A high-performance polar code belief propagation list decoding method based on double-end post-processing

Abstract

The application provides a high-performance polar code belief propagation list decoding method based on double-end post-processing, belongs to the technical field of wireless communication channel coding and decoding, and comprises the following steps: initialization, belief propagation basic iteration, hard decision and CRC check, U-end reliability measurement construction, segmented convergence determination, U-end reliable bit enhancement, X-end unreliable bit identification, X-end flip disturbance, and repeated iteration until decoding is completed. Through the targeted post-processing operation simultaneously performed on the U end and the X end, the problems of limited performance gain of the existing single-end post-processing, insufficient convergence determination accuracy, and a large performance gap between the BPL decoding and the CA-SCL decoding are solved. The method simultaneously introduces the U-end reliable bit enhancement and the X-end unreliable bit flip disturbance on the basis of the traditional BPL decoding, so as to improve the ability of the decoder to get rid of the local error convergence state, thereby improving the decoding performance.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication channel coding and decoding technology, specifically relating to a decoding method for polar codes in 5G and future mobile communication systems, and particularly a high-performance polar code belief propagation list (BPL) decoding method that combines prior information correction at the source end (U end) with factor graph perturbation at the channel end (X end). Background Technology

[0002] Polar codes, proposed by Professor Arikan in 2009, are a channel coding scheme that can be theoretically proven to achieve Shannon capacity. With the evolution of 5G mobile communication systems towards enhanced mobile broadband (eMBB), ultra-reliable ultra-low latency communication (URLLC), and other scenarios, polar codes, due to their ability to approximate channel capacity with short code lengths, have been adopted by the 3GPP standard as the control channel coding scheme for 5G eMBB scenarios. Among the many decoding algorithms for polar codes, Serial Cancellation (SC) decoding and its improved version, Serial Cancellation List (SCL) decoding, have excellent error correction performance. However, their inherent serial processing characteristics lead to high decoding latency, making it difficult to meet the demands of future ultra-low latency communication.

[0003] In contrast, the Belief Propagation (BP) decoding algorithm is based on the factor graph for parallel information transmission, which has the advantages of high throughput and low latency, and is very suitable for hardware parallel implementation. However, under short or medium-short code lengths, standard BP decoding is limited by the short loop structure in the factor graph, and its block error rate (BLER) performance is often inferior to that of the SCL decoding algorithm. In order to improve the performance of BP decoding, the existing technology proposes the Belief Propagation List (BPL) decoding algorithm (Reference [1]: A. Elkelesh, M. Ebada, S. Cammerer, and S. ten Brink, “Belief Propagation List Decoding of PolarCodes,” IEEE Communications Letters, vol. 22, no. 8, pp. 1536–1539, Aug.2018), which generates multiple sets of permutation factor graphs by rearranging the stage order of the polar code factor graph, and decodes in parallel to expand the candidate codeword search space. With a sufficiently large list size, it can approach the performance of SCL decoding. However, due to practical engineering constraints on list size (such as L=8, 32), there is still a significant performance gap between BPL decoding and CRC-assisted SCL (CA-SCL) decoding.

[0004] Polar code belief propagation algorithm is an iterative decoding algorithm. Post-processing the decoding process based on the intermediate information of the iteration is a kind of efficient performance improvement method. Existing research mainly focuses on single-end post-processing optimization: the channel end (X end) based method corrects local convergence errors through two-level error detection and post-processing (reference [2]: B. Feng, R. Liu, and K. Tian, ​​“A Novel Post-Processing Method for Belief Propagation List Decodingof Polar Codes,” IEEE Commun. Lett., vol. 25, no. 8, pp. 2468–2471, Aug.2021), but the accuracy of error location identification is insufficient; the source end (U end) based method accelerates convergence by dynamically updating the initial value of the right information, only obtains a very small performance gain under high signal-to-noise ratio, and cannot effectively correct the error convergence direction (reference [3]: Z. Yang, Z. Cait, L. Chen, and H. Zhang, “An Efficient Adaptive BeliefPropagation Decoder for Polar (Codes, in 2024 IEEE Information Theory Workshop (ITW), Nov. 2024, pp. 466–471). These single-end post-processing optimization schemes all suffer from limited performance improvement and poor adaptability to channel conditions, making it difficult to meet the stringent decoding reliability requirements of 5G systems. Therefore, there is an urgent need for a high-performance belief propagation decoding optimization method that balances performance gain and engineering implementation complexity.

[0005] Therefore, this invention proposes a high-performance decoding method based on the belief propagation algorithm of polar codes, which simultaneously performs post-processing from both the U and X ends. This method narrows the performance gap between BPL and CA-SCL while maintaining the complexity without excessive increase, in order to meet the needs of practical engineering applications. Summary of the Invention

[0006] This invention proposes a polar code BPL decoding method based on dual-end post-processing. By simultaneously performing targeted post-processing operations on both the U-end and X-end, it addresses the limitations of existing single-end post-processing methods, such as limited performance gain, insufficient convergence accuracy, and the significant performance gap between BPL and CA-SCL decoding. The core process includes: codeword segmentation, intra-segment reliability metric calculation, U-end reliability matrix construction, X-end unreliable location identification, and dual-end post-processing optimization on both the U-end and X-end. Ultimately, this achieves a significant improvement in decoding performance while maintaining low hardware complexity.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A high-performance polar code belief propagation list decoding method based on dual-end post-processing includes the following steps: Step 1: Initialize the decoding parameters and information matrix. Let the polar code length be... The log-likelihood ratio of the input channel at the receiving end is The information bit set is The set of frozen positions is The decoder list has a size of L and a maximum number of iterations of I. max The CRC generator polynomial has a length of L. crc Construct a left information matrix L and a right information matrix R on the polar code factor graph. These two matrices store soft information during the iteration process, satisfying... and ,in Indicates the factor layer number. Indicating bit positions, during the initialization phase, only the rightmost layer of the left information matrix L is considered. And the leftmost layer of the right information matrix R Perform initial assignment on the rightmost layer of the left information matrix L. Initialization command (1) For the leftmost layer of the right information matrix R During initialization, if the first One bit is the freeze bit ( ),but, (2) If the first Each bit is an information bit ( ),but, (3) Step 2: Perform BPL basic iterative decoding. For each branch of the permutation factor graph, alternately perform layer-by-layer updates of the left information matrix L in the factor graph according to the confidence propagation update rule (from...). The propagation of information from s = n to s = 0 is called leftward information update, and the layer-by-layer update of the right information matrix R (from...) The propagation from s = 0 to s = n (called rightward information update) is recursively defined as follows: (4a) (4b) (4c) (4d) in, This represents the value of the i-th bit position in the s-th layer of the left information matrix. Represents the s-th layer of the left information matrix. The value of each bit position This represents the value of the i-th bit position in the (s+1)-th layer of the right information matrix. This indicates the (s+1)th layer of the right information matrix. The value of each bit position. For box-type approximation, it is taken as follows in this invention: (5) In the formula, a and b are the two input variables of the box approximation operation, both of which are log-likelihood ratios representing confidence in the real number field; sign() is the sign function, which takes +1 when the input is positive, -1 when it is negative, and +1 when it is zero; min(|a|,|b|) means taking the smaller value between |a| and |b|; the coefficient 0.9375 is an empirical correction factor used to compensate for the estimation bias caused by the minimum approximation.

[0008] After each iteration, the values ​​of the left information matrix L and the right information matrix R at the U-end (layer s=0) are used to determine the optimal values. and The sum is used for hard judgment, and the position of the information bits is determined. ,make: (6) in, This represents the hard decision result for the i-th bit position, for the frozen bit position. Ordered directly without a judgment Then, the information sequence obtained from the decision is extracted according to the original information bit order, and the CRC remainder vector corresponding to the current iteration is calculated. If the CRC check passes, decoding stops and the result is output; if the CRC check fails, subsequent dual-end post-processing steps are initiated.

[0009] Step 3: Segment the information sequence and construct segmented information sub-blocks. At the U-end, the sequence containing information bits and freeze bits of length N described in Step 1 is evenly divided into P segments, each segment having a length of... , No. p The index range of the segment is: (7) in, For the p-th segment, extract the left information sub-block of the U-end of that segment. U-end right information sub-block Sub-block frozen bit set and sub-block information bit set .

[0010] Step 4: U-end information bits The soft information symbol fluctuation count is performed. To measure the convergence of each information bit in the U-terminal, the soft information symbol changes of all information bits within each segment are statistically analyzed in consecutive iterations. Let the th... t During the next iteration, the p-th segment... k The symbols for each position are: (8) in, This indicates the number of segments within the p-th segment at the t-th iteration. k ( k =0,1,…, The left information value of the U-end of the information bits. This indicates the number of segments within the p-th segment at the t-th iteration. k ( k =0,1,…, The left information symbol value of the U-end of ) information bits.

[0011] If the following conditions are met: (9) Then, the sign change count at the k-th information bit position within the p-th segment is incremented by one, denoted as: (10) in, This represents the cumulative number of symbol changes at the k-th information bit position of the p-th segment during the t-th iteration. This is the cumulative value from the previous iteration, and the initial value. The larger the count value, the more violently the corresponding position oscillates during the iteration.

[0012] Step 5: Calculate the reliability metric for the U-end information bits and construct the segmented reliability ranking matrix. The CRC check remainder is the same in two consecutive iterations, satisfying the following condition: (11) in, This indicates the hard decision result after the t-th iteration. The CRC remainder vector is extracted and calculated according to the information bit order; This represents the CRC remainder vector corresponding to the (t-1)th iteration. When both are equal, it indicates that the decoding result has not changed in two consecutive iterations, and the decoder may have entered a local error stable state. Therefore, to determine if the current decoding process has entered a local error stable state, it is necessary to identify reliable and unreliable bits from the U terminal. Based on the information bit symbol change count in step 4, a corresponding reliability metric can be constructed: (12) in, This represents the reliability metric value of the k-th information bit in the p-th segment at the t-th iteration. This is the cumulative number of sign changes at this position (see formula (10) in step 4). The larger the value, the more volatile the corresponding position is during iteration, and the lower the reliability. For each segment p, only the set of information bits is considered. The location in the middle, according to reliability metrics Sort the results from smallest to largest to obtain an ordered index sequence: (13) in, The most reliable information bit is the original sequence number within the p-th segment. The information bit with the lowest reliability is the original sequence number within the p-th segment. This satisfies: (14) in, This represents the reliability metric value corresponding to the j-th position after sorting. This sequence of inequalities indicates that the reliability decreases sequentially from front to back after sorting. The dimension is constructed according to this method. Reliability ranking matrix Its p-th column (p = 0, 1, ..., P-1) stores the reliability sorting sequence of the p-th segment (as shown in formula (13)). When the number of information bits of a certain segment When there is less than M, the end of the line Each position is filled with a value of -1, and the number of information bits in each segment is determined accordingly. Adaptively determine the maximum enhancement bits for this segment. (satisfy ).

[0013] Step 6: Determine the convergence status of the frozen points for each segment. For each segment... p Detect the left information value of the U-end corresponding to the frozen position within this segment. If the following conditions are met: (15) in, This indicates the position of the k-th frozen position within the p-th segment ( The left information value of the U end of the ) For the frozen position subset within segment p, at this time This indicates that the left information of the U-end of the frozen bit has converged towards the correct 0 value direction. Therefore, the segment is determined to be in a reliable convergence state, and the convergence flag for this segment is recorded as [symbol missing]. Otherwise, record as The convergence flag is used to limit U-end post-processing to be performed only in segments where the frozen bits have been reliably converged.

[0014] Step 7: Perform post-processing to enhance the reliability of the U-end bit. For those that meet the requirements... The segment p is determined from the reliability ranking matrix of that segment. The enhancement set is constructed by selecting several of the most reliable information bits from the front end: (16) in, Let be the number of augmented bits in the current iteration of this segment, and satisfy: (17) For enhanced sets For any information bit number k in the sequence, the right information at the U end corresponding to the position of this information bit will be... Updated to: (18) in, This represents the right information value at the U-end of the k-th information bit within the p-th segment. Let be the left information value of the U-end at this position. The meaning of formula (18) is: directly copy the current left information value of the reliable information bit to the right information bit as an enhanced prior for the next iteration, thereby enhancing the correct convergence direction of the reliable information bit in subsequent iterations.

[0015] Step 8: Perform unreliable position identification and flip perturbation post-processing at the X end. Same as steps 6 and 7, i.e., when the CRC check remainder vectors obtained from two consecutive iterations are equal ( When the condition is met (see formula (11)), it indicates that the decoding has entered a local error stable state. At this time, while performing post-processing (steps 6-7) at the U end, unreliable position identification and flip perturbation post-processing (step 8) are also performed at the X end. In other words, the U end post-processing and the X end post-processing are activated synchronously by the same triggering condition and are executed at the same time.

[0016] At this point, the reliability of location identification at end X based on comprehensive soft information is as follows: (19) in, The comprehensive soft information value (i = 0, 1, ..., N-1) representing the bit position of the i-th codeword is defined as the left information of the X-end at that position. Information from the X end sum. The smaller the value, the lower the confidence level of the current decision at that position, and the more likely it is to be an unreliable position.

[0017] Specifically, calculate the comprehensive soft information of all N codeword bit positions. (i = 0, 1, ..., N-1), press Select directly in ascending order. The four positions with the smallest values ​​are considered the least reliable positions globally, denoted as . ,satisfy: (20) in, for Minimum position index, The second smallest position index, The third smallest position index, Let j be the fourth smallest position index, and j be the divisor. The indices of any codeword bit position other than those specified. The meaning of this set of inequalities is: the selected 4 positions... The value is not greater than any other value. The value, that is, these four positions are the positions with the lowest decision confidence. Then, for the four globally least reliable positions... Apply a flip perturbation and update the rules as follows: , (twenty one) in, This represents the j-th globally least reliable position. The left information value at the X end (j = 1, 2, 3, 4). This is the right information value at the X end of this position. To preset a fixed disturbance amplitude, this disturbance amplitude will be the left information value at the X end of the most unreliable position. It forces the direction to the opposite of the current decision direction, thereby breaking the local error stability point.

[0018] Step 9: Repeat the iteration until decoding is complete. Use the U-end enhancement result obtained in Step 7 (i.e., the updated value) Write back the right information matrix R. For the bit position i = s·M + k in layer 0, the X-end flip perturbation result obtained in step 8 (i.e., the updated value) is... Write back the left information matrix L Bit position corresponding to the nth layer After completing the above writing, continue to execute the next round of confidence propagation iteration, repeating steps 2 to 9 until the CRC check passes or the maximum number of iterations is reached, and output the corresponding decoding result when decoding terminates.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention performs post-processing from both the U and X ends simultaneously, which not only enhances the correct convergence direction of reliable information bits, but also applies reverse intervention to unreliable positions, giving it a stronger ability to overcome local errors compared to schemes that rely solely on the U or X ends.

[0020] 2. This invention introduces a segmented convergence determination mechanism, which only starts post-processing when a local sub-block meets the reliable freezing point condition. This can significantly improve the accuracy of post-processing triggering and reduce the performance loss caused by premature intervention.

[0021] 3. This invention adopts a reliability metric based on the number of changes in soft information symbols, which is easy to implement using counters and shift logic, has low hardware complexity, and is suitable for high-parallelism hardware deployment requirements.

[0022] 4. According to the simulation results, the dual-end post-processing BPL (L=32) of the present invention can achieve a performance improvement of nearly 1.5dB at a frame error rate of about 10^(-4) compared with the traditional BPL (L=32), and can reach the performance level of CA-SCL8. It also has good adaptability to different code lengths and code rates. Attached Figure Description

[0023] Figure 1 This is a flowchart of the overall process of the high-performance polar code belief propagation list decoding method based on dual-end post-processing of the present invention.

[0024] Figure 2 This is a schematic diagram illustrating the convergence of information at the left end of the U-shaped frame in this invention, showing the location of the erroneous bit.

[0025] Figure 3 This is a schematic diagram illustrating the convergence of information at the left end of the U-terminal in the case of the correct bit position of the misaligned frame in this invention.

[0026] Figure 4 The diagram shows a comparison of the frame error rate performance of the decoding algorithm of this invention with the traditional BPL decoding algorithm and the CA-SCL decoding algorithm when the list size is L=32, the code length is N=128, and K=20.

[0027] Figure 5 The diagram shows a comparison of the frame error rate performance of the decoding algorithm of this invention with the traditional BPL decoding algorithm and the CA-SCL decoding algorithm when the list size is L=32, the code length is N=128, and K=40.

[0028] Figure 6 The diagram shows a comparison of the frame error rate performance of the decoding algorithm of this invention with the traditional BPL decoding algorithm and the CA-SCL decoding algorithm when the list size is L=32, the code length is N=128, and K=72.

[0029] Figure 7 The diagram shows a comparison of the frame error rate performance of the decoding algorithm of this invention with the traditional BPL decoding algorithm and the CA-SCL decoding algorithm when the list size is L=32, the code length is N=1024, and K=232. Detailed Implementation

[0030] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] This invention proposes a high-performance polar code belief propagation list decoding method based on dual-end post-processing, applied to the belief propagation list decoding process of polar codes. This method, based on traditional BPL decoding, simultaneously introduces reliable bit enhancement at the U-end and unreliable bit flipping perturbation at the X-end to improve the decoder's ability to escape local error convergence states, thereby enhancing decoding performance.

[0032] like Figure 1 As shown, the decoding method of the present invention includes the following steps: initialization, confidence propagation basic iteration, hard decision and CRC check, U-end reliability metric construction, segmented convergence determination, U-end reliable bit enhancement, X-end unreliable position identification, X-end flip perturbation, and repeated iteration until decoding ends.

[0033] Example: Step 1: Initialize the decoding parameters and information matrix. Let the polar code length be... Where n=7 is the maximum number of layers in the factor graph, the information bit length K=40, the CRC length is 24 bits, and after receiving the channel output, the receiver obtains the log-likelihood ratio sequence corresponding to each codeword position. During decoding initialization, the left information matrix L and the right information matrix R on the polar code factor graph are established, satisfying... and ,in Indicates the factor layer number. Indicates the codeword position index. Initializes the rightmost channel information. At the same time, based on the set of frozen bits and the set of information bits, the leftmost and rightmost information bits are... Perform initialization.

[0034] Step 2: Perform BPL basic iterative decoding. In each iteration, first perform the layer-by-layer update of the left information matrix L in standard belief propagation decoding, then perform the layer-by-layer update of the right information matrix R. After completing one round of left and right information updates, based on the values ​​of the left information matrix L and the right information matrix R at the U end (layer s=0), and The sum is used for hard decision. Then, K=20 information bits are extracted from the decision result in the original information bit order and a CRC check is performed. If the CRC check passes, the decoding result is output and decoding ends; if the CRC check fails, the double-ended post-processing process begins.

[0035] Step 3: Segment the information sequence and construct segmented information sub-blocks. To improve the accuracy of post-processing, this invention first uniformly segments the codeword, dividing a codeword of length N into P=4 consecutive sub-blocks, each sub-block having a length M=32. For each segment, the corresponding U-end left information sub-block is extracted. , k=0,1,…,31 and the right information sub-block k=0,1,…,31 and record the set of frozen bits and the set of information bits in this segment.

[0036] Step 4: U-end information bits The soft information symbol fluctuation count is then performed. Subsequently, the number of soft information symbol fluctuations in each segment is counted to characterize its convergence degree. If the symbol of the left information at the U end at the k position of the p-th segment is different in two consecutive iterations, the symbol change counter at that position is incremented by 1. If the symbol remains unchanged in two consecutive iterations, the original count is kept unchanged. Figure 2 The convergence of the erroneous bit position in the left information of the U-end is shown in the case of frame error. It can be seen that the erroneous bit position often crosses repeatedly near zero and oscillates multiple times. Figure 3 The diagram illustrates the convergence of the correct bit position in the left information of the U-end under frame errors. It shows that the correct bit position typically converges faster in a single direction, with significantly fewer symbol changes. Therefore, this invention employs a reliability metric based on the number of symbol changes, effectively distinguishing between reliable and unreliable positions.

[0037] Step 5: Calculate the reliability metric of the U-end information bits and construct the segmented reliability ranking matrix. Activate the post-processing states of the U-end and X-end using CRC stability features. When two consecutive iterations of CRC verification fail and the CRC remainder vectors are the same, it can be determined that the current decoding has entered a locally stable but erroneous convergence state. At this point, post-processing of the U-end and X-end is initiated.

[0038] For the U-terminal, the reliability measure of each segment information bit is updated based on the value of the symbol fluctuation counter. The larger the value, the more frequently the corresponding position oscillates around zero during the iteration process, and the lower the reliability. The smaller the value, the more stable the convergence direction of the corresponding position, and the higher the reliability.

[0039] After obtaining the reliability metric, the information bits in each segment are processed according to... Sort the data in ascending order to obtain the reliability ranking sequence for that segment. ,in This indicates the number of information bits in the segment. The dimension is constructed using this method. The reliability ranking matrix, in this embodiment, consists of 4 segments. Furthermore, based on the number of information bits in each segment Configure the maximum enhancement bit depth for each segment. .

[0040] Step 6: Determine the convergence status of the freeze points for each segment. To determine the appropriate post-processing timing, for each segment, first determine whether its freeze points have reliably converged. p When all the frozen bits in a segment are greater than 0, that is, only when all the frozen bits in the segment converge in the correct direction, is the segment considered to have entered a reliable convergence state and subsequent U-end post-processing operations allowed to take effect.

[0041] Step 7: Perform post-processing to enhance the reliability of the U-end bit. For those that meet the requirements... The segmentation is performed, and reliable bit enhancement post-processing is carried out at the U end. The corresponding segment is selected from the front of the reliability sorting matrix. Iterative enhancement is performed on the most reliable information bits, i.e. This update will update the reliable information bit to the left information of the current iteration. This feedback is then fed back into the next iteration, thereby further enhancing its correct convergence trend.

[0042] Step 8: Perform unreliable position identification and flip perturbation post-processing at the X end. In the X-end post-processing, first calculate the comprehensive soft information value of the N codeword bit positions. ,because The smaller the value, the lower the confidence level of the current decision at that position. Therefore, this invention uses... The position with the smallest value is selected as a candidate for an unreliable position at the X end. Preferably, the position is selected directly. The 4 positions with the smallest values As the least reliable position globally, for each selected position, the flip direction factor is determined based on the sign of its current synthesized soft information: (twenty two) Assume a fixed disturbance amplitude of Then, the following flipping perturbation is applied to the unreliable position: , (twenty three) This operation is equivalent to forcibly pushing the left information of the X end at the most unreliable position to the opposite direction of the original decision direction, in order to disrupt the local error stability point.

[0043] Step 9: Repeat the iteration until decoding is complete. After completing the reliable bit enhancement at the U end in Step 7 and the X end flipping perturbation in Step 8, rewrite the updated information into the decoding matrix and continue to execute the next round of confidence propagation iterations. Repeat the above process until the CRC check passes in a certain iteration or the number of iterations reaches the preset maximum number of iterations. When the CRC check passes, output the corresponding decoding result; when the maximum number of iterations I=200 is reached and the CRC check still fails, output the current candidate decision result.

[0044] The performance of the method of this invention was verified under several typical polar code parameters. Figure 4The results show the frame error rate performance comparison between the decoding algorithm of this invention, the traditional BPL decoding algorithm, and the CA-SCL decoding algorithm when the list size L=32, the code length N=128, the information length K=20, and the CRC is 24 bits. The simulation results show that the method of this invention is almost similar to the performance of CA-SCL8. Compared with the traditional BPL, the method of this invention has a performance gain of 0.8dB when the BLER reaches 10^(-4).

[0045] Figure 5 The results show the frame error rate performance comparison between the decoding algorithm of this invention, the traditional BPL decoding algorithm, and the CA-SCL decoding algorithm when the list size L=32, the code length N=128, the information length K=40, and the CRC is 24 bits. The simulation results show that when the BLER reaches 10^(-4), the performance degradation of the method of this invention CA-SCL8 is no more than 0.1dB compared with the traditional BPL, and the performance gain of the method of this invention is 1.3dB compared with the traditional BPL.

[0046] Figure 6 The results show the frame error rate performance comparison between the decoding algorithm of this invention, the traditional BPL decoding algorithm, and the CA-SCL decoding algorithm when the list size L=32, the code length N=128, the information length K=72, and the CRC is 24 bits. The simulation results show that when the BLER reaches 10^(-3), the performance degradation of the method of this invention CA-SCL8 is no more than 0.2dB compared with the traditional BPL, and the performance gain of the method of this invention is 0.7dB compared with the traditional BPL.

[0047] Figure 7 The results show the frame error rate performance comparison between the decoding algorithm of this invention, the traditional BPL decoding algorithm, and the CA-SCL decoding algorithm when the list size L=32, the code length N=1024, the information length K=232, and the CRC is 24 bits. The simulation results show that when the BLER reaches 10^(-4), the performance degradation of the method of this invention CA-SCL8 is no more than 0.1dB compared with the traditional BPL, and the performance gain of the method of this invention is 0.8dB compared with the traditional BPL.

Claims

1. A high-performance polar code belief propagation list decoding method based on dual-end post-processing, characterized in that, Includes the following steps: Step 1: Initialize decoding parameters and information matrix; let the polar code length be... The log-likelihood ratio of the input channel at the receiving end is The information bit set is The set of frozen positions is The decoder list has a size of L and a maximum number of iterations of I. max The CRC generator polynomial has a length of L. crc Construct a left information matrix L and a right information matrix R on the polar code factor graph. These two matrices store soft information during the iteration process, satisfying... and ,in, Indicates the factor layer number. Indicates bit position; Step 2: Perform BPL basic iterative decoding; for each permutation factor graph branch, alternately perform layer-by-layer updates of the left information matrix L and the right information matrix R in the factor graph according to the confidence propagation update rule; Step 3: Segment the information sequence and construct segmented information sub-blocks; at the U end, divide the sequence of length N, containing information bits and freeze bits, into P segments, each segment having a length of... ; Step 4: U-end information bits The soft information symbol fluctuation count; in order to measure the convergence of each information bit in the U end, the change of soft information symbols in continuous iteration is counted for all information bits in each segment. Step 5: Calculate the reliability metric of the U-end information bits and construct the segmented reliability ranking matrix; Step 6: Determine the convergence status of the frozen points of each segment; for each segment... p Detect the left information value of the U end corresponding to the frozen position within this segment; Step 7: Perform U-end reliability bit enhancement post-processing; Step 8: Perform unreliable position identification and flip perturbation post-processing at the X end; when the CRC check remainder vectors obtained from two consecutive iterations are equal, it indicates that the decoding has fallen into a local error stable state. At this time, while performing post-processing at the U end, unreliable position identification and flip perturbation post-processing are also performed at the X end; that is, the U end post-processing and the X end post-processing are activated synchronously by the same triggering condition and are executed simultaneously. Step 9: Repeat the iteration until decoding is complete; write the U-end enhancement result back to the right information matrix R. For the bit position i = s·M + k in layer 0, write the X-end flip perturbation result back to the left information matrix L. Bit position corresponding to the nth layer After writing is complete, continue to execute the next round of confidence propagation iteration, repeat steps 2 to 9 until the CRC check passes or the maximum number of iterations is reached, and output the corresponding decoding result when decoding is terminated.

2. The high-performance polar code belief propagation list decoding method based on dual-end post-processing according to claim 1, characterized in that: In step 1, during the initialization phase, only the rightmost layer of the left information matrix L is processed. And the leftmost layer of the right information matrix R Perform initial assignment on the rightmost layer of the left information matrix L. Initialization command: , (1) For the leftmost layer of the right information matrix R During initialization, if the first Each bit is a freeze bit. ,but, , (2) If the first Each bit is an information bit. ,but, (3)。 3. The high-performance polar code belief propagation list decoding method based on dual-end post-processing according to claim 1, characterized in that: In step 2, the recursive relation is: (4a) (4b) (4c) (4d) in, This represents the value of the i-th bit position in the s-th layer of the left information matrix. Represents the s-th layer of the left information matrix. The value of each bit position This represents the value of the i-th bit position in the (s+1)-th layer of the right information matrix. This indicates the (s+1)th layer of the right information matrix. The value of each bit position; For box approximation, we take: (5) In the formula, a and b are the two input variables of the box approximation operation, both of which are log-likelihood ratios representing confidence levels in the real number field; sign() is the sign function, which takes +1 when the input is positive, -1 when it is negative, and +1 when it is zero; min(|a|,|b|) means taking the smaller value between |a| and |b|; the coefficient 0.9375 is an empirical correction factor used to compensate for the estimation bias caused by the minimum approximation. After each iteration, the values ​​of the left information matrix L and the right information matrix R at the U end are used as the basis for the iteration. and The sum is used for hard judgment, and the position of the information bits is determined. ,make: (6) in, This represents the hard decision result for the i-th bit position, for the frozen bit position. Ordered directly without a judgment Then, extract the information sequence obtained from the decision according to the original information bit order, and calculate the CRC remainder vector corresponding to the current iteration. If the CRC check passes, decoding stops and the result is output; if the CRC check fails, proceed to the subsequent dual-end post-processing steps.

4. The high-performance polar code belief propagation list decoding method based on dual-end post-processing according to claim 1, characterized in that: In step 3, the first p The index range of the segment is: (7) in, For the p-th segment, extract the left information sub-block of the U-end of that segment. U-end right information sub-block Sub-block frozen position set and sub-block information bit set .

5. The high-performance polar code belief propagation list decoding method based on dual-end post-processing according to claim 1, characterized in that: In step 4, let the first t During the next iteration, the p-th segment... k The symbols for each position are: ， (8) in, This indicates the number of segments within the p-th segment at the t-th iteration. k The left information value at the U end of each information bit. k =0,1,…, ; This indicates the number of segments within the p-th segment at the t-th iteration. k The left information symbol value at the U end of each information bit; If the following conditions are met: ， (9) Then, the sign change count at the k-th information bit position within the p-th segment is incremented by one, denoted as: ， (10) in, This represents the cumulative number of symbol changes at the k-th information bit position of the p-th segment during the t-th iteration. This is the cumulative value from the previous iteration, and the initial value. The larger the count value, the more violently the corresponding position oscillates during the iteration.

6. The high-performance polar code belief propagation list decoding method based on dual-end post-processing according to claim 1, characterized in that: In step 5, if the CRC check remainders obtained from two consecutive iterations are the same, then the following condition is met: ， (11) in, This indicates the hard decision result after the t-th iteration. The CRC remainder vector is extracted and calculated according to the information bit order; Let represent the CRC remainder vector corresponding to the (t-1)th iteration. When both are equal, it indicates that the decoding result has not changed in two consecutive iterations, and the decoder may have entered a local error stable state. Therefore, to determine if the current decoding process has entered a local error stable state, reliable and unreliable bits need to be identified from the U-end. Construct the corresponding reliability metric: ， (12) in, This represents the reliability metric value of the k-th information bit in the p-th segment at the t-th iteration. This represents the cumulative number of sign changes. The larger the value, the more violent the oscillation at the corresponding position during iteration, and the lower the reliability; for each segment p, only the information bit set is considered. The location in the middle, according to reliability metrics Sort the results from smallest to largest to obtain an ordered index sequence: ， (13) in, The most reliable information bit is the original sequence number within the p-th segment. The information bit with the lowest reliability is the original sequence number within the p-th segment; satisfying: ， (14) in, This represents the reliability metric value corresponding to the j-th position after sorting. The sequence of inequalities indicates that the reliability decreases sequentially from front to back after sorting. The construction dimension is... Reliability ranking matrix The p-th column stores the reliability ranking sequence of the p-th segment, where the number of information bits in a segment is... When M is less than 1, the end of the line Each position is filled with a value of -1, and the number of information bits in each segment is determined accordingly. Adaptively determine the maximum enhancement bits for segmentation ,satisfy .

7. The high-performance polar code belief propagation list decoding method based on dual-end post-processing according to claim 1, characterized in that: In step 6, if the following conditions are met: (15) Wherein, represents the left information value of the U end at the position of the k-th frozen bit within the p-th segment. For the frozen position subset within segment p, at this time If the left information at the U end of the frozen bit has converged towards the correct 0 value, it is determined to be in a reliable convergence state, and the convergence flag is recorded as [symbol missing]. Otherwise, record as The convergence flag is used to limit the U-end post-processing to be performed only in segments where the frozen bits have been reliably converged.

8. The high-performance polar code belief propagation list decoding method based on dual-end post-processing according to claim 1, characterized in that: In step 7, for those that satisfy The segment p is determined from the reliability ranking matrix of that segment. The enhancement set is constructed by selecting several of the most reliable information bits from the front end: , (16) in, Let be the number of enhancement bits in the current iteration, and satisfy: , (17) For enhanced sets For any information bit sequence number k in the data, the right information at the U end corresponding to the information bit position will be... Updated to: , (18) in, This represents the right information value at the U-end of the k-th information bit within the p-th segment. The left information value of the U end; the meaning of formula (18) is: the current left information value of the reliable information bit of the U end is directly copied to the right information of the U end as the enhanced prior of the next iteration, thereby enhancing the correct convergence direction of the reliable information bit in the subsequent iteration.

9. The high-performance polar code belief propagation list decoding method based on dual-end post-processing according to claim 1, characterized in that: In step 8, the reliability of location identification at the X end is determined based on the integrated soft information: ， (19) in, The comprehensive soft information value representing the position of the i-th codeword bit is defined as the left information at position X. Information from the X end sum; The smaller the value, the lower the confidence level of the current decision regarding the location, and the more likely it is to be an unreliable location.

10. The high-performance polar code belief propagation list decoding method based on dual-end post-processing according to claim 9, characterized in that: Calculate the comprehensive soft information of all N codeword bit positions. ,according to Select directly in ascending order. The four positions with the smallest values ​​are considered the least reliable positions globally, denoted as . ,satisfy: ， (20) in, for Minimum position index, The second smallest position index, The third smallest position index, Let j be the fourth smallest position index, and j be the divisor. The index of any codeword bit position other than the one specified in the equation; the inequality means that the selected 4 positions... The value is not greater than any other value. The values, that is, these 4 positions are the positions with the lowest decision confidence; then, the 4 globally least reliable positions are... Apply a flip perturbation and update the rules as follows: ， (21) in, This represents the j-th globally least reliable position. The left information value at the X end, The right information value at the X end of the position. To preset a fixed disturbance amplitude, the disturbance amplitude will be the left information value at the X end of the least reliable position. It forces the direction to the opposite of the current decision direction, thereby breaking the local error stability point.

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