A method and apparatus for decoding BPL codes with non-zero core coefficients of 1 in a multi-polar code.

Abstract

A BPL decoding method and apparatus suitable for multi-polar codes with non-zero kernel coefficients of 1 are disclosed. The method includes: inputting L factor graph permutations of the multi-polar code with non-zero kernel coefficients of 1; the BPL decoder first performs the given L permutations on the channel received samples, calculates the log-likelihood ratio using the L permuted received samples, generates L sets of permutation LLR sequences, and inputs them to L belief propagation decoders for parallel decoding; when all branch BP decoders have finished decoding, the codeword sequence determined by the decoding is inversely permuted, and the Euclidean distance is compared with the original received signal sequence, with the codeword sequence having the smallest Euclidean distance being the final BPL decoded output. This invention proposes a BPL decoding method by exploring multiple factor graph equivalent permutations of multi-polar codes with non-zero kernel coefficients of 1, significantly improving the decoding performance of multi-polar codes with non-zero kernel coefficients of 1; it is applicable to communication systems using multi-polar codes with non-zero kernel coefficients of 1.

Description

Technical Field

[0001] This invention belongs to the field of channel coding and decoding technology, specifically relating to a BPL decoding method and apparatus suitable for multi-polar codes with non-zero core coefficients of 1. Background Technology

[0002] Binary polar codes are a channel coding technique that has been proven to reach the Shannon limit on binary-input symmetric memoryless channels. They primarily utilize the channel polarization effect to transform the original channel into a reliable channel and an unreliable channel. Information bits are transmitted on the reliable channel, while frozen bits known to both parties are transmitted on the unreliable channel. Thanks to its excellent performance and theoretical rigor, it has been adopted as the coding scheme for the control channel in 5G mobile communication standards. Currently, polar code decoding is divided into serial decoding and parallel decoding. Serial decoding algorithms, such as Successive Cancellation (SC) decoding and Successive Cancellation List (SCL) decoding, have good performance but high decoding latency. Parallel decoding algorithms, such as Belief Propagation (BP) decoding, can achieve parallel decoding, effectively solve the latency problem, and achieve high throughput decoding. However, compared with serial decoding, its main disadvantages are performance degradation and high bit error rate. Later, Belief Propagation List (BPL) decoding was proposed and applied to binary polar codes. Its performance is better than BP decoding, and it has lower decoding latency than SCL decoding.

[0003] With the increasing demand for high spectral efficiency in communication systems, multi-polar codes have gradually attracted attention. Multi-polar codes are a generalization of classical binary polar codes to higher-order domains. Their core idea is to extend the concept of channel polarization from the traditional binary domain (GF(2)) to multi-polar domains (such as GF(4), GF(8), ..., GF(q)). Compared to binary polar codes, multi-polar codes process symbols individually, enabling them to be combined with higher-order modulation without requiring additional bit-to-symbol mapping, thus achieving better performance. Multi-polar codes do not simply combine multiple binary codes in parallel; instead, they directly perform encoding and polarization operations in the multi-polar domain. Existing decoding methods, such as multi-polar serial cancellation (SC) decoding algorithms, have complexity that increases exponentially with the size of the domain q, leading to a surge in computational resource consumption.

[0004] In the field of multivariate polar code decoding, current research mainly focuses on reducing complexity and improving decoding performance. As a typical example of parallel decoding, multivariate backpropagation (BP) decoding algorithms can perform message passing on the factor graph of multivariate polar codes. Similar to binary BP decoding, multivariate BP decoding has the advantages of low latency and high throughput, making it more suitable for high-speed communication scenarios. However, the message calculation and update rules of multivariate BP decoding are more complex, and its performance is generally inferior to multivariate SC decoding. While belief propagation list (BPL) decoding has demonstrated excellent performance in binary polar codes, its application in the field of multivariate polar codes has not been fully explored. The parallel processing and error correction capabilities unique to BPL remain a gap in this area.

[0005] A search revealed that Chinese invention patent CN110278002A discloses a polar code belief propagation list decoding method based on bit flipping, using a concatenated code formed by CRC and polar codes. In cases where the BPL decoding result fails CRC verification, the method in this invention analyzes the decoding result of the BPL decoding method, constructs a flip bit set (FBS), and flips the information bits of the polar code located within the FBS (the bit flipping in this invention is achieved by setting the prior log-likelihood ratio of the bit to be flipped to infinity). This can correct some errors in the BPL decoder, thereby improving the bit error rate and frame error rate performance of the BPL decoding method.

[0006] The aforementioned prior art differs from this application in the following ways:

[0007] 1. The comparative document focuses on providing an error correction strategy after BPL decoding failure for binary polar codes using CRC concatenation. It activates when the decoding result fails the CRC check, "fixing" the error by analyzing and flipping key bits; this is a general post-processing enhancement technique. In contrast, this application targets the specific field of "multi-polar codes," especially "multi-polar codes with a non-zero core coefficient of 1," and does not process binary codes. It does not wait for decoding failure; instead, it innovates at the architectural level by designing a parallel native decoding system to improve the performance of multi-polar codes, representing a specialized, high-performance solution. The application scenarios of the two are significantly different.

[0008] 2. The core mechanism of the comparative document is "analysis-based iterative bit flipping," which involves constructing a "flipped bit set" (FBS) through algorithmic analysis after decoding failure. Then, by setting the prior log-likelihood ratio (LLR) of these bits to infinity, a logical "flip" is forced, and decoding is performed again. This is a serial error correction process that relies on feedback and iteration. In contrast, the core mechanism of this application is "structured parallel processing and optimal decision-making." It generates L different permutation sequences before decoding, feeds them into L parallel decoders, and finally selects the optimal solution from multiple independent results using Euclidean distance. This is a fully parallel feedforward process that does not rely on failure feedback. The core working principles of the two are fundamentally different.

[0009] 3. The system architecture of the comparative document adds a failure detection (CRC) and feedback control module to the standard BPL decoder to perform bit flipping and re-decoding. Architecturally, it's an enhancement of a single decoder, and its error correction philosophy is "precision strike," assuming most decoding results are correct and only needing to accurately locate and correct a few erroneous bits. In contrast, the architecture of this application is a parallel array of L complete BPL decoders, belonging to a multi-decoder system. Its philosophy is "broadcasting," meaning it doesn't presuppose decoding failure but explores multiple possible decoding paths in parallel, fundamentally increasing the probability of successful decoding on the first attempt. The two system constructions are significantly different.

[0010] A search revealed that Chinese invention patent CN110233628A discloses an adaptive belief propagation list decoding method for polar codes. First, based on the number of BP decoders at the receiving end, the maximum list size is determined. Then, a BP decoding factor map that achieves good decoding results is calculated using the Gaussian approximation method. Next, different BP decoding factor maps are selected for decoding the BP decoders recorded in the list. After sorting the decoding results, cyclic redundancy check (CRC) is performed. If a result passes the CRC check, decoding is successful and stops; otherwise, the list size is automatically adjusted, doubling the list size, and the BP decoders in the list continue to be used for decoding.

[0011] The aforementioned prior art differs from this application in the following ways:

[0012] 1. The technical implementation of the comparison file relies on CRC check to determine whether the decoding was successful, and uses this as a signal to trigger list expansion. Therefore, its application is for binary polar codes concatenated with CRC. This application, however, explicitly targets "multi-polar codes," whose symbols come from a larger symbol set, and its optimal decision mechanism is based on the Euclidean distance from the received signal. The application scenarios of the two are significantly different.

[0013] 2. The core mechanism of the comparison file is "resource adaptive adjustment." It dynamically changes the size of the list based on whether decoding is successful (determined by CRC checksum). If decoding fails, the list size is doubled to increase computing resources and improve the success rate. This is a "reactive" design that dynamically expands based on demand and iterates serially. In contrast, the core mechanism of this application is "fixed parallel exploration." It constructs L fixed parallel processing paths at the beginning of decoding, completes the decoding of all paths at once, and then makes a selection decision based on the best result. It does not involve any dynamic adjustment based on the results, and is a "forward-looking" parallel architecture design. The core working mechanisms of the two are fundamentally different.

[0014] 3. The comparative documents exhibit uncertainty in decoding latency. While the latency is short when decoding is successful on the first attempt, it accumulates significantly with multiple list expansions, resulting in substantial latency jitter. In contrast, this application, due to the parallel execution of all paths, has a fixed decoding latency equal to the processing time of a single path, providing predictable and stable low-latency performance. The decoding latency characteristics of the two are clearly different.

[0015] 4. The prior art employs an "on-demand allocation" strategy for system resources. Under favorable channel conditions, it completes decoding with a smaller list size, resulting in high resource utilization. Only under challenging conditions is the number of decoders gradually increased, potentially leading to lower average hardware complexity and power consumption. In contrast, this application adopts a "full resource commitment" strategy, ensuring that L parallel decoders are always operational regardless of channel conditions. This design has fixed hardware costs and power consumption, guaranteeing peak performance under all circumstances. The two applications differ in their resource consumption patterns. Summary of the Invention

[0016] To address the shortcomings mentioned in the background section, the present invention aims to provide a BPL decoding method and apparatus suitable for multi-polar codes with a non-zero core coefficient of 1, achieving superior decoding performance compared to existing decoding schemes.

[0017] The specific plan is as follows:

[0018] A BPL decoding method suitable for multi-polar codes with non-zero core coefficients of 1, characterized by comprising the following steps:

[0019] S101. L types of factor graph permutation methods for multi-polar codes with non-zero kernel coefficients of 1, where L≥2;

[0020] S102 and BPL decoders first perform L given permutations on the channel received samples respectively. They then calculate the log-likelihood ratio using the received samples after the L permutations, generate L sets of permutation LLR sequences, and input them into L belief propagation decoders for parallel decoding. The decoding results of each decoder are recorded.

[0021] S103. When all branch BP decoders have finished decoding, the codeword sequence determined by the decoding is inversely permuted and compared with the original received signal sequence in terms of Euclidean distance. The codeword sequence with the smallest Euclidean distance is taken as the final BPL decoding output.

[0022] Furthermore, step S101 specifically includes:

[0023] Factor graph of multi-polar codes with non-zero kernel coefficients of 1 is obtained through We obtain, where G = , is the kernel for generating multi-polar codes with a non-zero kernel coefficient of 1;

[0024] The layer number of the given standard factor plot is ,by Represents the set of integers Then the mapping Represents a set A permutation of the above, the multi-polar code encoding with a non-zero core coefficient of 1 has Given L equivalent permutations, the input must contain L permutation methods. , ... It should be A subset of equivalent permutations.

[0025] Furthermore, step S102 specifically includes:

[0026] The BPL decoder terminal receives a signal sequence The demodulation yields the original log-likelihood ratio sequence, denoted as . = ,in, Let represent the q-dimensional log-likelihood ratio vector over the finite field GF(q), and each vector... Each element Calculated by the following formula: ;

[0027] in, It is the received signal sequence The One element, It is the standard deviation of the Gaussian white noise in the received signal. It is the sequence obtained by mapping the binary form of j through BPSK (0→+1, 1→-1);

[0028] For L received signal sequences with different permutations , ... Simultaneously, BP decoding is performed. Each decoder executes a confidence propagation iterative process on the multi-polar code factor graph with a non-zero kernel coefficient of 1. In each iteration, each decoder updates the LLR value of the factor graph node according to the current confidence information. After each iteration, a decision information symbol sequence is generated. and codeword sequence When the result of a certain decoder satisfies the decision criterion Record the decoded output when the preset maximum number of iterations is reached.

[0029] Furthermore, step S103 specifically includes:

[0030] When all branch BP decoders have finished decoding, the codeword sequence determined by all decoders is... Perform inverse permutation:

[0031] ;

[0032] Then compared with the original received signal sequence Compare the Euclidean distances and use the decoder with the smallest Euclidean distance as the final belief propagation list decoder output. :

[0033] .

[0034] The present invention also provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor. When the processor loads and executes the computer program, it employs the above-described BPL decoding method suitable for multi-polar codes with a non-zero core coefficient of 1.

[0035] The present invention also provides a computer-readable storage medium storing a computer program, wherein the computer program, when running, controls the device or apparatus containing the computer-readable storage medium to execute the above-described BPL decoding method suitable for multi-polar codes with a non-zero core coefficient of 1.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] 1. By mining multiple factor graph equivalent permutations of multi-polar codes with non-zero kernel coefficients of 1, a BPL decoding method is proposed, which significantly improves the decoding performance of multi-polar codes with non-zero kernel coefficients of 1.

[0038] 2. A parallel decoding structure is adopted, which improves performance while maintaining low decoding latency, and selects the optimal decoding result by comparing Euclidean distance, thereby improving the reliability of decoding;

[0039] 3. Applicable to communication systems using multi-polar codes with a non-zero core coefficient of 1. Attached Figure Description

[0040] Figure 1 This is a flowchart of the method of the present invention;

[0041] Figure 2 This is a performance comparison chart of simulation results between existing technologies and the method of this invention. Detailed Implementation

[0042] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The specific implementation methods of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0043] Example 1:

[0044] like Figure 1 The present invention discloses a BPL decoding method suitable for multi-polar codes with non-zero core coefficients of 1. The method includes the following steps:

[0045] S101. L types of factor graph permutation methods for multi-polar codes with non-zero kernel coefficients of 1, where L≥2;

[0046] Factor graph of multi-polar codes with non-zero kernel coefficients of 1 is obtained through We obtain, where G = , is the kernel for generating multi-polar codes with a non-zero kernel coefficient of 1;

[0047] The layer number of the given standard factor plot is ,by Represents the set of integers Then the mapping Represents a set A permutation of the above, the multi-polar code encoding with a non-zero core coefficient of 1 has Given L equivalent permutations, the input must contain L permutation methods. , ... It should be A subset of equivalent permutations.

[0048] S102 and BPL decoders first perform L given permutations on the channel received samples respectively. They then calculate the log-likelihood ratio using the received samples after the L permutations, generate L sets of permutation LLR sequences, and input them into L belief propagation decoders for parallel decoding. The decoding results of each decoder are recorded.

[0049] The BPL decoder terminal receives a signal sequence The demodulation yields the original log-likelihood ratio sequence, denoted as . = ,in, Let each vector be a q-dimensional log-likelihood ratio over the finite field GF(q); and each vector... Each element Calculated by the following formula: ;

[0050] in, It is the received signal sequence The One element, It is the standard deviation of the Gaussian white noise in the received signal. It is the sequence obtained by mapping the binary form of j through BPSK (0→+1, 1→-1);

[0051] For L received signal sequences with different permutations , ... Simultaneously, BP decoding is performed. Each decoder executes a confidence propagation iterative process on the multi-polar code factor graph with a non-zero kernel coefficient of 1. In each iteration, each decoder updates the LLR value of the factor graph node according to the current confidence information. After each iteration, a decision information symbol sequence is generated. and codeword sequence When the result of a certain decoder satisfies the decision criterion Record the decoded output when the preset maximum number of iterations is reached.

[0052] S103. When all branch BP decoders have finished decoding, the codeword sequence determined by the decoding is inversely permuted and compared with the original received signal sequence in terms of Euclidean distance. The codeword sequence with the smallest Euclidean distance is taken as the final BPL decoding output.

[0053] When all branch BP decoders have finished decoding, the codeword sequence determined by all decoders is... Perform inverse permutation:

[0054] ;

[0055] Then compared with the original received signal sequence Compare the Euclidean distances and use the decoder with the smallest Euclidean distance as the final belief propagation list decoder output. :

[0056] .

[0057] Example 2:

[0058] In this embodiment, the number of information symbols is set to... Code length ,parameter Defined in a finite field Above, parameters Non-zero kernel coefficients All are 1. The BPL decoding algorithm sets the number of parallel BP decoding branches, i.e., the list length, to L=3. Each branch obtains the decoding result through iterative decoding, and the maximum number of iterations for each branch is [not specified]. Decode according to the steps in Example 1.

[0059] S101. L types of factor graph permutation methods for multi-polar codes with non-zero kernel coefficients of 1, where L = 3;

[0060] Factor graph of multi-polar codes with non-zero kernel coefficients of 1 is obtained through We obtain, where G = , is the kernel for generating multi-polar codes with a non-zero kernel coefficient of 1;

[0061] The layer number of the given standard factor plot is , Represents the set of integers , Represents a set There are 3! possible permutations given the above. , , It is a subset of 3! permutations, which are used to permutate the standard factor graph.

[0062] S102. At this point, the factor graph of the multi-polar code contains three layers. There are two cases of adjacent swapping, so there are a total of three decoders. First, a permutation operation is performed on the original received signal sequence. That is to Performing a permutation involves swapping corresponding entries in the binary index; that is, the original sequence index is... The index after replacement is The permuted received signal sequence is obtained. The log-likelihood ratio is Then, a permutation operation is performed on the original received signal sequence. That is to Perform a replacement, i.e., the index after the replacement is Obtain the permuted received signal sequence The log-likelihood ratio is Finally, the original factor graph order is retained, denoted as... , is the original log-likelihood ratio ;

[0063] Three received signal sequences with different permutations , , Simultaneously, BP decoding is performed. Each decoder executes a confidence propagation iterative process on the multi-polar code factor graph with a non-zero kernel coefficient of 1. In each iteration, each decoder updates the LLR value of the factor graph node according to the current confidence information. After each iteration, a decision information symbol sequence is generated. and codeword sequence When the result of a certain decoder satisfies the decision criterion Record the decoded output when the preset maximum number of iterations is reached.

[0064] S103. When all branch BP decoders have finished decoding, process the codeword sequences determined by all decoders. Perform inverse permutation:

[0065] ;

[0066] Then compared with the original received signal sequence Compare the Euclidean distances and use the decoder with the smallest Euclidean distance as the final belief propagation list decoder output. :

[0067] ;

[0068] If the Euclidean distance of the second decoder is minimized at this time, that is The BPL decoding output is a codeword sequence. .

[0069] Example 3:

[0070] Simulation verification was performed based on the above embodiments. The multi-polar code with a non-zero kernel coefficient of 1 was decoded using both the previous BP decoding method and the BPL decoding method of this invention, and the respective frame error rates were obtained as follows: Figure 2 (a) Figure 2 As shown in (b) in the figure, Figure 2 In this context, (a) represents the code length of the multipolar code C. Number of information symbols Number of decoders , Figure 2 In the diagram, (b) represents the code length of the multipolar code C. Number of information symbols Number of decoders All belong to finite fields ,parameter Non-zero kernel coefficients All are 1, representing the maximum number of iterations for each decoder. .

[0071] Figure 2In (a) of the figure, the blue curve represents the frame error rate of the BP decoding of the multi-polar code, and the red curve represents the frame error rate of the BPL decoding of the proposed multi-polar code. As can be seen from the simulation figure, the BPL decoding algorithm of the multi-polar code has a significant improvement in performance compared with BP.

[0072] Figure 2 In (b) of the figure, the blue curve represents the frame error rate of the BP decoding of the multi-polar code, and the red curve represents the frame error rate of the BPL decoding of the proposed multi-polar code. As can be seen from the simulation figure, the decoding performance of the proposed algorithm is improved by about 0.5dB compared with BP.

[0073] Example 4:

[0074] This embodiment provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program that can run on the processor. When the processor loads and executes the computer program, it employs the decoding method described in Embodiment 1. The processor may be a central processing unit (CPU), a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices. It serves as the computing and control core, used to load and execute instructions stored in a computer-readable medium, thereby implementing the various technical solutions described in this invention.

[0075] Example 5:

[0076] This embodiment provides a computer-readable storage medium storing a computer program. When the computer program runs, it controls the device or apparatus containing the computer-readable storage medium to execute the decoding method described in Embodiment 1. The storage medium can be any combination of one or more computer-readable media, such as, but not limited to, electrical, magnetic, optical, infrared, or semiconductor systems, devices, or components, or any combination thereof. More specific examples include, but are not limited to, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, or magnetic storage devices. Without departing from the spirit of the invention, any tangible medium containing or storing a program can serve as the computer-readable storage medium of this invention.

[0077] The above embodiments are for illustrative purposes only and are not intended to limit the scope of this application. Although this application has been described in detail with reference to the embodiments, those skilled in the art should understand that various combinations, modifications, or equivalent substitutions of the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application and should be covered within the scope of the claims of this application.

Claims

1. A BPL decoding method suitable for a non-zero nuclear coefficient of 1 multivariate polar code, characterized in that, The method comprises the following steps: S101, input L factor graph permutation modes of non-zero core coefficient 1 multivariate polar code, wherein L≥2; S102, the BPL decoder first performs the given L permutations on the channel received samples respectively, calculates the log likelihood ratio through the L permuted received samples, generates L groups of permutation LLR sequences, and inputs them into L belief propagation decoders for parallel decoding, and records the decoding results of each decoder; The step S102 specifically comprises: The terminal of the BPL decoder receives the signal sequence , demodulates to obtain the original log-likelihood ratio sequence = , where represents a q-dimensional log-likelihood ratio vector on a finite field GF(q), and each vector has each element calculated by the following formula: ​ wherein is a received signal sequence is a first element of the received signal sequence is a standard deviation of a Gaussian white noise in the received signal is a sequence obtained by BPSK mapping (0→+1, 1→-1) of a binary form of j; L received signal sequences with different permutations , , The BP decoding is performed simultaneously, and each decoder performs a belief propagation iteration process on the factor graph of the multivariate polar code with non-zero core coefficients being 1. In each iteration, the decoder updates the LLR value of the factor graph node according to the current belief information. After each iteration, the decision information symbol sequence and the codeword sequence are obtained. When the result of a certain decoder satisfies the decision criterion or the preset maximum number of iterations is reached, the decoding output is recorded. S103, when all branch BP decoders finish decoding, perform inverse permutation on the code word sequence determined by decoding, compare the Euclidean distance with the original received signal sequence, and take the code word sequence with the minimum Euclidean distance as the final BPL decoding output; The step S103 specifically comprises: When all the branch BP decoders have finished decoding, the codeword sequences decoded by all the decoders are judged performing inverse permutation: ； Then the original received signal sequence The Euclidean distance is compared, and the decoding result of the decoder with the minimum Euclidean distance is taken as the final belief propagation list decoder output : 。 2.The BPL decoding method for non-zero core coefficient being 1 of the multi-polar code according to claim 1, characterized in that, The step S101 specifically comprises: Factor graph of a non-zero core coefficient 1 multivariate polar code is obtained, where G= is the generator core of the non-zero core coefficient 1 multivariate polar code; The layer number of the given standard factor plot is ,by Represents the set of integers Then the mapping Represents a set A permutation of the above, the multi-polar code encoding with a non-zero core coefficient of 1 has Given L equivalent permutations, the input must contain L permutation methods. , ... It should be A subset of equivalent permutations.

3. A terminal device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The memory stores a computer program capable of running on the processor, and when the processor loads and executes the computer program, the BPL decoding method for non-zero core coefficient 1 multivariate polar code as claimed in any one of claims 1 to 2 is adopted.

4. A computer-readable storage medium having stored therein a computer program, characterized in that, The computer program controls the device or apparatus where the computer readable storage medium is located to execute the BPL decoding method for non-zero core coefficient 1 multivariate polar code as claimed in any one of claims 1 to 2 when running.

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