A method for decoding a multi-ary polar code based on path reliability metric

Abstract

The application provides a method for decoding a multi-ary polar code based on path reliability measurement, a sub-channel reliability model of the multi-ary polar code is established by using Gaussian approximation theory, and the symbol error probability of an information bit is determined by recursively calculating statistical moments; in a multi-ary successive cancellation list (NBSCL) decoding process, a reliability threshold is constructed according to the symbol error probability, and a hard decision is made on a path meeting a high reliability condition; for a path needing to be split, an accumulated reliability deviation (ARD) measurement mechanism is introduced, and the ARD value of a candidate branch is calculated in real time in a branch expansion stage. The ARD value is compared with a preset tolerance threshold, and a candidate branch exceeding the threshold and being non-local optimal is removed, thereby realizing non-full path splitting. The application can reduce the number of path splitting and the number of activated decoding paths in the decoding process, and can reduce the calculation complexity and memory consumption while ensuring the error performance.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and channel coding technology, and specifically relates to a simplified method for decoding multi-level polar codes based on path reliability measurement. Background Technology

[0002] Non-Binary Polar Codes (NBPCs), as an important evolution in the field of channel coding, extend channel polarization theory from the binary domain to discrete memoryless channels of arbitrary bases. Compared to traditional binary schemes, in the finite domain... Based on optimization Multi-level polar codes constructed from kernels have been shown to have faster polarization rates with finite code lengths. Studies have shown that as the order increases... With the increase of multi-level polar codes, channel capacity can be utilized more thoroughly, and significant error correction performance advantages are shown in high-order modulation systems and high-reliability transmission scenarios, making it a key technology for improving the spectrum efficiency and error correction performance of communication systems.

[0003] The computational complexity of multi-base polar code decoding increases exponentially with the number of bases. In multi-base serial cancellation list (NBSCL) decoding algorithms, theoretically, it is necessary to exhaustively enumerate all possible values ​​when decoding each information symbol. All possible values ​​within the domain, i.e., each level of path expansion will produce... There are 10 candidate branches. This means that the complexity of path splitting is mainly determined by the size of the list. AND base number Domination. When applied to higher-order domains, the full-path splitting strategy leads to an explosive growth in the number of candidate paths, making the hardware resource consumption and processing latency caused by path metric calculation, sorting, and pruning operations unacceptable, severely restricting its engineering application in real-time communication systems.

[0004] While existing technologies have proposed some simplification strategies for polar code decoding, such as split-reduction decoding or pruning algorithms based on auxiliary path metrics, most of these studies focus on binary codes. Existing decoding schemes lack fine-grained awareness of channel conditions and the reliability of intermediate nodes. Regardless of the severity of the channel environment for the current decoding symbol, traditional algorithms mechanically perform full fork expansion, resulting in a significant waste of computational resources on extremely low-probability erroneous path branches. Currently, there is a lack of an adaptive decoding mechanism that can accurately identify high-reliability nodes to skip redundant splits and utilize accumulated metric biases to perform early and effective pruning of low-reliability nodes, tailored to the characteristics of multi-ary channels. Summary of the Invention

[0005] To address the shortcomings of existing multi-base polar code decoding algorithms, such as the exponential increase in computational complexity with increasing base due to the full-path splitting strategy, and the limitations of traditional NBSCL decoders in terms of hardware resource consumption and latency control, this invention provides a simplified multi-base polar code decoding method based on path reliability metrics. By integrating Gaussian approximation theory and dynamic pruning mechanisms, the method reduces the number of path splits and the number of active decoding paths. Furthermore, through an innovative reliability assessment model and a non-full-path expansion strategy, the complexity of multi-base decoding is effectively reduced.

[0006] This method constructs a decoding framework of "prediction modeling - dynamic decision - real-time pruning": it uses Gaussian approximation theory to model the sub-channels of multi-level polar codes, recursively calculates the statistical moments of the LLR vector, and pre-determines the symbol error probability of each information bit; during the decoding process, a dynamic decision mechanism is constructed to calculate the posterior probability of the current path in real time. If the high reliability condition is met, the splitting step is skipped and hard decision is performed directly; for low-reliability nodes that need to be split, an accumulated reliability deviation (ARD) measurement mechanism is introduced to calculate the degree of deviation of the candidate path from the local optimum during the branch generation stage, and performs non-full path splitting in combination with the search set threshold, retaining a very small number of effective branches into the candidate list.

[0007] Its core innovation lies in:

[0008] Channel reliability prediction model: based on multi-level polar codes The kernel structure utilizes Gaussian approximation recursively to calculate the mean of LLR and the symbol error probability of information bits, providing an accurate physical layer benchmark for dynamic decision-making;

[0009] Adaptive split-decision strategy: Define the risk of the ARD value quantification path deviating from the local optimum, in Low-reliability paths exceeding ARD limits are removed in real time during branch generation;

[0010] ARD-based non-full path pruning: Unlike the full path splitting mechanism of the traditional NBSCL algorithm, this algorithm introduces a metric threshold during the path expansion stage. By pruning early, it avoids low-quality paths from participating in subsequent sorting and storage, thereby significantly reducing computational complexity and storage space while maintaining decoding performance.

[0011] Compared to traditional solutions, this invention addresses the issue of the number of candidate branches varying with the radix by using path reliability metrics. The problem of doubling is avoided, and redundant searches of all paths are avoided in low-noise environments. The non-full path splitting is achieved through the ARD mechanism, which reduces the number of path splits (PSN) by more than 90% and significantly suppresses the peak value of the number of active decoding paths. This effectively solves the problems of high complexity and high storage requirements faced by multi-level polar codes in practical applications.

[0012] To achieve the above objectives, the technical solution of the present invention is as follows:

[0013] A simplified decoding method for multi-level polar codes based on path reliability metrics includes:

[0014] In multi-level polar code communication systems, for additive white Gaussian noise (AWGN) channels, the sub-channel reliability of the multi-level polar code is modeled using Gaussian approximation theory. By recursively calculating the statistical moments of the LLR vector, the symbol error probability of each information bit is pre-determined. ;

[0015] In the multi-level serial cancellation list decoding process, for the current information symbol to be decoded, a dynamic reliability threshold is constructed based on the symbol error probability, and the symbol posterior probability of the current path is calculated. If the symbol posterior probability of the current path meets the high reliability condition, it is determined that the current path does not need to be split, and a hard decision is performed directly. If the symbol posterior probability of the current path does not meet the high reliability condition, the path splitting stage is entered, and the cumulative reliability deviation (ARD) measurement mechanism is introduced: during execution During the branch expansion process, the ARD value of each candidate branch is calculated and compared with a preset tolerance threshold. For candidate branches whose ARD value exceeds the tolerance threshold and are not locally optimal, they are pruned before being added to the path list, thus avoiding the forced full expansion of a parent path. Sub-paths enable non-full path splitting that preserves valid branches;

[0016] A counter mechanism based on the number of consecutive unsplits is used to prune the path list;

[0017] At the end of decoding, the candidate codeword with the best path metric is selected from the list of surviving paths as the decoding output.

[0018] Preferably, the pre-established symbol error probability for each information bit is as follows:

[0019] Assuming finite field transmission over an additive white Gaussian noise channel All-zero codewords on the receiving symbol The corresponding LLR vector approximately follows a multivariate Gaussian distribution and satisfies the generalized symmetry condition;

[0020] Based on the multi-level polarization transform structure, the Gaussian approximation method is used to recursively calculate the first... LLR vector mean of each sub-channel ;

[0021] Substitute the calculated LLR vector mean into the Q function to calculate the first... Probability of symbol error per information bit :

[0022]

[0023] in, For a finite field The order of .

[0024] Preferred, based on multi-base The polarization transformation structure of the nucleus is recursively calculated using the Gaussian approximation method. LLR vector mean of each sub-channel The details are as follows:

[0025]

[0026]

[0027] in, For mathematical expectation calculation, For the corresponding LLR vector, , They are respectively through The two sub-channel symbols after polarization kernel transformation , These are the corresponding received signals. for The Gaussian approximation function, for The inverse function of .

[0028] Preferably, the high reliability condition is determined in the following way:

[0029] Decisions based on the probability domain:

[0030] For the path list, the first The barcode decoding path, in processing the first When the symbol is given, the calculation is performed on the given received signal. and correctly decoded symbols Posterior probability under given conditions If the following inequality is satisfied:

[0031]

[0032] Then determine the symbol of the current path. The decoding result has high confidence, no path splitting operation is required, the current path is preserved and hard decision is made based on the LLR vector;

[0033] Conversely, if the inequality does not hold, it indicates that the current node has low reliability, and the current path should be split into... 10 paths to cover possible errors;

[0034] By utilizing Bayes' theorem and the Min-Sum approximation, the decision in the probability domain is transformed into a numerical comparison in the LLR domain to facilitate engineering implementation:

[0035] Define decision threshold And calculate the log-likelihood ratio parameter. ;in, , Symbols Relative to symbols The LLR value, and They represent the first time. Current information symbols on the path Values The sum can be set to a value of 1. The posterior probability;

[0036] The formula for determining splits is simplified to:

[0037]

[0038] If any condition of the split decision formula is satisfied, then the first... No path needs to be split; the symbol pair of the current path is obtained according to the split decision formula. The decoding result Otherwise, the execution path is split.

[0039] Preferably, the counter mechanism based on the number of consecutive unsplits is as follows:

[0040] This mechanism is based on the statistical characteristic that "correct paths tend to be straight, while incorrect paths tend to split frequently," and assigns each path in the path list a specific path. Allocate a counter Used to record paths The number of consecutive stages without splitting; the counter update rules are as follows:

[0041] In decoding When, if the path If the high reliability condition is met and path splitting is not performed, then the counter is incremented:

[0042]

[0043] If path It splits and expands into If there are 10 paths, then the path list contains 10 paths. All counters for new split paths and original paths have been reset:

[0044]

[0045] in, Representing a path The counter for one of the new splitting paths;

[0046] Set counter threshold When the path counter value At that time, path Marked as a high-confidence path;

[0047] Trigger pruning: When a high-confidence path is found, force pruning is performed immediately, retaining only paths with counter values ​​greater than the threshold. The path will be forcibly deleted if the counter value is less than [a certain value]. The path; when channel conditions are good, this mechanism can significantly compress the list size. .

[0048] Preferably, the cumulative reliability deviation measurement mechanism is as follows:

[0049] The path splitting simplification algorithm, considering the structural characteristics of multi-level polar codes, defines a critical set (CS). Since channel polarization exists within the Rate-1 nodes of each polar code sub-block, and the degree of polarization varies, the first symbol within the sub-block often has the worst channel quality. Therefore, the index position of the first symbol of each Rate-1 sub-block is included in the critical set, and a search set is defined based on this critical set. This serves as a set of nodes that require close monitoring and enforcement of split decisions.

[0050] Define ARD value Used to count decoding paths in the search set Cumulative error risk within; The calculation is based on the estimated symbol of the current path. With search set The distance between the local optimal hard decision results corresponding to the current decoding node, and the ARD value update formula is:

[0051]

[0052] in, Indicates the first The barcode decoding path is at the 1st Each decoding stage estimates the symbol The LLR metric value, Indicates the first The barcode decoding path is at the 1st The locally optimal hard-decision symbol for each decoding stage; the ARD value increases only when the decoding path selects a non-locally optimal symbol, quantifying the degree to which the path deviates from a locally greedy path;

[0053] Determine the tolerance threshold for ARD This threshold is not a fixed threshold; it is selected based on the statistical characteristics of the sub-channel calculated using a Gaussian approximation. The maximum expected reliability value in the set is used as the upper bound of the maximum deviation that the correct path can tolerate.

[0054] Calculate the cost of splitting: in processing When encountering a node, assuming the path splits, calculate the ARD value for each candidate branch. Among them, if If the current node does not belong to the search set, the ARD accumulation and ARD-based path splitting operations are not performed, and a hard decision is made directly based on the symbol LLR vector.

[0055] Perform adaptive pruning: if the ARD value If the branch path deviates too much, it is highly likely to be an incorrect path; if the symbol corresponding to the current candidate branch... If the hard decision symbol is not equal to the local optimum, then the current candidate branch is directly pruned; if If the current candidate branch is not found, the current candidate branch is retained. This mechanism ensures that the list resources are focused on the most likely path, avoiding the overexpansion of invalid paths.

[0056] A simplified multi-level polar code decoding system based on path reliability measurement, wherein the system is implemented using any of the above-mentioned simplified multi-level polar code decoding methods, including:

[0057] The channel polarization module is configured to perform:

[0058] For additive white Gaussian noise channels, a subchannel reliability model for multi-level polar codes is established using Gaussian approximation theory. The symbol error probability of each information bit is pre-determined by recursively calculating the statistical moments of the LLR vector.

[0059] The path splitting decision module is configured to execute:

[0060] During the decoding process, a dynamic reliability threshold is constructed based on the symbol error probability, and the posterior probability of the current path is calculated.

[0061] If the posterior probability of the current path meets the high reliability condition, then no splitting is required, and a hard decision is made directly.

[0062] If the posterior probability of the current path does not meet the high reliability condition, a path splitting operation is triggered to generate a new path. There are 10 candidate branches;

[0063] The dynamic pruning control module is configured to execute:

[0064] A cumulative reliability deviation measurement mechanism is adopted to calculate the ARD value of each candidate branch in real time during the process of generating candidate branches in the path split decision module;

[0065] Compare ARD values ​​with search set Calculated tolerance threshold Perform a comparison;

[0066] Implement a non-full-path splitting strategy: For candidate branches whose ARD values ​​exceed the tolerance threshold and are not locally optimal, delete them directly before adding them to the candidate list, and only retain the valid branches for subsequent sorting;

[0067] The decoding output module is configured to execute:

[0068] Maintain a list of surviving paths after dynamic pruning. At the end of decoding, select the candidate codeword with the best path metric from the final surviving path list as the system's decoding output.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] 1. Significantly reduces decoding latency and computational complexity: By introducing a path splitting simplification rule based on Gaussian approximation theory, the error probability of sub-channels is calculated and a dynamic reliability threshold is constructed. For nodes that meet the high reliability condition, hard decision is directly performed, fundamentally reducing invalid path splitting operations and subsequent path metric update calculations;

[0071] 2. Optimize storage resources and sorting efficiency: Utilize the ARD metric mechanism to implement a non-full path expansion strategy. When a path must split, by calculating the degree to which candidate branches deviate from the local optimum, inferior branches with deviations exceeding the tolerance threshold are immediately eliminated before entering the candidate list. This reduces the number of paths participating in the list sorting, thereby reducing hardware storage requirements and the power consumption of the sorting logic.

[0072] 3. Enhance decoding convergence speed under high signal-to-noise ratio: A counter mechanism based on the number of consecutive non-splitting times is designed. Taking advantage of the statistical characteristic that the correct path tends to be a single straight path, it can quickly identify high confidence paths and forcibly remove the remaining redundant paths when the signal-to-noise ratio is high or the channel quality is good, effectively compressing the list size and accelerating decoding convergence while ensuring performance.

[0073] 4. Achieving an adaptive balance between performance and complexity: By combining key set and Gaussian approximation modeling, the algorithm can adaptively adjust the pruning intensity according to channel state and codeword structure characteristics. It performs a fine-grained search at the beginning and end of unreliable Rate-1 sub-blocks, while quickly traversing high-reliability regions, ensuring that while significantly reducing average complexity, it maintains a bit error rate performance comparable to the traditional full-search NBSCL algorithm. Attached Figure Description

[0074] Figure 1 This is a flowchart illustrating the implementation of a simplified system for decoding multi-level polar codes using serial cancellation lists, as described in an embodiment of the present invention.

[0075] Figure 2 This is a comparison of the bit error rate curves of the ESR-NBSCL scheme and the NBSCL scheme under different counter thresholds in this invention embodiment;

[0076] Figure 3 This is a comparison of the average number of activation paths at different nodes for the ESR-NBSCL scheme and the NBSCL scheme according to embodiments of the present invention.

[0077] Figure 4 This is a comparison of the bit error rate curves of the PSD-NBSCL scheme, ESR-NBSCL and NBSCL scheme under different counter thresholds and different ARD thresholds in the embodiments of the present invention;

[0078] Figure 5 This is a comparison of the average path split count curves of the PSD-NBSCL scheme, ESR-NBSCL and NBSCL scheme under different counter thresholds and different ARD thresholds in the embodiments of the present invention;

[0079] Figure 6 This is a comparison of the average number of active paths curves for the PSD-NBSCL scheme, ESR-NBSCL, and NBSCL scheme under different counter thresholds and different ARD thresholds in embodiments of the present invention. Detailed Implementation

[0080] The following is in conjunction with the appendix Figure 1-6 The technical solution of the present invention will be described in detail below.

[0081] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0082] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0083] To overcome the limitations of multi-base polar codes (NBPCs) in NBSCL decoding due to the number of bases... To address the bottleneck of exponentially increasing computational complexity and storage overhead caused by excessive computational load, this invention proposes a simplified multi-level polar code decoding scheme (PSD-NBSCL) based on path reliability metrics, employing channel statistical modeling and dynamic path management techniques. Considering the limitations of the NBSCL algorithm, which ignores the reliability differences between different sub-channels and forces full path extension, this scheme is carefully designed with a collaborative mechanism of static model prediction and dynamic pruning control. While reducing computational load, error correction performance is maintained. The decoding path extension process is jointly optimized using the idea of ​​accumulating reliability deviations. The newly constructed non-full path splitting mechanism can significantly eliminate invalid and redundant branches, improving the real-time decoding efficiency of the system.

[0084] This scheme targets high-order modulation and high-throughput communication systems, aiming to accurately quantify subchannel risks using Gaussian approximation theory. First, it investigates the multidimensional LLR distribution characteristics of multi-level polar codes in AWGN channels and derives a symbol error probability model based on the LLR mean. A dynamic threshold is constructed to achieve fast hard decision-making for high-confidence nodes. In the decoding stage, an ARD metric mechanism and a continuous non-splitting counter are introduced to pre-screen candidate paths, preventing invalid paths from entering the sorting list. Furthermore, based on the proposed algorithm framework, a complexity evaluation system for path splitting number (PSN) and the number of active paths is established, verifying the scheme's adaptability under different signal-to-noise ratios (SNRs). Simulation results show that as the SNR increases, the performance difference between this scheme and the standard NBSCL algorithm is less than 0.1 dB under different SNRs. The PSN of this scheme decreases exponentially, saving more than 90% of computational resources compared to the NBSCL algorithm.

[0085] like Figure 1 As shown, this embodiment of the invention provides a simplified method for decoding multi-level polar codes based on path reliability metrics, including the following steps:

[0086] Step S1: For the multi-level polar code communication system, before decoding begins, the multi-level polar code sub-channel under the AWGN channel is modeled using Gaussian approximation theory; the symbol error probability of each information bit is pre-determined by recursively calculating the statistical moments of the LLR vector. Based on this, a dynamic reliability threshold is generated for subsequent online decisions;

[0087] Step S2: Entering the decoding stage, for the information symbol to be decoded, the decoder calculates the posterior probability of the current path in real time and compares it with the dynamic threshold generated in step S1. If the high reliability condition is met, it is determined that the current path does not need to be split, and a hard decision is made directly, thereby skipping the time-consuming path expansion operation.

[0088] Step S3: If the current path does not meet the high reliability condition, the splitting phase begins. At this point, instead of traditional full path expansion, an ARD (Advanced Path Reliability) metric mechanism is introduced. The estimated ARD value for each potential candidate branch is calculated and compared with a preset threshold. Before being added to the candidate list, inferior branches with excessive deviations are immediately removed, leaving only a small number of valid branches in the sorting list.

[0089] Step S4: Utilizing the statistical property that "correct paths tend to be single-path straight," maintain a counter for each path to record the number of consecutive stages without splitting. When the counter exceeds a set threshold, forcibly retain high-confidence paths and delete the remaining paths, further compressing the list size;

[0090] Step S5: Quantify the algorithm complexity by statistically analyzing the actual number of path splits during the decoding process and the number of active decoding paths corresponding to each decoding node; combine the frame error rate (FER) simulation curve to verify that this scheme can maintain a bit error rate performance comparable to the full search NBSCL algorithm while significantly reducing the amount of computation.

[0091] This invention addresses high-performance communication scenarios using multi-level polar codes. It innovatively utilizes Gaussian approximation theory and the statistical characteristics of decoding paths, combining subchannel reliability modeling with the ARD metric mechanism to effectively achieve an adaptive balance between decoding complexity and error correction performance. At the decoding end, a non-full path splitting (PSD-NBSCL) method based on reliability metrics is adopted, which can skip redundant splits and accurately eliminate invalid branches while ensuring high reliability. Compared with the full search NBSCL scheme, it can achieve a significant reduction in the number of path splits and list sorting overhead. The system has more flexible channel adaptability and faster decoding convergence speed.

[0092] As a preferred embodiment, step S1 includes the following steps:

[0093] Step S11: In this embodiment, the code length is defined as... The information bit length is Multi-base polar codes. Defining a finite field. ,in Unlike binary polar codes, this implementation uses a method based on... Construct a multi-ary kernel on the domain.

[0094] Generating matrix The Kronecker product is constructed using a recursive method. Let... Represents the core matrix The nth power of the Kronecker product, where Arikan core of 2×2 Extended forms on domains:

[0095]

[0096] The generating matrix can be represented as ,in This is the bit-flipping permutation matrix. The vector to be encoded. Contains a set of information symbols and the set of frozen symbols The encoding process is as follows: .

[0097] Step S12: Assume the encoded symbol has a variance of Transmitted over an AWGN channel. At the receiving end, for each received symbol... Its LLR is a length of The vector, defining the received signal The corresponding LLR vector is The corresponding field element in the vector The components are represented as:

[0098]

[0099] This embodiment is based on the Gaussian approximation theory, assuming that the LLR vector of the channel output follows a multivariate Gaussian distribution and satisfies the generalized symmetry condition. Under this model, the probability density function of the LLR vector maintains Gaussianness and symmetry.

[0100] Step S13: To determine the reliability of each sub-channel, a multi-level polarization transform structure is used to recursively calculate the reliability of the first sub-channel. Sub-channels LLR vector mean :

[0101]

[0102]

[0103] in, for Channel capacity mapping function in radix. This embodiment uses the following simplified fitting formula for calculation to reduce engineering complexity:

[0104]

[0105] in, The total number of samples taken in Monte Carlo. For the sample index, The index of the non-zero sign component in the LLR vector. No. The LLR vector obtained from the nth sampling is the th Each component.

[0106] By from arrive The recursion eventually yields the LLR mean for each sub-channel. .

[0107] Step S14: Using the joint bound of the pairwise error probability (PEP), the mean of the LLR is transformed into the first... Probability of symbol error per information bit :

[0108]

[0109] This characterizes the inherent risk of decoding errors caused by channel noise at this location under ideal assumptions. Based on this, a decision threshold is calculated for each location. :

[0110]

[0111] As a preferred embodiment, step S2 includes the following steps:

[0112] Step S21, based on the received signal and path The correct symbols already translated Calculate the current symbol The LLR vector.

[0113] Step S22: Define path splitting rules:

[0114]

[0115] If any one of the inequalities in the above equation is satisfied, then the inequality is... The barcode decoding path can be split without splitting. Based on Bayes' theorem and the Min-Sum approximation, the splitting rule can be simplified to:

[0116]

[0117] As a preferred embodiment, step S3 includes the following steps:

[0118] If the high reliability condition in step S2 is not met, it indicates that the current node is at risk of misjudgment, and the traditional algorithm will force a split. A path. This embodiment introduces the ARD mechanism to perform non-full path splitting.

[0119] Step S31: For the polarization phenomenon within the Rate-1 sub-block of the polar code, define the first symbol index position of each Rate-1 sub-block as the key set (CS). Define the search set based on the CS. ARD monitoring is performed on the nodes within this set.

[0120] Step S32, Definition For the first The path in the first Stage (decoded to) The ARD value (at time). This value quantifies the degree to which the current path deviates from the local optimum decoding. Its update formula is:

[0121]

[0122] That is, the ARD value will only increase when the path selects a non-locally optimal symbol.

[0123] Step S33: At nodes that must be split, the system will not directly generate... Instead of adding a new path to the list, it is... Potential candidate symbols Preliminary selection:

[0124] 1. Calculate the local optimal symbol ;

[0125] 2. For each candidate symbol Calculate its estimated ARD value ;

[0126] 3. With a threshold set based on the statistical characteristics of the search set Compare:

[0127] like or If so, the candidate branch is retained and added to the subsequent path sorting list;

[0128] like and If so, then discard the branch directly.

[0129] As a preferred embodiment, step S4 includes the following steps:

[0130] Step S41: Update the counter. For each path in the list... Maintain a counter If the node does not split during step S2 while meeting the high reliability condition, then... If a split occurs in step S3, the counters for all related paths are reset: .

[0131] Step S42: Set the counter threshold During any decoding stage, check the counters for all paths:

[0132] If a path exists that satisfies If so, it is marked as a high-confidence path.

[0133] Once a high-confidence path is found, immediately perform forced pruning to preserve all paths. Delete all paths The path.

[0134] As a preferred embodiment, step S5 includes the following steps:

[0135] Step S51: Count the total number of path splitting events that occur in all information symbol bits during the entire decoding process.

[0136] Let the set of information bits be In position The actual number of splits that occurred at a given location is denoted as . The total number of path splits is:

[0137]

[0138] Step S52: Count the number of paths actually maintained in the active path list at the current decoding node. This is a key indicator for measuring real-time computational complexity and memory usage.

[0139] Set at position At this point, after pruning in steps S3 and S4, the number of paths in the list is... The average number of activation paths is:

[0140]

[0141] The effectiveness of the above solution in this embodiment is verified through a specific test example:

[0142] This example simulates the decoding performance and complexity of multi-level polar codes in an AWGN channel. The simulation parameters are set as follows: code length Information bit length bitrate The list size is set to The simulations were conducted in... and The algorithm's universality was verified by performing the test on a domain. The comparison scheme was the traditional full-search NBSCL decoding algorithm.

[0143] Figure 2 Comparison in and In this invention, the improved split-reduce decoding algorithm based on a counter mechanism (ESR-NBSCL) and the NBSCL algorithm are compared in terms of FER performance. The figure compares different counter thresholds. The performance curve is shown below. As can be seen from the graph, with the threshold... With the increase of [unclear], the performance of ESR-NBSCL gradually approaches that of the standard NBSCL algorithm. When the two curves almost overlap, it proves that the strategy of screening high-confidence paths by using continuous non-splitting counters is feasible while ensuring almost no loss in bit error rate performance.

[0144] Figure 3 The figure illustrates the variation in the number of active decoding paths at each stage (Indices) during the decoding process under different signal-to-noise ratios. As can be seen from the figure, the NBSCL algorithm maintains [a certain level of activity] throughout the entire decoding cycle. In contrast, the simplified algorithm of this invention can dynamically adjust the number of paths based on channel conditions. Especially... Figure 3 At a high signal-to-noise ratio, the number of activation paths converges rapidly to 1 in most decoding stages, which means that the algorithm adaptively degenerates into low-complexity SC decoding, greatly reducing redundant computation.

[0145] Figure 4 The figure shows a comparison of the FER of the PSD-NBSCL scheme proposed in this invention with the baseline scheme. The figure focuses on examining different tolerance thresholds after introducing the ARD mechanism. Impact on performance. As can be seen from the graph, with... With the relaxation of the value, the FER performance of PSD-NBSCL is consistent with that of NBSCL, which shows that the ARD-based predictive pruning strategy can accurately identify and retain effective paths without introducing additional error layers.

[0146] Figure 5The average split path number (PSN) of different schemes under different signal-to-noise ratios (SNRs) was compared. PSN directly reflects the average computational complexity of the decoder. As shown in the figure, with increasing SNR, the PSN of the proposed schemes (ESR-NBSCL and PSD-NBSCL) decreases exponentially, while NBSCL remains constant. Notably, the PSD-NBSCL scheme incorporating the ARD mechanism has a lower PSN than the ESR-NBSCL scheme using only a counter.

[0147] Figure 6 This figure shows a detailed comparison of the suppression effects of the proposed solution on path expansion at low signal-to-noise ratios. As can be seen from the figure, the PSD-NBSCL scheme, due to the introduction of ARD prediction pruning, eliminates inferior branches at the source of path splitting, thus resulting in a significantly lower number of activated paths compared to the ESR-NBSCL scheme. This strongly validates the advantages of the proposed non-full path splitting strategy in suppressing list expansion and reducing the sorter load.

[0148] Based on the same inventive concept, this invention also provides a computer device, comprising: one or more processors, and a memory for storing one or more computer programs; the programs include program instructions, and the processor executes the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, used to implement one or more instructions, specifically for loading and executing one or more instructions stored in a computer storage medium to implement the above-described method.

[0149] It should be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, performs the above-described method. This storage medium can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0150] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0151] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0152] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive various other forms of polar code cooperation methods in free-space optical communication systems. All equivalent variations and modifications made within the scope of the claims of this invention should be included within the scope of this invention.

Claims

1. A simplified decoding method for multi-level polar codes based on path reliability measurement, characterized in that, include: In multi-level polar code communication systems, for additive white Gaussian noise channels, the reliability of sub-channels of multi-level polar codes is modeled using Gaussian approximation theory. By recursively calculating the statistical moments of the LLR vector, the symbol error probability of each information bit is pre-determined. In the multi-level serial cancellation list decoding process, for the current information symbol to be decoded, a dynamic reliability threshold is constructed based on the symbol error probability, and the symbol posterior probability of the current path is calculated. If the symbol posterior probability of the current path meets the high reliability condition, it is determined that the current path does not need to be split, and a hard decision is performed directly. If the symbol posterior probability of the current path does not meet the high reliability condition, the path splitting stage is entered, and a cumulative reliability deviation measurement mechanism is introduced: during execution During the branch expansion process, the ARD value of each candidate branch is calculated and compared with the preset tolerance threshold. For candidate branches whose ARD value exceeds the tolerance threshold and are not locally optimal, they are pruned before being added to the path list to achieve non-full path splitting that retains effective branches. A counter mechanism based on the number of consecutive unsplits is used to prune the path list; At the end of decoding, the candidate codeword with the best path metric is selected from the list of surviving paths as the decoding output.

2. The simplified decoding method for multi-level polar codes based on path reliability measurement according to claim 1, characterized in that, The pre-determined symbol error probability for each information bit is as follows: Assuming finite field transmission over an additive white Gaussian noise channel All-zero codewords on the receiving symbol The corresponding LLR vector approximately follows a multivariate Gaussian distribution and satisfies the generalized symmetry condition; Based on the multi-level polarization transform structure, the Gaussian approximation method is used to recursively calculate the first... LLR vector mean of each sub-channel ; Substitute the calculated LLR vector mean into the Q function to calculate the first... Probability of symbol error per information bit : in, For a finite field The order of .

3. The simplified decoding method for multi-level polar codes based on path reliability measurement according to claim 2, characterized in that, Based on multi-base The polarization transformation structure of the nucleus is recursively calculated using the Gaussian approximation method. LLR vector mean of each sub-channel The details are as follows: in, For mathematical expectation calculation, For the corresponding LLR vector, , They are respectively through The two sub-channel symbols after polarization kernel transformation , These are the corresponding received signals. for The Gaussian approximation function, for The inverse function of .

4. The simplified decoding algorithm for multi-level polar codes based on path reliability measurement according to claim 1, characterized in that, The high reliability condition is determined in the following way: Decisions based on the probability domain: For the path list, the first The barcode decoding path, in processing the first When the symbol is given, the calculation is performed on the given received signal. and correctly decoded symbols Posterior probability under given conditions If the following inequality is satisfied: Then determine the symbol of the current path. The decoding result has high confidence, no path splitting operation is required, the current path is preserved and hard decision is made based on the LLR vector; Conversely, if the inequality does not hold, it indicates that the current node has low reliability, and the current path should be split into... 10 paths to cover possible errors; By utilizing Bayes' theorem and the Min-Sum approximation, the decision in the probability domain is transformed into a numerical comparison in the LLR domain to facilitate engineering implementation: Define decision threshold And calculate the log-likelihood ratio parameter. ;in, , Symbols Relative to symbols The LLR value, and They represent the first time. Current information symbols on the path Values The sum can be set to a value of 1. The posterior probability; The formula for determining splits is simplified to: If any condition of the split decision formula is satisfied, then the first... No path needs to be split; the symbol pair of the current path is obtained according to the split decision formula. The decoding result Otherwise, the execution path is split.

5. The simplified decoding algorithm for multi-level polar codes based on path reliability measurement according to claim 1, characterized in that, The counter mechanism based on the number of consecutive unsplits is as follows: For each path in the path list Allocate a counter Used to record paths The number of consecutive stages without splitting; the counter update rules are as follows: In decoding When, if the path If the high reliability condition is met and path splitting is not performed, then the counter is incremented: If path It splits and expands into If there are 10 paths, then the path list contains 10 paths. All counters for new split paths and original paths have been reset: in, Representing a path The counter for one of the new splitting paths; Set counter threshold When the path counter value At that time, path Marked as a high-confidence path; Trigger pruning: When a high-confidence path is found, force pruning is performed immediately, retaining only paths with counter values ​​greater than the threshold. The path will be forcibly deleted if the counter value is less than [a certain value]. The path.

6. The simplified decoding method for multi-level polar codes based on path reliability measurement according to claim 1, characterized in that, The cumulative reliability deviation measurement mechanism is as follows: The first symbol index position of Rate-1 for each polar code block is included in the key set, and the search set is defined based on the key set. ; Define ARD value Used to count decoding paths in the search set Cumulative error risk within; The calculation is based on the estimated symbol of the current path. With search set The distance between the local optimal hard decision results corresponding to the current decoding node, and the ARD value update formula is: in, Indicates the first The barcode decoding path is at the 1st Each decoding stage estimates the symbol The LLR metric value, Indicates the first The barcode decoding path is at the 1st The locally optimal hard-decision symbol in each decoding stage; the ARD value only increases when the decoding path selects a non-locally optimal symbol. Determine the tolerance threshold for ARD The statistical characteristics of the sub-channels were calculated using the Gaussian approximation and then selected. The maximum expected reliability value in the set is used as the upper bound of the maximum deviation that the correct path can tolerate. Calculate the cost of splitting: in processing When encountering a node, assuming the path splits, calculate the ARD value for each candidate branch. Among them, if If the current node does not belong to the search set, the ARD accumulation and ARD-based path splitting operations are not performed, and a hard decision is made directly based on the symbol LLR vector. Perform adaptive pruning: if the ARD value And the symbol corresponding to the current candidate branch If the hard decision symbol is not equal to the local optimum, then the current candidate branch is directly pruned; if If so, the current candidate branch is retained.

7. A simplified decoding system for multi-level polar codes based on path reliability measurement, characterized in that, The system is implemented using a simplified multi-level polar code decoding method as described in any one of claims 1-6, including: The channel polarization module is configured to perform: For additive white Gaussian noise channels, a subchannel reliability model for multi-level polar codes is established using Gaussian approximation theory. The symbol error probability of each information bit is pre-determined by recursively calculating the statistical moments of the LLR vector. The path splitting decision module is configured to execute: During the decoding process, a dynamic reliability threshold is constructed based on the symbol error probability, and the posterior probability of the current path is calculated. If the posterior probability of the current path meets the high reliability condition, then no splitting is required, and a hard decision is made directly. If the posterior probability of the current path does not meet the high reliability condition, a path splitting operation is triggered to generate a new path. There are 10 candidate branches; The dynamic pruning control module is configured to execute: A cumulative reliability deviation measurement mechanism is adopted to calculate the ARD value of each candidate branch in real time during the process of generating candidate branches in the path split decision module; Compare ARD values ​​with search set Calculated tolerance threshold Perform a comparison; Implement a non-full-path splitting strategy: For candidate branches whose ARD values ​​exceed the tolerance threshold and are not locally optimal, delete them directly before adding them to the candidate list, and only retain the valid branches for subsequent sorting; The decoding output module is configured to execute: Maintain a list of surviving paths after dynamic pruning. At the end of decoding, select the candidate codeword with the best path metric from the final surviving path list as the system's decoding output.

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