponding polar channel (the larger the LLR value, the higher the reliability of the corresponding polar channel), and the reliability ranking of all polar channels is obtained, and the complexity is less than that of common construction methods such as Monte Carlo simulation construction method, density evolution algorithm, Gaussian approximation algorithm and polarization weight algorithm; then the present application gives the structural characteristics of the reliability ranking of the polar channel; the second embodiment of the present application provides a polarization channel reliability ranking generation algorithm with lower complexity, namely a binary expansion reliability ranking generation algorithm, which also discloses the key structural factors affecting the performance at medium and high signal-to-noise ratios; finally, the third embodiment of the present application constructs a polar code with an arbitrary code length and code rate according to the reliability ranking of the polar channel; numerical results show that the error correction performance of the low-complexity polar code construction method provided by the present application is better than that of the Monte Carlo simulation construction method, the Gaussian approximation algorithm and the polarization weight algorithm in the low frame error rate region.

[0081] The entire process of the low-complexity polar code construction method provided by the present application is shown in Figure 1 First, the binary expansion reliability ranking generation algorithm is used to obtain the reliability ranking of N polar channels, and then NR polar channels with higher reliability are selected according to the specific code rate R, and the indexes of the remaining N-NR polar channels are used as frozen bits.

[0082] To verify the effectiveness of the present application, numerical simulation experiments are carried out, and the performance is compared with the Monte Carlo simulation construction method, the Gaussian approximation algorithm and the polarization weight algorithm under the same conditions.

[0083] In the numerical simulation, the channel is an AWGN channel, BPSK modulation (0→1, 1→-1), SC decoding, the design-SNR of the Monte Carlo simulation construction method and the Gaussian approximation algorithm is 2.5 dB. In all simulation figures, the signal-to-noise ratio of the AWGN channel is represented by E b / N0, the error correction performance is represented by the block error rate (BLER), and the low-complexity polar code construction method provided by the present application, the Monte Carlo simulation construction method, the Gaussian approximation algorithm and the polarization weight algorithm are represented by Proposed construction, Monte-Carlo, GA and PW respectively. In order to ensure the accuracy of the simulation results, the calculation of BLER under each E b / N0 at least counts 100 error frames.

[0084] Figure 2 、 Figure 3 and Figure 4 respectively show the frame error rate performance of different code rates under the condition of code length N = 64, N = 256 and N = 512. Under the condition of code length N = 64 and code rate R = 0.5, the polar codes obtained by all the construction methods have the same information bits and frozen bits, and thus have the same error correction performance. In addition, under other code length and code rate conditions, the low-complexity polar code construction method provided by the present application has better performance than the Monte Carlo simulation construction method, the Gaussian approximation algorithm and the polar weight algorithm in the low frame error rate range, and the performance gain is greater and greater as the frame error rate decreases. For example, when N = 64 and R = 0.625, at BLER = 10 -5 -3, the low-complexity polar code construction method provided by the present application has a performance gain of 0.5 dB compared with the Monte Carlo simulation construction method, the Gaussian approximation algorithm and the polar weight algorithm.

[0085] 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 low-complexity polar code construction method, characterized in that: The following steps are involved: Step 101. According to the code length N=2 n , the reliability ranking of all N polarized channels is obtained by using the noiseless SC decoding analysis method o=(o0,o1,…,o N-1 ), with reliability arranged from high to low from left to right. The reliability of each polarized channel is represented by the LLR value output after noiseless SC decoding. A larger LLR value indicates a higher reliability of the corresponding polarized channel, where n is a non-negative integer. Step 102: Based on the code rate R, in the reliability ranking o of the N polarized channels, the indices of the most reliable NR polarized channels are selected as information bits. The indices of the remaining N-NR polarized channels are used as frozen bits. This completes the construction of a polar code with code length N and code rate R, where 0 < R < 1. The noise-free SC decoding analysis method in step 101 includes: First, let the input sequence of the polar code encoder be For BPSK modulation, the N input LLRs of the noiseless SC decoder are all finite values ​​a, and Among them, the code length N = 2 n , n is a non-negative integer. If 0≤n≤2, the threshold of the noiseless SC decoder input LLR is Otherwise, the threshold of the noiseless SC decoder input LLR is d is the binary expansion of polarization channel index j (j n-1 ,j n-2 ,…,j0), and Then after SC decoding, each bit u is obtained i Or each polarization channel LLR value Able to comprehensively reflect polarization channels All structural characteristics of represent its reliability, where i = 0, 1, ... N-1; Finally, the LLR values ​​of the N polarized channels are sorted from large to small, and the corresponding index sorting is o=(o0,o1,…,o N-1 ) is the reliability ranking of N polarized channels, and the reliability decreases from left to right, that is, In the noiseless SC decoding analysis method, if the input sequence is a random 0-1 sequence. At this time, each input LLR value of the noiseless SC decoder is sign(y i )×a, and After SC decoding, Represents polarized channel The reliability of all N polarized channels is obtained by calculating the reliability ranking, which is the same as the reliability ranking when the input sequence is all zero, and the absolute values ​​of the LLRs of the same polarized channels are equal, where the code length N = 2 n , n is a non-negative integer. If 0≤n≤2, the threshold of the noiseless SC decoder input LLR is Otherwise, the threshold of the noiseless SC decoder input LLR is d is the binary expansion of polarization channel index j (j n-1 ,j n-2 ,…,j0), j=1,2,…,N-2,y i is the output symbol of the noiseless channel, i=0,1,…,N-1.

2. The method according to claim 1, characterized in that Each polarization channel of the noiseless SC decoding analysis method in step 101 LLR value The calculation can be further simplified to Among them, i=0,1,...N-1, (i n-1 ,i n-2 ,…,i0) is the binary expansion of index i, and If the kth element i k =1, then otherwise z is the input of the current function, and a is the input LLR value of the noiseless SC decoder.

3. The method according to claim 1, characterized in that If you need to design polar codes with multiple code lengths, the following steps are included: Step 201. Determine the longest code length N; Step 202: Generate a reliability ranking of the polarized channels with the longest code length N using a noise-free SC decoding analysis method and store the ranking. Step 203: Based on the nested nature of the reliability rankings of the polarized channels, obtain the reliability ranking of the polarized channels with the required code length. Step 204: Complete the construction of the corresponding polar code according to the code length and code rate.

4. A low-complexity polar code construction method, characterized in that: The following steps are involved: Step 301. According to the code length N=2 n , the reliability ranking of all N polarized channels is obtained by using the binary expansion reliability ranking generation algorithm o=(o0,o1,…,o N-1 ), the reliability is arranged from high to low from left to right, where n is a non-negative integer; Step 302: Based on the code rate R, the indices of the most reliable NR polarized channels are selected as information bits from the reliability ranking of the N polarized channels. The indices of the remaining N-NR polarized channels are used as frozen bits. This completes the construction of a polar code with code length N and code rate R, where 0 < R < 1. The binary expansion reliability ranking generation algorithm in step 301 includes: First, for each polarization channel Compute the binary expansion of its index i (i n-1 ,i n-2 ,…,i0), and find (i n-1 ,i n-2 ,…,i0), where the code length N=2 n , n is a non-negative integer, i=0,1,…,N-1, d=0,1,…,n; Then, all polarized channels are grouped according to the Hamming weight of the binary expansion of the polarized channel index. All polarized channel groups are {WH d ,0≤d≤n}, if Then (i n-1 ,i n-2 ,…,i0) and (j n-1 ,j n-2 ,…,j0) are all d. The larger the Hamming weight, the higher the reliability of the polarized channel group. Therefore, in the reliability ranking o, o0=o(0)=N-1, o N-1 =o(N-1)=0; Then, when the Hamming weight d decreases from n-1 with a step size of 1, the polarization channel group WH is determined. d Reliability ranking of different polarization channels in d ,if and The smaller the WH d Medium polarization channel The more reliable, where 1≤d≤n-1, n≥2, i k for (i n-1 ,i n-2 ,…,i0), Indicates (i n-1 ,i n-2 ,…,i0) of the subvector (i k-1 ,…,i0), and Next when And β i =β j When i and j are further determined at o d In the order, if we follow the dictionary order, (i n-1 ,i n-2 ,…,i0) has a zero element ratio (j n-1 ,j n-2 ,…,j0) are in the more significant position, then the polarization channel The reliability is higher than that of polarized channels In o d In the example, i is placed before j; The final code length is N=2 n The reliability ranking of all polarized channels of the polar code is o=(o n ,o n-1 ,o n-2 ,…,o 1 ,o 0 )=(N-1,o n-1 ,o n-2 ,…,o 1 ,0).

5. The method according to claim 4, characterized in that If you need to design polar codes with multiple code lengths, the following steps are included: Step 401: Determine the longest code length N. Step 402: Generate a reliability ranking of polarized channels with a maximum code length of N using a binary expansion reliability ranking generation algorithm and store the ranking. Step 403: Based on the nested nature of the reliability rankings of the polarized channels, obtain the reliability ranking of the polarized channels with the required code length. Step 404: Complete the construction of the corresponding polar code according to the requirements of code length and code rate.

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