Soft iterative decoding method for BCH codes

Abstract

The present application belongs to the technical field of iterative decoding, and particularly relates to a soft iterative decoding method of BCH code, steps of which comprise: for the BCH code, extending and optimizing the standard check matrix of the BCH code to obtain a pretreated check matrix; performing quasi-BP iterative decoding, carrying out inflation pretreatment on input information based on an inflation factor, completing an iterative decoding process, and optimizing and combining weight coefficients; constructing a quasi-BP iterative decoding and ordered statistical decoding (OSD) hybrid decoding architecture, triggering the OSD to perform secondary decoding when the quasi-BP iterative decoding is determined as undetectable decoding error (UDE); introducing a scatter-type external information transfer graph analysis tool to optimize parameters; and performing soft iterative decoding on subsequent input BCH codes and optimizing parameters. The present application introduces a scatter-type EXIT tool to quantitatively optimize parameters, and the quasi-BP algorithm is universal and parallel, and can balance high reliability, low complexity and low latency of decoding.

Description

Technical Field

[0001] This invention belongs to the field of iterative decoding technology, specifically relating to a soft iterative decoding method for BCH codes. Background Technology

[0002] In 5G / 6G Ultra Reliable Low Latency Communication (URLLC) systems, BCH codes have attracted widespread attention due to their strict minimum distance guarantee and excellent performance in short to medium code lengths. Unlike LDPC codes, BCH codes have a high-density parity-check matrix (HDPC code). Traditional hard-decision decoding (such as the Berlekamp-Massey algorithm), while computationally simple, has limited performance. Furthermore, iterative decoding algorithms based on sparse graphs, such as Belief Propagation (BP), face significant challenges when processing BCH codes. The dense matrix results in numerous short cycles in the Tanner graph, severely compromising the independence assumption of message passing and leading to poor convergence and degraded error correction performance. To address these issues, several improvement schemes have been proposed: Patent CN119154894B proposes an improved Normalized Minimum Sum (NMS) algorithm based on automorphic input expansion and parity-check matrix redundancy optimization; Patent CN120342407B proposes a hybrid decoding architecture combining ordered statistical decoding (OSD), reducing OSD complexity through neural network assistance and dynamic path construction.

[0003] However, existing technologies still have significant shortcomings. First, although the improved NMS algorithm can achieve parallel processing on BCH codes, its FER performance is still more than 0.5dB lower than that of layered BP decoding of LDPC codes with the same code rate. This leads to the need for frequent calls to the subsequent OSD decoder in the low to medium signal-to-noise ratio region, increasing the overall decoding latency. Second, OSD and its improved versions are essentially serial algorithms, relying on Gaussian elimination and enumeration of test error patterns. The computational complexity increases exponentially with the order, making it difficult to fully utilize the throughput advantages of parallel processing hardware such as GPUs. More importantly, systematic theoretical analysis tools for iterative decoding algorithms of BCH codes have long been lacking. Mature EXIT graph and scattered EXIT analysis methods in the LDPC code field have not been effectively applied to the quasi-BP algorithm optimization of BCH codes. This results in a lack of quantitative basis for the selection of key parameters such as input expansion factor, parity check matrix redundancy, and maximum number of iterations, and decoder design remains in a rough stage of trial and error. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the purpose of this invention is to provide a soft iterative decoding method for BCH codes, introduce a scattered EXIT analysis tool to quantitatively optimize the decoding parameters, and adopt a general parallel architecture design for the quasi-BP algorithm, which can simultaneously take into account high reliability, low computational complexity and low decoding latency.

[0005] To achieve the above objectives, this invention provides a soft iterative decoding method for BCH codes, comprising the following steps:

[0006] S1. For BCH codes, determine the redundancy, expand the standard parity-check matrix of the BCH code using the redundancy, and then optimize the expanded parity-check matrix to obtain the preprocessed parity-check matrix. ;

[0007] S2, based on The process involves performing quasi-BP iterative decoding, utilizing the automorphism of BCH codes, and performing preprocessing of the input information based on the expansion factor. The iterative decoding process is completed through variable node information distribution, check node message update, and message alignment and merging, and the merging weight coefficient is optimized.

[0008] S3. Construct a hybrid decoding architecture of quasi-BP iterative decoding and ordered statistical decoding (OSD). When the quasi-BP iterative decoding determines an undetectable decoding error (UDE), the ordered statistical decoder (OSD) is triggered to perform secondary decoding.

[0009] S4. The Scattered EXIT analysis tool for external information transfer graphs is introduced to optimize parameters. The optimized parameters include the maximum number of iterations in quasi-BP iterative decoding, the inflation factor during inflation preprocessing, and the redundancy of the parity check matrix.

[0010] S5. Based on S1~S2, perform soft iterative decoding on the subsequent input BCH code, and optimize the parameters based on S4.

[0011] As a preferred embodiment of the present invention, in S1, for a BCH code with a code length of N and an information bit length of K, the number of rows in its standard parity check matrix is ​​reduced from... Expand to , For redundancy.

[0012] As a preferred embodiment of the present invention, in S2, the input dilation method utilizing the automorphic property of BCH codes is at least one of interleaved permutation mapping, Frobenius mapping, and cyclic shift mapping.

[0013] As a preferred embodiment of the present invention, the quasi-BP iterative decoding process in S2 is as follows:

[0014] S2.1 Initialization: Iteration index t=0, based on the received sequence Calculate the initial log-likelihood ratio:

[0015] ;

[0016] In the formula, The variance of the channel additive white Gaussian noise is estimated. This represents the i-th received signal, where N is the code length; express The corresponding initial log-likelihood ratio;

[0017] S2.2, Input Inflation: For Preprocessing is performed using the automorphism property of BCH codes to obtain the dilated... Double the input information, It is the expansion factor;

[0018] S2.3, Variable Node Update: Update each variable node in the expanded input information. The corresponding log-likelihood ratio is used as the message distribution to the connected verification nodes. The message passing formula is:

[0019] ;

[0020] In the formula, Indicates the time of the t-th iteration The corresponding log-likelihood ratio; This represents the i-th variable node; Indicates and The j-th connected verification node, , To and A set of connected verification nodes; Indicates from Distribute to External news; Indicates an expansion operation;

[0021] S2.4, Verification Node Update: For each Calculated and sent according to the BP algorithm Message:

[0022] ;

[0023] In the formula, This indicates that at the t-th iteration, from Send to External news; Indicates the variable node index, referring to and Connected and Excluded Other variable nodes besides Indicates and A set of connected variable nodes; This is the product operator; This indicates that at the t-th iteration, from Send to External information;

[0024] S2.5, Align and Merge: [This part is incomplete and requires more context to translate accurately.] Perform an inverse transformation based on the automorphism mapping during input dilation, then align and merge the blocks to obtain... Each message block is updated, and the log-likelihood ratio sequence before inflation is updated.

[0025] ;

[0026] In the formula, This indicates that in the w-th message block at the t-th iteration, from Send to External news; Indicates the time at the (t+1)th iteration The corresponding log-likelihood ratio; The merging weight coefficients to be optimized; express The inverse function;

[0027] S2.6, Decision: Output the hard decision result based on the updated log-likelihood ratio sequence. If the hard decision result... Satisfying the verification matrix test If the iteration fails, the iteration terminates and the result is output; otherwise, the iteration count is t=t+1, and the process returns to S2.2 to continue iterating until the maximum number of iterations is reached.

[0028] As a preferred embodiment of the present invention, in S2.5, The optimization uses a binary search method, where e is the natural constant and x is the variable to be optimized, specifically:

[0029] S2.5.1 Selecting the initial optimization interval Let a and b be the lower and upper limits of the initial optimization interval, respectively, and take the midpoint of the interval. ;

[0030] S2.5.2 Select a value , To find the minimum value, calculate separately. , The corresponding frame error rate (FER) index , ;

[0031] S2.5.3, if If the interval is not equal, then update the upper limit of the interval b=d; otherwise, update the lower limit of the interval a=d.

[0032] S2.5.4 Repeat steps S2.5.1 to S2.5.3 until the interval length is reduced to the preset threshold, and take the d at this time as the optimal x value.

[0033] As a preferred embodiment of the present invention, the step of parameter optimization using the ScatteredEXIT scatter plot analysis tool in S4 includes:

[0034] S4.1 Maximum number of iterations Selection: Select frame error rate Using the corresponding signal-to-noise ratio (SNR) as a reference point, the average mutual information output by the variable nodes is calculated. Average mutual information between the curve and the output of the check node The iteration number corresponding to the curve intersection point plus 2 to 5 is used as... The optimal reference value;

[0035] S4.2, Expansion Factor Selection: Set redundancy factor , Based on S4.1, in In scenarios where the initial value asymptotically increases and the SNR takes multiple different values, the records are... The slope and saturation value of the curve as a function of iteration number are selected. along with When an increase leads to stagnation As the optimal value;

[0036] S4.3, Redundancy Select: Set the expansion factor , Based on S4.1, in In scenarios where the initial value asymptotically increases and the SNR takes multiple different values, the records are... The slope and saturation value of the curve as a function of iteration number are selected. along with When an increase leads to stagnation As the optimal value.

[0037] As a preferred embodiment of the present invention, in step S4, parameter optimization further includes:

[0038] Based on scattered external information transfer analysis, establish Correlation model with FER: Select a uniform mutual information threshold and utilize the iterative process The bimodal distribution characteristic of the signal can be used to quickly predict the FER performance under different SNR by statistically analyzing the proportion of received sequences that are less than the mutual information threshold.

[0039] The beneficial effects of this invention are:

[0040] This invention overcomes the limitation of traditional BP-type algorithms being only applicable to LDPC sparse parity-check matrices. By exploiting the automorphic characteristics of BCH codes, a quasi-BP iterative decoding algorithm is designed. Combined with parity-check matrix redundancy expansion and input dilation preprocessing, the FER performance of BCH code decoding is significantly improved. Its error correction performance is only about 0.15dB different from that of layered BP decoding of LDPC codes with the same code rate. Moreover, the hybrid decoding architecture of quasi-BP+OSD reduces the OSD call frequency due to the stronger error correction capability of the quasi-BP decoder. While approaching the maximum likelihood decoding performance, it significantly improves the data throughput and solves the latency problem caused by frequent OSD calls under medium and low signal-to-noise ratios in the existing NMS+OSD architecture.

[0041] This invention introduces a scattered external information transfer (Scattered EXIT) analysis tool, providing quantitative optimization basis for key parameters such as maximum iteration count, expansion factor, and parity check matrix redundancy, thus breaking away from the traditional experience-based trial-and-error design mode. It also optimizes the message merging weight coefficient through a binary search method and achieves rapid prediction of frame error rate by combining the correlation model of mutual information and FER. Furthermore, the quasi-BP algorithm has good versatility and can be directly applied to higher code rates, longer code lengths of BCH codes, and even RS codes. At the same time, the algorithm supports parallel processing, which can give full play to the throughput advantages of hardware such as GPUs. In 5G / 6G URLLC systems, it balances high reliability, low complexity, and low latency in decoding. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating the principle of this invention;

[0043] Figure 2 This is a schematic diagram of the hybrid decoding architecture in this invention;

[0044] Figure 3 This is a schematic diagram of the quasi-BP decoding algorithm from an information theory perspective in Embodiment 1 of the present invention;

[0045] Figure 4 This is a performance comparison of various decoding algorithms for BCH(127,64) and LDPC(128,64) codes in Embodiment 1 of the present invention;

[0046] Figure 5 This is a performance comparison of various decoding algorithms for the BCH(127,99) code in Embodiment 1 of the present invention;

[0047] Figure 6 This is a performance comparison of various decoding algorithms for the BCH(255,239) code in Embodiment 1 of the present invention;

[0048] Figure 7 This is the maximum number of iterations selected in Embodiment 1 of the present invention. , Intersection diagram;

[0049] Figure 8 This is a schematic diagram illustrating the relationship between average mutual information and error correction FER in Embodiment 1 of the present invention. Detailed Implementation

[0050] The embodiments of the present invention will be further described below with reference to the accompanying drawings:

[0051] Example 1: As Figure 1 As shown, the soft iterative decoding method for BCH codes includes the following steps:

[0052] S1. For BCH codes, determine the redundancy, expand the standard parity-check matrix of the BCH code using the redundancy, and then optimize the expanded parity-check matrix to obtain the preprocessed parity-check matrix. ;

[0053] S2, based on The process involves performing quasi-BP iterative decoding, utilizing the automorphism of BCH codes, and performing preprocessing of the input information based on the expansion factor. The iterative decoding process is completed through variable node information distribution, check node message update, and message alignment and merging, and the merging weight coefficient is optimized.

[0054] S3. Construct a hybrid decoding architecture of quasi-BP iterative decoding and ordered statistical decoding (OSD). When the quasi-BP iterative decoding determines an undetectable decoding error (UDE), the ordered statistical decoder (OSD) is triggered to perform secondary decoding.

[0055] S4. The Scattered EXIT analysis tool for external information transfer graphs is introduced to optimize parameters. The optimized parameters include the maximum number of iterations in quasi-BP iterative decoding, the inflation factor during inflation preprocessing, and the redundancy of the parity check matrix.

[0056] S5. Based on S1~S2, perform soft iterative decoding on the subsequent input BCH code, and optimize the parameters based on S4.

[0057] S1 can be extended and optimized based on the content disclosed in CN119154894B, the normalized minimum sum decoding of BCH codes and its post-processing decoding method.

[0058] In S3, such as Figure 2As shown, the ordered statistical decoding hybrid decoding architecture is specifically as follows: In the NMS+OSD hybrid decoding architecture disclosed in CN120342407B, a BCH code-based error correction decoding method, the NMS is replaced with a quasi-BP decoder with stronger decoding capabilities, while the subsequent OSD (the OSD disclosed in CN120342407B, i.e., the improved OSD) is kept as an auxiliary decoder. This hybrid architecture, which triggers the OSD only when the quasi-BP decoding fails, can achieve near-maximum likelihood (ML) performance while significantly improving overall data throughput due to the reduced OSD call frequency caused by the stronger error correction capability of the quasi-BP decoder.

[0059] A variable node, in a Tanner graph (a bipartite graph used to represent the parity-check matrix of a linear block code), represents a single bit (information bit or parity bit) in the codeword. During the decoding iteration, the variable node collects messages from connected parity-check nodes and initial channel information, updates them, and passes them to the parity-check nodes.

[0060] In the Tanner graph, a check node represents a node in a parity check equation. During the decoding iteration, the check node calculates the extrinsic information of each variable node under the check constraint based on the messages from the connected variable nodes and then transmits it back.

[0061] In S1, for a BCH code of length N and information bit length K, the number of rows in its standard parity-check matrix is ​​reduced from... Expand to , Redundancy (initial value is 1, subsequent...) The minimum increment for optimization is 0.5.

[0062] The input dilation method utilizing the automorphism property of BCH codes is at least one of the following: interleaved permutation mapping, Frobenius mapping, and cyclic shift mapping.

[0063] The process of quasi-BP iterative decoding is as follows:

[0064] S2.1 Initialization: Iteration index t=0, based on the received sequence Calculate the initial log-likelihood ratio:

[0065] ;

[0066] In the formula, The variance of the channel additive white Gaussian noise is estimated. This represents the i-th received signal, where N is the code length; express The corresponding initial log-likelihood ratio;

[0067] S2.2, Input Inflation: For Preprocessing is performed using the automorphism property of BCH codes to obtain the dilated... Double the input information, It is the expansion factor;

[0068] The initial value is 3, and the expansion logic is to increase the original input... The expansion can be superimposed in three forms:

[0069] The original input itself: the initial information remains unchanged;

[0070] Interleaved permutation mapping of the original input: the version after interleaving (permutation) the original input;

[0071] The Frobenius mapping of the original input: the version after transforming the input using the Frobenius automorphism of BCH code over a finite field;

[0072] When these three pieces of information are combined, the amount of input information becomes three times the original amount. The initial value is 3.

[0073] Follow-up The minimum increment for optimization is 3 (that is, during cyclic shifting, all three pieces of information superimposed above must be cyclically shifted simultaneously).

[0074] S2.3, Variable Node Update: Update each variable node in the expanded input information. The corresponding log-likelihood ratio is used as the message distribution to the connected verification nodes. The message passing formula is:

[0075] ;

[0076] In the formula, Indicates the time of the t-th iteration The corresponding log-likelihood ratio; This represents the i-th variable node; Indicates and The j-th connected verification node, , To and A set of connected verification nodes; Indicates from Distribute to External news; This represents the expansion operation caused by the introduction of various mappings;

[0077] S2.4, Verification Node Update: For each Calculated and sent according to the BP algorithm Message:

[0078] ;

[0079] In the formula, This indicates that at the t-th iteration, from Send to External news; Indicates the variable node index, referring to and Connected and Excluded Other variable nodes besides Indicates and A set of connected variable nodes; This is the product operator; This indicates that at the t-th iteration, from Send to External information;

[0080] S2.5, Align and Merge: [This part is incomplete and requires more context to translate accurately.] Perform an inverse transform based on the automorphism mapping during input dilation, then align and merge the blocks to obtain... Each message block is updated, and the log-likelihood ratio sequence before inflation is updated.

[0081] ;

[0082] In the formula, This indicates that in the w-th message block at the t-th iteration, from Send to External news; Indicates the time at the (t+1)th iteration The corresponding log-likelihood ratio; The merging weight coefficients to be optimized; express The inverse function;

[0083] The optimization uses a binary search method, where e is the natural constant and x is the variable to be optimized, specifically:

[0084] S2.5.1 Selecting the initial optimization interval a=-10 and b=10 are the lower and upper limits of the initial optimization interval, respectively, and the midpoint of the interval is taken. ;

[0085] S2.5.2 Select a value , To find the minimum value, calculate separately. , The corresponding frame error rate (FER) index , ;

[0086] S2.5.3, if If the interval is not equal, then update the upper limit of the interval b=d; otherwise, update the lower limit of the interval a=d.

[0087] S2.5.4 Repeat steps S2.5.1 to S2.5.3 until the interval length is reduced to the preset threshold of 0.1, and take the d at this time as the optimal x value;

[0088] S2.6, Decision: Output the hard decision result based on the updated log-likelihood ratio sequence. If the hard decision result... Satisfying the verification matrix test If the iteration fails, the iteration terminates and the result is output; otherwise, the iteration count is t=t+1, and the process returns to S2.2 to continue iterating until the maximum number of iterations is reached.

[0089] The quasi-BP decoding algorithm flow from an information theory perspective is as follows: Figure 3 As shown, by Figure 3 It is known that the operations of the variable nodes in the quasi-BP decoding algorithm include message combining, input dilation, and message dispatch, which together constitute the update function of the variable nodes. From the perspective of mutual information (MI) evolution, input dilation and message dispatch operations themselves do not directly improve mutual information; only message combining can substantially improve mutual information. Figure 3 The input switch indicates The input is used only once during initialization, after which the switch toggles. It no longer works, making subsequent iterations rely solely on internal message exchanges. Figure 3 In this context, the dispatcher is used for message distribution, and the merger is used for alignment and merging. It is the average mutual information of the variable node inputs. It is the average mutual information corresponding to the received sequence transmitted from the channel when decoding begins.

[0090] Scattered EXIT Analysis is an improved EXIT analysis method based on actual simulation data. Unlike traditional methods that use theoretical derivation or simplified models to draw smooth EXIT curves, this method more realistically and meticulously depicts the convergence dynamics of the decoder by sampling extensively and drawing scatter plots of the external information exchanged between variable nodes and check nodes in each decoding iteration.

[0091] Use the Scattered EXIT tool to obtain mutual information of the output of variable nodes. ) and mutual information output by the verification node ( The metric uses three expectation approximation methods to measure the mutual information of node outputs in iterative decoding:

[0092] The first method involves taking a fixed received sequence and then averaging the mutual information of all edges between the variable nodes and the check nodes during the iterative decoding process to approximate the result. Alternatively, the mutual information of all edges between the verification node and the variable node can be averaged to approximate the result. In the first type of metric The first method is applicable in the fast computation and FER correlation model; the second method is to select an edge for message passing between the variable node and the check node, and approximate the result by averaging the corresponding mutual information of all received sequences along this edge from the variable node to the check node during iterative decoding. Alternatively, one can approximate the result by averaging the mutual information of all received sequences along the direction from the verification node to the variable node during iterative decoding. .

[0093] The second metric can be used to study the difference in the distribution of average mutual information between the sides as the number of received sequences increases. This second metric is not used in this invention; it is only proposed for the sake of definitional completeness.

[0094] The third metric is the average of the joint distribution of all edges between the variable node and the check node and all received sequences, which is approximated by the average of the mutual information in the direction from the variable node to the check node. It is approximated by the average of the mutual information in the direction from the verification node to the variable node. The third metric applies by default to all discussions (except...). Outside of the fast calculation and FER correlation model.

[0095] All three approximations are based on log-likelihood ratio soft information, and are calculated through mutual information kernel functions. Then, a large number of channel realizations and Tanner graph edge samples are statistically analyzed to finally obtain the evolutionary scatter cloud and average trajectory of the mutual information output by variable nodes and check nodes, providing a quantitative basis for parameter optimization of the quasi-BP iterative decoding algorithm.

[0096] In S4, the steps for parameter optimization using the Scattered EXIT scatter plot analysis tool for external information transfer include:

[0097] S4.1 Maximum number of iterations Selection: Select frame error rate Using the corresponding signal-to-noise ratio (SNR) as a reference point, the average mutual information output by the variable nodes is calculated. Average mutual information between the curve and the output of the check node The iteration count corresponding to the curve intersection point is increased by 2 to 5, representing a compromise to control computational complexity. The optimal reference value;

[0098] S4.2, Expansion Factor Selection: Set redundancy factor , Based on S4.1, in Asymptotically increasing from the initial value (e.g.) Furthermore, in scenarios where SNR takes multiple different values, the record... The slope and saturation value of the curve as a function of iteration number are selected. along with When an increase leads to stagnation As the optimal value;

[0099] S4.3, Redundancy Select: Set the expansion factor , Based on S4.1, in Asymptotically increasing from the initial value (e.g.) Furthermore, in scenarios where SNR takes multiple different values, the record... The slope and saturation value of the curve as a function of iteration number are selected. along with When an increase leads to stagnation As the optimal value.

[0100] Parameter optimization also includes:

[0101] Based on scattered external information transfer analysis, establish Correlation model with FER: A uniform mutual information threshold (0.7) is selected, and the correlation is established during the iteration process. The bimodal distribution characteristic of the signal can be used to quickly predict the FER performance under different SNR by statistically analyzing the proportion of received sequences that are less than the mutual information threshold.

[0102] The effectiveness of the method in this embodiment is verified through decoding examples of three different BCH codes:

[0103] For BCH(127,64) code, set , The FER performance of quasi-BP iterative decoding is as follows: Figure 4 As shown. Figure 4 The paper also demonstrates the bit error rate (BER) of the improved BP-RNN based on traditional BP (only BER data is available in existing literature), the improved NMS (NMS mentioned in CN119154894B), the neural network version of NBP based on CCSDS LDPC(128,64) code, and the FER performance of layered BP decoding.

[0104] All algorithms follow The increase leads to an exponential decrease in the bit error rate / frame error rate. It is the energy carried by each bit of information. (This is the power spectral density of additive white Gaussian noise). At low SNR (1-2 dB), the differences between algorithms are small. At high SNR (4-5 dB), the performance gap is significant. Because BCH codes belong to the HDPC family, although BP-RNN uses a neural network, its BER performance is severely uncompetitive due to the strong correlation between messages. Figure 4 The dashed line shows that even compared to the FER of other algorithms, the BER of BP-RNN is lower at BER=10. -2 The current level still lags behind by more than 1.5 dB, and because this slope is the smallest, it indicates that the gap will widen as the SNR increases. Improved NMS ( The FER of ) has been greatly improved, but the layered BP of the CCSDSLDPC(128,64) code with a similar code rate is still comparable. Compared to FER=10 -3 There is still a gap of about 1dB. Even if the maximum number of iterations is increased to 50, the NBP algorithm with neural network support still lags behind the layered BP algorithm with layered scheduling strategy by about 0.1dB due to the flooding scheduling strategy.

[0105] The quasi-BP algorithm (quasi-BP iterative decoding) proposed in this embodiment shows a performance in FER on BCH codes that lags behind the hierarchical decoding algorithm on LDPC codes by only about 0.15 dB. Furthermore, the NBP and BP decoders for LDPC codes, and the quasi-BP decoder for BCH codes, all exhibit almost the same performance degradation slope, indicating that the performance gap does not widen with increasing SNR. In the extremely high SNR region where LDPC codes typically exhibit error-floor effects, BCH codes, with their excellent minimum distance and dense parity check structure, are expected to effectively reduce or eliminate error-floor effects, thus offering a greater advantage.

[0106] For BCH(127,99) code, set , The performance of quasi-BP iterative decoding FER is as follows Figure 5 As shown.

[0107] Regarding BER, BP-RNN performs well at FER=10. -3 The performance of the quasi-BP proposed in this embodiment lags behind the improved NMS by at least 1 dB, and the gap widens as the SNR increases. However, in terms of FER or BER, the quasi-BP proposed in this embodiment leads the improved NMS by at least 0.5 dB. Nevertheless, its FER is still approximately 1 dB behind the maximum likelihood decoding performance.

[0108] For longer, higher code rates of BCH(255,239), set , The FER performance of quasi-BP iterative decoding is as follows: Figure 6 As shown.

[0109] Depend on Figure 6 It can be seen that the quasi-BP distance ML performance is at FER=10 -4 The difference is only about 0.6 dB, and because the descent slopes are similar, the difference does not increase with increasing SNR. In contrast, the BM (Berlekamp-Massey) based hard iterative decoding algorithm HDD is a serial process, and at FER=10... -4 The FER performance lags behind the standard BP by about 1 dB, and due to the smaller slope, the FER performance lags behind even more as the SNR increases.

[0110] Clearly, the quasi-BP algorithm proposed in this embodiment has good versatility and can be applied to longer and higher code rates BCH codes without modification.

[0111] CN120342407B proposed a hybrid decoding architecture of improved NMS + improved OSD and verified its ability to achieve maximum likelihood decoding FER performance on short codes in BCH. This embodiment replaces the improved NMS, which serves as a sub-decoder, with a more powerful quasi-BP decoder, while retaining the subsequent improved OSD as an auxiliary decoder. Clearly, this hybrid decoding architecture of quasi-BP + improved OSD can also achieve maximum likelihood FER performance. Furthermore, because the quasi-BP algorithm performs better in parallel decoding, the frequency of calling the serially operating improved OSD is reduced, which will further improve the data throughput of the entire hybrid decoding architecture.

[0112] An example of parameter optimization using the Scattered EXIT tool, a scatter plot-based external information transfer graph, is shown below:

[0113] For BCH(127,64) code, set At SNR=3.0dB and FER≈0.07, such as Figure 7 visible, and The intersection occurs at iteration number 16, so 16 + 2 = 18 can be chosen as the intersection. The reference value. Continue to increase. It has limited effect on improving FER.

[0114] As shown in Table 1, for the BCH(127,64) code, in setting hour, These correspond to the input inflation factors. As shown in Table 1, with... Increase, The corresponding increase is applied at every SNR point, ensuring a stable improvement in decoding performance. Meanwhile, The situation is more than There has been a significant improvement, and it has further increased to The benefits are significantly reduced, and a trade-off between performance and complexity must be struck.

[0115] Table 1 Example of the expansion factor selection process

[0116]

[0117] As shown in Table 2, for the BCH(127,64) code, in setting hour, The corresponding row numbers of the parity-check matrix are 63, 94, and 126, respectively. As shown in Table 2, with... Increase, The redundancy is increased at every SNR point, ensuring a stable improvement in decoding performance. Meanwhile, it can be observed that as the number of iterations increases, the high redundancy leads to... Revenue narrowed.

[0118] Table 2 Example of Redundancy Selection Process

[0119]

[0120] Define the threshold for change ,set up , , In all received sequences, the following condition is met: The percentage count in the Monte Carlo simulation is very close to the FER result obtained by observing failed cases through traditional counting verification, such as... Figure 8 As shown, where, This represents the average mutual information between all messages passed from the check node to the variable node and the actual transmitted bits at the end of the iterative decoding of this received sequence. Because... It is a continuous value, and its statistical properties show better convergence than FER based on traditional counting. Furthermore, due to... Figure 8 It can be seen that as the number of iterations increases, The improvement in the proportion can also be used as a selection criterion. The basis for this.

[0121] Example 2: A soft iterative decoding device for BCH codes, comprising:

[0122] One or more processors;

[0123] Memory, used to store one or more computer programs;

[0124] When one or more programs are executed by one or more processors, the one or more processors execute the method in Example 1.

[0125] Example 3: A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, cause the processor to perform the method in Example 1.

Claims

1. A soft iterative decoding method for BCH codes, characterized in that... Includes the following steps: S1. For BCH codes, determine the redundancy, expand the standard parity-check matrix of the BCH code using the redundancy, and then optimize the expanded parity-check matrix to obtain the preprocessed parity-check matrix. ; S2, based on The process involves performing quasi-BP iterative decoding, utilizing the automorphism of BCH codes, and performing preprocessing of the input information based on the expansion factor. The iterative decoding process is completed through variable node information distribution, check node message update, and message alignment and merging, and the merging weight coefficient is optimized. The process of quasi-BP iterative decoding is as follows: S2.1 Initialization: Iteration index t=0, based on the received sequence Calculate the initial log-likelihood ratio: ； In the formula, The variance of the channel additive white Gaussian noise is estimated. This represents the i-th received signal, where N is the code length; express The corresponding initial log-likelihood ratio; S2.2, Expansion Pretreatment: For Preprocessing is performed using the automorphism property of BCH codes to obtain the dilated... Double the input information, It is the expansion factor; S2.3, Variable Node Information Distribution: Distribute each variable node in the expanded input information. The corresponding log-likelihood ratio is used as the message distribution to the connected verification nodes. The message passing formula is: ； In the formula, Indicates the time of the t-th iteration The corresponding log-likelihood ratio; This represents the i-th variable node; Indicates and The j-th connected verification node, , To and A set of connected verification nodes; Indicates from Distribute to External news; Indicates an expansion operation; S2.4, Verification Node Message Update: For each Calculated and sent according to the BP algorithm Message: ； In the formula, This indicates that at the t-th iteration, from Send to External news; Indicates the variable node index, referring to and Connected and Excluded Other variable nodes besides Indicates and A set of connected variable nodes; This is the product operator; This indicates that at the t-th iteration, from Send to External information; S2.5, Message Alignment and Merging: Perform an inverse transformation based on the automorphic mapping during dilation preprocessing, then merge the blocks after alignment to obtain... Each message block is updated, and the log-likelihood ratio sequence before inflation is updated. ； In the formula, This indicates that in the w-th message block at the t-th iteration, from Send to External news; Indicates the time at the (t+1)th iteration The corresponding log-likelihood ratio; The merging weight coefficients to be optimized; express The inverse function; S2.6, Decision: Output the hard decision result based on the updated log-likelihood ratio sequence. If the hard decision result... Satisfying the verification matrix test If the iteration fails, the iteration terminates and the result is output; otherwise, the iteration count is t=t+1, and the process returns to S2.2 to continue iterating until the maximum number of iterations is reached. S3. Construct a hybrid decoding architecture of quasi-BP iterative decoding and ordered statistical decoding (OSD). When the quasi-BP iterative decoding determines an undetectable decoding error (UDE), the ordered statistical decoder (OSD) is triggered to perform secondary decoding. S4. The Scattered EXIT analysis tool for external information transfer graphs is introduced to optimize parameters. The optimized parameters include the maximum number of iterations in quasi-BP iterative decoding, the inflation factor during inflation preprocessing, and the redundancy of the parity check matrix. S5. Based on S1~S2, perform soft iterative decoding on the subsequent input BCH code, and optimize the parameters based on S4.

2. The soft iterative decoding method for BCH codes according to claim 1, characterized in that, In S1, for a BCH code with a code length of N and an information bit length of K, the number of rows in its standard parity check matrix is ​​reduced from... Expand to , For redundancy.

3. The soft iterative decoding method for BCH codes according to claim 1, characterized in that, In S2, the method of using the automorphic property of BCH codes for dilation preprocessing is at least one of interleaved permutation mapping, Frobenius mapping, and cyclic shift mapping.

4. The soft iterative decoding method for BCH codes according to claim 1, characterized in that, In S2.5, The optimization uses a binary search method, where e is the natural constant and x is the variable to be optimized, specifically: S2.5.1 Selecting the initial optimization interval Let a and b be the lower and upper limits of the initial optimization interval, respectively, and take the midpoint of the interval. ; S2.5.2 Select a value , To find the minimum value, calculate separately. , The corresponding frame error rate (FER) index , ; S2.5.3, if If the interval is not equal, then update the upper limit of the interval b=d; otherwise, update the lower limit of the interval a=d. S2.5.4 Repeat steps S2.5.1 to S2.5.3 until the interval length is reduced to the preset threshold, and take the d at this time as the optimal x value.

5. The soft iterative decoding method for BCH codes according to claim 1, characterized in that, In step S4, the parameter optimization step using the Scattered EXIT scatter plot analysis tool includes: S4.1 Maximum number of iterations Selection: Select frame error rate Using the corresponding signal-to-noise ratio (SNR) as a reference point, the average mutual information output by the variable nodes is calculated. Average mutual information between the curve and the output of the check node The iteration number corresponding to the curve intersection point is increased by 2 to 5, which is used as... The optimal reference value; S4.2, Expansion Factor Selection: Set redundancy factor , Based on S4.1, in In scenarios where the initial value asymptotically increases and the SNR takes multiple different values, the records are... The slope and saturation value of the curve as a function of iteration number are selected. along with When an increase leads to stagnation As the optimal value; S4.3, Redundancy Select: Set the expansion factor , Based on S4.1, in In scenarios where the initial value asymptotically increases and the SNR takes multiple different values, the records are... The slope and saturation value of the curve as a function of iteration number are selected. along with When an increase leads to stagnation As the optimal value.

6. The soft iterative decoding method for BCH codes according to claim 5, characterized in that, In S4, parameter optimization further includes: Based on scattered external information transfer analysis, establish Correlation model with FER: Select a uniform mutual information threshold and utilize the iterative process The bimodal distribution characteristic of the signal can be used to quickly predict the FER performance under different SNR by statistically analyzing the proportion of received sequences that are less than the mutual information threshold.

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