SCLF decoding method based on information bit metric improved flipping set

Abstract

The invention relates to an SCLF decoding method based on an information bit metric improved flipping set. According to the method, a special relation between R1 codes of adjacent special nodes with different lengths and decoding errors is analyzed, information bit measurement in longer R1 codes is calculated according to the special relation to screen positions where deletion errors easily occur, and the positions are added into a correction key set and arranged in an ascending order according to reliability to obtain a flipping set; and when the CA-SCL decoding has an error, the SCLF decoding exchanges and flips the path decision result of the index in the SC state in the set. Simulation results show that compared with a CA-SCL decoding method, an RCS-SCLF decoding method and an ICS-SCLF decoding method, the provided IBMIFS-SCLF decoding method has better bit error rate performance and lower complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of channel coding, and relates to a SCLF (Successive Cancellation List Bit-Flip based on the IBMIFS, IBMIFS-SCLF) decoding method based on the Improved Flip Set of the Information Bit Metric, IBMIFS in channel coding. The method mainly combines bits with deletion errors in the decoding process with a correction key set to form an improved flip set, and then exchanges the decision results on the successive cancellation (SC) state path in the improved flip set when the first cyclic redundancy check aided serial cancellation list (CA-SCL) decoding fails. Background Art

[0002] The polar code channel coding scheme proposed by Professor Arikan, combined with the SC decoding method, was theoretically proven for the first time to achieve channel capacity in a general discrete memoryless symmetric channel. Compared with traditional channel coding schemes, polar code coding has lower coding complexity and better error correction performance. Therefore, polar code coding is a current research hotspot, and polar code has been successfully selected as the channel coding scheme for the control channel in the 5G (5th Generation mobile communication, 5G) enhanced mobile broadband (enhanced Mobile Broadband, eMBB) scenario, playing an important role in the new generation of mobile communication systems.

[0003] However, due to its serial characteristics, SC decoding will cause serious error propagation during the decoding process, resulting in poor SC decoding performance under limited code length. In order to improve the performance of polar code SC decoding methods, scholars proposed a serial cancellation list (SCL) decoding method. SCL decoding improves error performance by retaining L best candidate paths during the decoding process. In order to improve the SCL decoding method, scholars proposed a CA-SCL decoding method, which adds a cyclic redundancy check (CRC) code to check the L paths generated at the end of SCL decoding. The path that passes the check and has the relatively smallest path metric (PM) value is used as the final decoding result. If there is no path that passes the CRC check, the path with the smallest PM value is directly used as the final decoding result.

[0004] In the process of continuously improving the polar code decoding algorithm, scholars proposed a serial cancellation bit flip (SCF) decoding method. When SC decoding fails, re-decoding is performed, and an error information bit is flipped each time the re-decoding process is performed to avoid error propagation and improve the error performance. Based on the research on the SCF decoding method, scholars use distributed CRC codes to verify the SC decoding process. Once an SC decoding error is found, the decoding process is immediately terminated, which greatly reduces the complexity of the SCF decoding method. In order to improve the error performance of the SCF decoding method, scholars use CRC codes and distributed parity check codes to detect and identify error information bits, so that the position of the first error information bit caused by channel noise is more accurate, thereby improving the error performance. In order to improve the SCF decoding method, scholars proposed the SCLF decoding method, which is a combination of the SCF decoding method and the CA-SCL decoding method. If the CA-SCL decoding does not generate an information sequence that passes the CRC code check, a re-decoding process is performed to exchange the path competition results of the error bit to achieve the purpose of correcting the error bit. Based on the study of SCLF decoding methods, scholars proposed a key set containing most of the error bits. By flipping the bits in the key set, the error performance can be improved. However, due to the influence of dynamic noise, the key set cannot accurately locate the position of the first error bit. Therefore, scholars proposed an advanced decision post-processing method (Decision Post-Processing, D-Post), which defines a new metric for finding error bits. The confidence of each bit is calculated by the PM value obtained during the CA-SCL decoding process, and the bits are flipped from small to large according to the confidence. In view of the problem that the polar code serial cancellation list SCL decoding algorithm has deletion errors during path decision-making, the present invention proposes a SCLF decoding method based on an improved flip set based on information bit metric. This method can effectively screen out locations where deletion errors are prone to occur, and obtain better error performance and lower complexity. Summary of the invention

[0005] In view of this, the object of the present invention is to provide a SCLF decoding method based on information bit metric improved flip set. The method analyzes the special relationship between adjacent special node R1 codes of different lengths and the occurrence of decoding errors, calculates the information bit metric in the longer R1 code according to the special relationship to screen the positions where deletion errors are prone to occur, adds them to the correction key set and arranges them in ascending order of reliability to obtain IBMIFS, when CA-SCL decoding errors occur, SCLF decoding exchanges the path decision results of the indexes in the SC state in IBMIFS, and the remaining bits still perform traditional SCL decoding, and the purpose of correcting the decoding process is achieved by flipping the error bits, thereby improving the error performance and reducing the complexity compared with the traditional SCLF decoding method.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] First, the first critical set (CS) is constructed according to the partial order relationship of the polarization channels. The CS consists of the index of the worst polarization channel in the R1 code corresponding to the polarization code, and the CS is used as the initial critical set. Since the bit decoding paths in the set A′ are all in the cloned state, the decoding always retains and There are two results. Therefore, it is meaningless to flip the bits in A′. It is necessary to remove the bits in A′ in CS to obtain a modified key set suitable for SCLF.

[0008] Then, the special relationship between adjacent R1 codes of different lengths and the occurrence of decoding errors is analyzed. When there are two consecutive R1 code sub-blocks A and B, and the B sub-block is larger, the probability of an erasure error in the B sub-block is greater than that in the A sub-block, and the longer the B sub-block is, the greater the probability of two or more errors. According to this special relationship, the information bit metric in the longer R1 code is calculated to screen the positions prone to erasure errors. The information bit metric of the correct bit is equal to the channel capacity, while the information bit metric of the wrong bit is less than or equal to zero. The information bit metric is used to locate the first information bit of the non-R1 code in the R1 code with a length greater than or equal to the threshold μ in the SCL, and add it to the corrected key set, and the constructed flip set IBMIFS is obtained by arranging them in ascending order of reliability.

[0009] Finally, CA-SCL decoding is performed. If the CA-SCL decoding is successful, the correct decoding path is output. Otherwise, re-decoding is performed. Each re-decoding process sequentially flips a bit of IBMIFS. If there is a path that passes the CRC check during the re-decoding process, the decoding result of this path is output. Otherwise, the next re-decoding process is performed. If the maximum number of re-decoding times has been reached and no path that passes the CRC check has appeared, the path with the smallest PM value in the first CA-SCL decoding is output to achieve IBMIFS-SCLF decoding.

[0010] The beneficial effects of the present invention are:

[0011] The method of the present invention can quickly and accurately locate the bits where deletion errors occur, improve the error performance of the SCLF decoding method, and reduce the decoding complexity. Simulation results show that the proposed IBMIFS can more accurately identify the first error bit caused by channel noise than the RCS in the document [1] "YU Yongrun, PAN Zhiwen, LIU Nan, et al. Successive cancellation list bit-flip decoder for polar codes [C]. 2018 10th International Conference on Wireless Communications and Signal Processing (WCSP). Hangzhou: IEEE, 2018: 1-6.". Compared with the ICS-SCLF decoding method in the document [2] "Liu H, Sha J, Wang X. An improved critical set for list decoding of polar codes [J]. IEEE Communications Letters, 2023, 27 (9): 2269-2273.", the flip set proposed in the IBMIFS-SCLF decoding method can effectively reduce unnecessary re-decoding processes, and obtain better error performance and lower complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0013] Figure 1 A technical roadmap for the method of the present invention;

[0014] Figure 2 It is a schematic diagram of CS;

[0015] Figure 3 Schematic diagram of CA-SCL and SCLF decoding tree;

[0016] Figure 4 It is the block error rate curve of IBMIFS-SCLF decoding method under different R1 code length threshold μ;

[0017] Figure 5 It is the block error rate curve diagram of different decoding methods;

[0018] Figure 6It is a curve chart of average decoding times for different decoding methods; DETAILED DESCRIPTION

[0019] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0020] (1) Combined with Figure 1 The specific implementation process of a SCLF decoding method based on information bit metric improved flip set is as follows:

[0021] Step 1: Construct a critical set (CS) based on the partial order relationship of the polarization channel. The CS consists of the index of the worst polarization channel in the R1 code corresponding to the polarization code. For the CA-SCL decoder, the information bit index set is A. i When , if the path metric matrix is ​​sorted, and If both decoding sub-paths are retained, the path is said to be in a cloned state; if the path metric matrix is ​​sorted, and If both decoding sub-paths are deleted, the path is said to be in the deleted state; if the path metric matrix is ​​sorted, only and If there is only one decoding path, the path is said to be in the SC state.

[0022] The first log2 L bits of information are grouped into a set A′. The bit decoding paths in the set A′ are all in a cloned state. When decoding, the bits are always retained at the same time. and There are two results. Therefore, it is meaningless to flip the bits in A′. It is necessary to remove the bits in A′ in CS to obtain the revised critical set (RCS) suitable for SCLF, which is expressed as RCS=CS\A′.

[0023] Step 2: When the SCL decoder is decoding, there are two types of errors that will cause decoding failure: deletion errors and selection errors.

[0024] Selection error: After decoding, the decoder selects an incorrect path as the final output, and the correct path remains in the final L paths. Selection errors are usually detected through CRC codes.

[0025] Deletion error: During the decoding process, the correct path is deleted from the 2L split paths, and the event that the correct path is eliminated at information position i is recorded as E i , the Lth candidate path and the correct path in the list (index is l c ) are denoted as PM L and PM lcIn the SCL decoder based on the logarithm likelihood ratio (LLR), there are two cases of deletion errors:

[0026] (1) When the hard decision of a high-reliability bit channel fails, the correct path will be penalized by a larger LLR absolute value. In this case, it is difficult to correct the erasure error in a low signal-to-noise ratio environment, and the probability of the correct path being eliminated is expressed as formula (1).

[0027]

[0028] in Indicates bit channel The error probability of hard decisions.

[0029] (2) When the hard decision of a low-reliability bit channel fails, the correct path will be penalized by a smaller LLR absolute value. In SCL decoding, the penalty of a smaller LLR absolute value is unlikely to lead to the elimination of the correct path. If the correct path is repeatedly penalized, although the SCL decoding algorithm can tolerate a single penalty, it will still be eliminated during the decoding process. Assuming that the correct path is penalized k times, in this case, the probability of the correct path being eliminated is estimated as shown in formula (2).

[0030]

[0031] will have M=2 m The error probability of a sub-block of information bits is expressed as P s Now consider a sub-block containing continuous R1 codes. Assuming that the polarization code is encoded in a Gaussian approximation, the polarization channel is approximated as a binary input additive white Gaussian noise (AWGN) channel. Assuming that the transmitter is an all-zero codeword, the LLR mean of the polarization channel is numerically calculated, and then the channel reliability is obtained based on the LLR mean. The larger the mean, the more reliable the channel. The channel polarization law is obtained through the structural characteristics of the polarization code. Channel The mean LLR The calculation of is shown in formulas (3) and (4).

[0032]

[0033] in

[0034]

[0035] Channel Error Probability The calculation of is shown in formula (5).

[0036]

[0037] in erfc(x) is the complementary error function,

[0038] Simplified channel output LLR ~ N (α, 2α), P s Expressed as The probability of error for the first information bit is

[0039] When there are two consecutive R1 code sub-blocks A and B, and sub-block B is larger, the event that the correct path on R1 code sub-block A is deleted is recorded as E A Similarly, the event that the correct path on the B sub-block is deleted is recorded as E B , E A With E B The relationship is shown in formula (6).

[0040]

[0041] where p α is an optimized probability.

[0042] Difference It indicates the probability of two or more errors. A larger R1 code length M and a smaller channel LLR mean α increase the probability of two or more errors. In SCL decoding, due to the accumulated errors, the R1 code block length before sub-block B is smaller, and sub-block B is less reliable when μ of sub-block B is smaller. Therefore, in SCL decoding, the probability of two or more errors is high for R1 codes with larger lengths.

[0043] Step 3: For a given channel output y, SC decoding uses probability P(u i |y) to achieve, however, there is no effective way to calculate the information bit P(u i |y), using Bayes' rule, P(u i |y) is expressed as formula (7).

[0044]

[0045] Due to the symmetry of the channel, P(u i ) item on P(u i |y) has no effect on the maximum value. Formula (7) is replaced by Formula (8).

[0046]

[0047] Due to the monotonicity of the logarithmic function, when the monotonically increasing logarithmic function reaches its maximum value, P(u i|y) is also maximized when decoding to information bit u i When i The information bit metric of is defined as formula (9).

[0048]

[0049] For information bits, a channel with correct bit output, the expectation of the information bit metric is shown in formula (10).

[0050]

[0051] in For Channel capacity.

[0052] For information bits, the average information bit metric of the correct bit always increases, and the information bit metric value of the error bit is at most zero. Assuming that an error occurs in information bit i, the relationship is as shown in formula (11).

[0053] φ(u i ;y,u i-1 )≤0 (11)

[0054] When the information bit metric of information bit i satisfies formula (11), it indicates that the probability of erasure error occurring in information bit i is high.

[0055] Step 4: Establish a full binary tree corresponding to the polar code, divide the polar code into multiple R1 code sub-blocks, obtain the length of each R1 code sub-block, calculate the information bit metric of the R1 code sub-block with an R1 code length greater than or equal to the threshold μ, except for the first information bit. If the calculated information bit metric is less than 0 and the path is in the SC state, add the information bit to the modified key set and arrange it in ascending order of reliability to obtain IBMIFS, and finally apply the obtained IBMIFS to the IBMIFS-SCLF decoding method.

[0056] Step 5: Execute CA-SCL decoding. If the first CA-SCL decoding passes the CRC check, the path that passes the CRC check and has the smallest PM is directly output. Otherwise, re-decoding based on IBMIFS is performed. The re-decoding process sequentially flips the bits in IBMIFS, and only flips one bit each time the re-decoding is performed. If the re-decoding process passes the CRC check, the correct decoding path is output. Otherwise, the next re-decoding process is performed. When the number of re-decoding times reaches the maximum value and the correct decoding sequence has not been obtained, the decoding path with the smallest PM value in the first CA-SCL decoding is output. For the SCLF decoder, the flipping scheme of this decoding method makes the flipped bit u i The path competition decision results of the corresponding clone state path and deleted state path remain unchanged, and the path competition decision result of the SC state path is opposite to the standard CA-SCL decoding.

[0057] (2) Combined with attachment Figure 2 Explain the construction method of CS:

[0058] CS consists of the index of the worst polarization channel in the corresponding R1 code in the polar code. Figure 2 The polar code with code length N=8 and A={4,6,7,8} is shown. The black nodes indicate that all its leaf nodes are information bits, the white nodes indicate that all its leaf nodes are frozen bits, the gray nodes indicate that its leaf nodes have both information bits and frozen bits, the solid rectangular box indicates the sub-polar code with code rate 1, and the bit index in the dashed rectangular box constitutes CS, which is denoted as CS={4,6,7}.

[0059] (3) Combined with attachment Figure 3 The selection of the bit flipping scheme is described as follows:

[0060] According to the decoding u i The flipping schemes are divided into two types according to the state of the path at that time. Assume that the list size L = 4, u1, u2, u3 and u5 are information bits, u4 is a frozen bit, and u5 is a flip bit. The black nodes represent the retained paths, and the white nodes represent the deleted paths. Figure 3 (a) is the standard CA-SCL decoding process, in which both extended paths of node A are deleted and in the deleted state; both extended paths of node B are retained and in the cloned state; and only one extended path is retained for nodes C and D, both in the SC state. Figure 3 (b) and (c) are two flipping schemes of the SCLF decoding method. Figure 3 In the flipping scheme shown in (b), when decoding u5, the path competition decision results of all nodes are the same as Figure 3 In contrast to (a), it is possible to avoid obtaining the same codeword estimate as in standard CA-SCL decoding. Figure 3 In the flipping scheme shown in (c), nodes A and B keep Figure 3 The decision result of (a) is that nodes C and D are Figure 3 The decision result of (a) is the opposite. Figure 3 (c) is the flipping solution of the method proposed in the present invention.

[0061] (4) Combined with attachment Figure 4 The optimal length threshold μ of the R1 code of the method of the present invention is described as follows:

[0062] The optimal μ value is obtained by simulating the bit error performance of the IBM IFS-SCLF decoding method under different μ conditions. μ = 4, 8, 16 and 32 are selected for simulation analysis, and the maximum number of flips T = 50 is set. Figure 4 The error performance of the decoder is studied when μ=4, 8, 16, and 32, and it is found that the performance is best when μ=8.

[0063] (5) Combined with attachment Figure 5 ,6 illustrates the superiority of the method of the present invention, the simulation is as follows:

[0064] In order to verify the superiority of the method proposed in this invention, the error performance and complexity of the IBM IFS-SCLF decoding method are simulated and analyzed. The simulation conditions are: the polar code length N = 1024, the code rate R = 0.5, the list size L = 8, the codeword is modulated by BPSK and transmitted in the AWGN channel, the Gaussian approximation construction method with a signal-to-noise ratio SNR = 2.5dB is used, the CRC check code length r = 16, and the corresponding generating polynomial is g 16 (x) = x 16 +x 15 +x 2 +1, the number of simulation iterations is 10 6 .

[0065] The IBM IFS-SCLF decoding method proposed in the present invention is compared with the CA-SCL decoding method in the document [3] "NIU Kai, CHEN Kai. CRC-aided decoding of polar codes [J]. IEEE Communications Letters, 2012, 16 (10): 1668-1671.", the RCS-SCLF decoding method in the document [1] and the ICS-SCLF decoding method in the document [2], and the block error rate and average decoding times of the above methods are analyzed.

[0066] The IBM IFS-SCLF decoding method has better error performance than other decoding methods. -4 In the case of , the BMFS-SCLF decoding method has gains of 0.23dB, 0.09dB, 0.19dB, and 0.07dB respectively compared with the CA-SCL decoding method with list size L = 8 and 16, the RCS-SCLF decoding method and the ICS-SCLF decoding method.

[0067] The computational complexity of the bit flipping method can be described as the average number of decoding times. The higher the average number of decoding times, the higher the computational complexity. When the complexity of the CA-SCL decoder is normalized to 1 when the list size L=8, the IBMIFS-SCLF decoding method has a lower complexity than the RCS-SCLF decoding method and the ICS-SCLF decoding method. At 1dB, the complexity of the IBMIFS-SCLF decoding method is reduced by 31.1% and 21.6% compared with the RCS-SCLF decoding method and the ICS-SCLF decoding method, respectively. The number of indexes in the flipping set of the IBMIFS-SCLF decoding method is greater than the number of indexes in the corrected key set, but this flipping set contains more accurate decoding error positions, and the identification of erroneous bits is more accurate, thereby reducing the number of re-decoding and the complexity of the decoding algorithm.

[0068] The higher the error performance and the lower the complexity of the decoding method, the more superior it is. Therefore, the IBM IFS-SCLF decoding method proposed in the present invention has a strong advantage.

Claims

1. A SCLF (Successive Cancellation List Bit-Flipbased on the IBMIFS, IBMIFS-SCLF) decoding method based on the Improved Flip Set based on the Information Bit Metric, IBMIFS. The method aims at the problem of deletion error in path decision of the polar code serial cancellation list (SCL) decoding method, analyzes the special relationship between the adjacent special node R1 codes of different lengths and the occurrence of decoding errors, calculates the information bit metric in the longer R1 code according to the special relationship to screen the positions prone to deletion errors, adds them to the corrected key set and arranges them in ascending order of reliability to obtain the IBMIFS. When an error occurs in the cyclic redundancy check aided successive cancellation list (CA-SCL) decoding, the SCLF decoding exchanges the path decision results of the index in the SC state in the IBMIFS, and the remaining bits still perform traditional SCL decoding. The specific steps of the method are as follows: Step 1: Construct a critical set (CS) based on the partial order relationship of the polarization channel. The CS consists of the index of the worst polarization channel in the R1 code in the polarization code. For the CA-SCL decoder, the information bit index set is A. i When , if the path metric matrix is ​​sorted, and If both decoding sub-paths are retained, the path is said to be in a cloned state; if the path metric matrix is ​​sorted, and If both decoding sub-paths are deleted, the path is said to be in the deleted state; if the path metric matrix is ​​sorted, only and If one of the decoding paths is in the SC state, then the path is said to be in the SC state; The first log2L bits of information are grouped into a set A′. The bit decoding paths in the set A′ are all in a cloned state. When decoding, the bits are always retained at the same time. and There are two results. Therefore, it is meaningless to flip the bits in A′. It is necessary to remove the bits in A′ in CS to obtain the Revised Critical Set (RCS) suitable for SCLF, which is expressed as RCS = CS\A′. Step 2: When the SCL decoder is decoding, there are two types of errors that will cause decoding failure: deletion errors and selection errors; Selection error: After decoding, the decoder selects an incorrect path as the final output, and the correct path remains in the final L paths. The selection error is usually detected by a cyclic redundancy check (CRC) code; Deletion error: During the decoding process, the correct path is deleted from the 2L split paths, and the event that the correct path is eliminated at information position i is recorded as E i , the Lth candidate path and the correct path in the list (index is l c ) are denoted as PM L and PM lc In the SCL decoder based on the logarithm likelihood ratio (LLR), there are two cases of deletion errors: (1) When the hard decision of a high-reliability bit channel fails, the correct path will be penalized by a larger LLR absolute value. In this case, it is difficult to correct the erasure error in a low signal-to-noise ratio environment. The probability of the correct path being eliminated is expressed as formula (1): in Indicates bit channel The error probability of hard decisions; (2) When the hard decision of a low-reliability bit channel fails, the correct path will be penalized by a smaller LLR absolute value. In SCL decoding, the penalty of a smaller LLR absolute value is unlikely to lead to the elimination of the correct path. If the correct path is repeatedly penalized, it will still be eliminated during the decoding process even though the SCL decoding algorithm can tolerate a single penalty. Assuming that the correct path is penalized k times, in this case, the probability of the correct path being eliminated is estimated as formula (2): will have M=2 m The error probability of a sub-block of information bits is expressed as P s Now consider a sub-block containing continuous R1 codes. Assuming that the polarization code is encoded in a Gaussian approximation, the polarization channel is approximated as a binary input additive white Gaussian noise (AWGN) channel. Assuming that the transmitter is an all-zero codeword, the LLR mean of the polarization channel is numerically calculated, and then the channel reliability is obtained based on the LLR mean. The larger the mean, the more reliable the channel. The channel polarization law is obtained through the structural characteristics of the polarization code. Channel The mean LLR The calculation of is shown in formulas (3) and (4): in Channel Error Probability The calculation of is shown in formula (5): in erfc(x) is the complementary error function, Simplified channel output LLR ~ N (α, 2α), P s Expressed as The probability of error for the first information bit is When there are two consecutive R1 code sub-blocks A and B, and sub-block B is larger, the event that the correct path on R1 code sub-block A is deleted is recorded as E A Similarly, the event that the correct path on the B sub-block is deleted is recorded as E B , E A With E B There are the following relationships: where p α is an optimization probability; Difference It indicates the probability of two or more errors. A larger R1 code length M and a smaller channel LLR mean α increase the probability of two or more errors. In SCL decoding, due to the accumulation of errors, the R1 code block before sub-block B is smaller, and sub-block B is less reliable when μ of sub-block B is smaller. Therefore, in SCL decoding, the probability of two or more errors is high for R1 codes with larger lengths. Step 3: For a given channel output y, SC decoding uses probability P(u i |y) to achieve, however, there is no effective way to calculate the information bit P(u i |y), using Bayes' rule, P(u i |y) is expressed as: Due to the symmetry of the channel, P(u i ) item on P(u i |y) has no effect on the maximum value, and formula (7) is replaced by formula (8): Due to the monotonicity of the logarithmic function, when the monotonically increasing logarithmic function reaches its maximum value, P(u i |y) is also maximized when decoding to information bit u i When i The information bit metric is defined as: For information bits, the expectation of the information bit metric for a channel with correct bit output is: in For Channel Capacity; For information bits, the average information bit metric of the correct bit always increases, and the information bit metric value of the error bit is at most zero. Assuming that an error occurs in information bit i, the following relationship holds: φ(u i ;y,u i-1 )≤0 (11) When the information bit metric of information bit i satisfies formula (11), it indicates that the probability of deletion error occurring in information bit i is high; Step 4: Establish a full binary tree corresponding to the polar code, divide the polar code into multiple R1 code sub-blocks, obtain the length of each R1 code sub-block, calculate the information bit metric of the R1 code sub-block with an R1 code length greater than or equal to the threshold μ, except for the first information bit. If the calculated information bit metric is less than 0 and the path is in the SC state, add the information bit to the modified key set and arrange them in ascending order of reliability to obtain IBMIFS, and finally apply the obtained IBMIFS to the IBMIFS-SCLF decoding method; Step 5: Execute CA-SCL decoding. If the first CA-SCL decoding passes the CRC check, directly output the path that passes the CRC check and has the smallest PM. Otherwise, perform re-decoding based on IBMIFS. The re-decoding process sequentially flips the bits in IBMIFS, and only flips one bit each time the re-decoding process passes the CRC check. If the re-decoding process passes the CRC check, output the correct decoding path. Otherwise, perform the next re-decoding process. When the number of re-decoding times reaches the maximum value and the correct decoding sequence has not been obtained, output the decoding path with the smallest PM value in the first CA-SCL decoding. For the SCLF decoder, the decoding method flips the scheme to flip the bit u i The path competition decision results of the corresponding clone state path and deleted state path remain unchanged, and the path competition decision result of the SC state path is opposite to the standard CA-SCL decoding.

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