Polar code belief propagation decoding and stopping method based on soft information evolution

Abstract

This invention relates to a polar code confidence propagation decoding stop-control method based on soft information evolution, belonging to the field of communication signal processing. The invention constructs a soft information indicator function to characterize the evolution of soft information reliability during the decoding process, and combines this with hard decision change information between adjacent iterations to characterize and distinguish different states during the confidence propagation decoding process. By introducing an error convergence detection mechanism in the low-reliability region and combining comprehensive verification results with a dual-threshold decision mechanism in the high-reliability region, this invention effectively distinguishes between successful decoding states and uncorrectable failure states, thereby reducing the number of invalid iterations, lowering decoding latency and computational complexity, and improving the real-time processing efficiency of the communication receiver. Furthermore, this invention employs a comprehensive vector incremental update method based on hard decision difference vectors to reduce comprehensive verification overhead and improves the reliability of the final decoded output by retaining the optimal candidate results. This method is applicable to polar code confidence propagation decoding stop-control in wireless communication receivers.

Description

Technical Field

[0001] This invention relates to a method for determining the stopping of polar code confidence propagation decoding based on soft information evolution, belonging to the field of communication signal processing. Background Technology

[0002] As mobile communication systems evolve towards higher reliability and lower latency, the demands for reliable reception under conditions of short packet transmission, control signaling transmission, and complex wireless channels place higher requirements on the balance between decoding performance, processing latency, and implementation complexity in channel coding and decoding methods. Especially in scenarios such as ultra-reliable low-latency communication, the receiver needs to perform highly reliable decoding under limited latency and computational resources. Therefore, researching efficient polar code decoding methods suitable for communication receivers has significant engineering implications.

[0003] Polar codes, as the first channel coding method theoretically proven to achieve binary discrete memoryless channel capacity, possess a clear construction mechanism and good error correction performance. They have been applied to the New Radio (NR) control channel of 5G mobile communication and are considered one of the important candidate coding schemes for future 6G mobile communication. Among existing polar code decoding methods, Successive Cancellation (SC) and Belief Propagation (BP) are two representative technical routes. SC methods have lower complexity, but the decoding process is highly serial, resulting in significant latency and limited throughput. Furthermore, they typically rely on hard decision outputs, limiting their applicability in receiver processing links requiring iterative interaction of soft information. In contrast, BP decoding, based on factor graph iterative message passing, offers advantages such as good parallelism, lower latency, higher throughput, and support for soft input / soft output processing, making it more suitable for iterative receiver scenarios such as joint detection decoding.

[0004] However, the computational complexity and processing latency of BP decoding typically increase significantly with the number of iterations. If it is not possible to determine in a timely manner whether the decoding process has successfully converged or is unlikely to continue converging, it can easily lead to an increase in invalid iterations, thereby affecting the real-time performance and computational resource utilization efficiency of the communication receiver. Therefore, designing an effective stopping method suitable for polar code belief propagation decoding is of great significance for reducing the average number of iterations, decoding latency, and computational overhead.

[0005] Existing methods for early stopping in polar code belief propagation decoding mainly include methods based on generator matrices and log-likelihood ratio features, as well as methods based on comprehensive verification of parity-check matrices. Some methods reduce detection overhead by monitoring specific information bits, frozen bits, or processing unit states, while others determine whether the estimated codeword satisfies code constraints through comprehensive verification. These methods are primarily geared towards successful decoding identification under high signal-to-noise ratio conditions, but they are insufficient in identifying uncorrectable decoding failure states. Consequently, they may continue to perform subsequent iterations even when decoding is difficult to converge, leading to increased processing latency and computational overhead. Furthermore, existing methods are mostly validated in additive white Gaussian noise channels, and their applicability and robustness in real-world fading channel environments still need improvement.

[0006] Therefore, it is necessary to propose a polar code belief propagation decoding stopping method based on soft information evolution to improve the effectiveness of stopping determination, reduce invalid iterations, and enhance its adaptability under actual wireless communication channel conditions. Summary of the Invention

[0007] To address the problem that existing polar code confidence propagation decoding stopping methods are insufficient in identifying uncorrectable decoding failure states, leading to the communication receiver continuing subsequent iterations even when decoding convergence is difficult, thus increasing reception processing latency, computational resource consumption, and impacting real-time reception efficiency, this invention aims to provide a polar code confidence propagation decoding stopping method based on soft information evolution. This method constructs a soft information indicator function representing the evolution of decoding soft information reliability, and combines hard decision change information between adjacent iterations, comprehensive verification results, and a dual-threshold decision mechanism to distinguish between successful decoding states and uncorrectable failure states. This reduces unnecessary iterations, lowers decoding latency and computational complexity, and improves its adaptability in real-world wireless channel environments.

[0008] The objective of this invention is achieved through the following technical solution.

[0009] The present invention discloses The polar code confidence propagation decoding and stopping method based on soft information evolution includes the following steps:

[0010] Step 1: Construct a polar code encoding and channel transmission model to obtain the received signal;

[0011] The sending end generates the original information sequence Where N is the code length, and the information bit index set is... And the number of information bits is K, and the set of frozen bit indices is And for any ,have ; after the code rate After polar code encoding, the codeword is obtained. The generating matrix , For the kernel matrix, It is an nth-order Kronecker power, and The codewords are then subjected to Binary Phase Shift Keying (BPSK) modulation to obtain the transmitted symbol vector. After the transmitted symbol vector is transmitted through the fading channel, the receiving end obtains the received signal.

[0012]

[0013] in, This is the channel fading coefficient vector. For Hadamard product, Let be a Gaussian noise vector, and satisfy... .

[0014] Step 2: Determine the channel prior probability based on the received signal obtained in Step 1; initialize the confidence propagation decoding message based on the polar code factor diagram;

[0015] Construct a confidence propagation decoding factor graph based on the recursive structure of polar codes; for a polar code of length N, its factor graph contains n levels, each containing N / 2 processing units; let the node at the t-th iteration be... The right-to-left message at the location is denoted as Messages from left to right are denoted as Each message is represented as a bit value. The probability pairs; the receiver initializes the channel prior probability of the rightmost node based on the channel observations; the channel prior probability corresponding to the j-th symbol is...

[0016]

[0017] make For the prior message on the left, if the j-th bit corresponds to an information bit, then initialize it as follows: If the j-th bit corresponds to a frozen bit, then initialize it as follows: .

[0018] Step 3: Based on the prior channel probability obtained in Step 2, perform iterative message updates on the polarization code factor graph, calculate the posterior probability of each code element, and obtain the hard decision codeword vector and information bit estimation results.

[0019] In the t-th iteration, the messages of each node are updated according to the following rules.

[0020]

[0021] In the formula, the operator and Let represent the convolution operation in the probability domain and the multiplication operation in the probability domain, respectively; after completing the message update in the t-th iteration, calculate the posterior probability of each symbol based on the updated left and right propagation messages:

[0022]

[0023] The hard-decision codeword vector for the current iteration is obtained based on the posterior probability. ,in:

[0024]

[0025] And generate matrices and vectors based on polar codes. Recover the information bit estimation results of the current iteration. .

[0026] Step 4: Construct a soft information indicator function based on the posterior probability obtained in Step 3, and construct an adjacent iteration difference vector based on the hard decision codeword vector obtained in Step 3.

[0027] After the t-th iteration, a soft information indicator function is constructed based on the posterior probability of each symbol. :

[0028]

[0029] In the formula, This indicates that the j-th symbol takes the value in the t-th iteration. The posterior probability, the soft information indication function It represents the average of the maximum posterior probabilities of all symbols.

[0030] Construct the hard decision difference vector between the t-th iteration and the (t-1)-th iteration. ,in

[0031]

[0032] In the formula, This represents modulo-2 addition; when , indicating that the hard decision result of the j-th symbol is flipped in two adjacent iterations; when When this occurs, it indicates that the hard decision result for that code element has not changed.

[0033] Step 5: When the soft information indicator function is less than the switching threshold after the t-th iteration, perform low-reliability region error convergence detection and stop early;

[0034] After the t-th iteration, the soft information indicator function satisfies When the current decoding process is determined to have entered a low-reliability region, then... To set the switching threshold, the change in the soft information indicator function between the t-th iteration and the (t-1)-th iteration is defined as follows:

[0035]

[0036] If satisfied If the change in the soft information indicator function in the current iteration is considered to be below the preset tolerance range, it indicates that the decoding process tends to stabilize in the low reliability region. The tolerance threshold is changed; at this point, the error convergence counter is updated to...

[0037]

[0038] like Then reset the error convergence counter to ;when When the current confidence propagation decoding process enters a low-reliability error convergence state, it is determined that the current confidence propagation decoding process has entered a low-reliability error convergence state. This is the continuous counting threshold; at this time, the reliable stop flag is set low. If the value is 1, the current decoding iteration process is terminated early, and the information bit estimation result corresponding to the current iteration is output.

[0039] Step 6: When the soft information indication function is greater than or equal to the switching threshold after the t-th iteration, perform a high-reliability region dual-threshold comprehensive verification to stop the decision and retain the candidate output results;

[0040] After the t-th iteration, when the soft information indicator function satisfies When the current decoding process enters a high-reliability region, it is determined that the current decoding process has entered a high-reliability region; within the high-reliability region, the current hard-decision codeword vector is processed. Perform comprehensive verification; let the parity-check matrix of the polar code be... Then the comprehensive vector corresponding to the t-th iteration is

[0041]

[0042] when If the current hard decision codeword is valid, then the current hard decision codeword is invalid; otherwise, the current hard decision codeword is invalid, the iteration count is incremented by 1, and the process returns to step three for the next iteration message update.

[0043] For cases where the codeword is determined to be valid, when When the decoding result corresponding to the current valid codeword is determined to have reached a stable and highly reliable state, then, Set to high threshold; at this time, set the high reliability stop flag. The value is 1, and the information bit estimation result corresponding to the current iteration is used as the final output result; when When the current valid codeword is determined to be a transient valid output, the iteration count is incremented by 1, step three is continued, and the optimal candidate reliability value is set. and the corresponding optimal candidate information bit estimation results When the current soft information indicator function is greater than Update and .

[0044] Step 7: Based on the adjacent iteration difference vector obtained in Step 4, incrementally update the comprehensive vector, and output the final decoding result according to the stopping results of Step 5 and Step 6 or the maximum number of iterations.

[0045] Based on the hard decision difference vector between the t-th iteration and the (t-1)-th iteration The current hard decision codeword is represented as

[0046]

[0047] According to the definition of a composite vector, the composite vector in the t-th iteration satisfies

[0048]

[0049] Since the synthesis operation satisfies a linear superposition relationship over the binary field of the linear code, the incremental update formula for the synthesis vector can be obtained.

[0050]

[0051] Furthermore, let the check matrix be... The j-th column is The set of bit positions where a hard decision flip occurs is denoted as Then the incremental update formula for the composite vector can be rewritten as follows:

[0052]

[0053] If the current iteration count reaches the preset maximum iteration count And not satisfied and Then output the optimal candidate reliability value. The corresponding optimal candidate information bit estimation result As the final decoded output; if the current iteration count has not yet reached the preset maximum iteration count. And not satisfied and If the iteration count is not met, the iteration count is incremented by 1, and the process returns to step three to perform the next iteration message update, posterior probability calculation, hard decision output, and stop decision until the stop condition is met or the maximum number of iterations is reached, at which point the final decoding result is output.

[0054] Beneficial effects:

[0055] 1. The polar code confidence propagation decoding stopping method based on soft information evolution disclosed in this invention constructs a soft information indicator function to characterize the iterative evolution state of soft information reliability during the decoding process. It can effectively distinguish between low-reliability error convergence state and high-reliability decoding state during the decoding process, thereby improving the pertinence and effectiveness of stopping determination.

[0056] 2. The polar code confidence propagation decoding termination method based on soft information evolution disclosed in this invention introduces an error convergence detection mechanism in the low reliability region and uses the changing characteristics of the soft information indicator function in continuous iteration to identify uncorrectable decoding failures. It can terminate invalid iterations in time when decoding is difficult to continue to converge, thereby reducing the average number of iterations and reducing decoding latency and computational overhead.

[0057] 3. The polar code confidence propagation decoding stopping method based on soft information evolution disclosed in this invention, by combining the comprehensive verification result and the soft information reliability in the high reliability region to make a dual-threshold stopping decision, can further distinguish between stable high-reliability output and transient valid output on the basis of satisfying code constraints, thereby reducing the probability of false stopping and improving the accuracy of stopping decision and the reliability of decoding results.

[0058] 4. The polar code confidence propagation decoding stopping method based on soft information evolution disclosed in this invention can output better candidate decoding results when the maximum number of iterations is reached without triggering the stopping condition by setting the optimal value of candidate reliability and retaining the corresponding optimal candidate information bit estimation results, thereby improving the robustness of the decoding output.

[0059] 5. The polar code confidence propagation decoding and stopping method based on soft information evolution disclosed in this invention adopts an incremental synthesis update method based on hard decision difference vector, which only updates the check items corresponding to the bit positions that are flipped between two adjacent iterations, avoiding the full synthesis calculation in each iteration, thereby effectively reducing the computational complexity of synthesis verification in high reliability areas.

[0060] 6. The polar code confidence propagation decoding stopping method based on soft information evolution disclosed in this invention achieves adaptive stopping under different decoding states by jointly designing an error convergence detection mechanism in low-reliability regions and a dual-threshold comprehensive verification mechanism in high-reliability regions. It ensures decoding performance while taking into account complexity and processing latency, and has good engineering implementation value.

[0061] 7. The polar code confidence propagation decoding stop determination method based on soft information evolution disclosed in this invention is not only applicable to polar code confidence propagation decoding stop determination under additive white Gaussian noise channel conditions, but also adaptable to the changing characteristics of decoding state under fading channel conditions, thus having good environmental adaptability and application range.

[0062] 8. The polar code confidence propagation decoding stopping method disclosed in this invention, based on soft information evolution, achieves the above-mentioned beneficial effects by performing error convergence detection in the low reliability region, performing dual-threshold comprehensive verification stopping decision in the high reliability region, and combining incremental comprehensive update mechanism to realize adaptive stopping for polar code confidence propagation decoding. This reduces unnecessary iterations, lowers decoding latency and computational complexity while ensuring decoding performance. Attached Figure Description

[0063] Figure 1 This is a flowchart of the polar code confidence propagation decoding and stopping method based on soft information evolution described in this invention.

[0064] Figure 2 (8, 4) is a schematic diagram of the factor graph structure of the polar code confidence propagation decoding and stopping method based on soft information evolution according to the embodiments of the present invention.

[0065] Figure 3 This is a probability statistic of different received frame types under different signal-to-noise ratios under the soft information indication function described in the embodiments of the present invention, with the polar code (1024, 512) constructed by Bach and the Nakagami-m fading channel parameter m=2.

[0066] Figure 4 The graph shows the block error rate performance comparison curves for different parameter settings under the conditions of the polar code (1024, 512) constructed by Bach and the Nakagami-m fading channel parameter m=2.

[0067] Figure 5 The graph shows the average number of iterations for different parameter settings under the conditions of the polar code (1024, 512) constructed by Bach and the Nakagami-m fading channel parameter m=2. Detailed Implementation

[0068] To make the above-mentioned objects, features and advantages of the present invention more readily understood, they will be further described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment uses a (1024, 512) polar code under the Balotelli construction and uses the Nakagami-m model to simulate the wireless communication channel, where m=2. The system parameters are shown in the table below:

[0069]

[0070] The overall flowchart of the polar code belief propagation decoding and stopping method based on soft information evolution, which is the basis of this embodiment, is as follows: Figure 1 As shown, the factor graph model of the polar code belief propagation decoding and stopping method based on soft information evolution proposed in this embodiment is as follows: Figure 2 As shown.

[0071] like Figure 2 As shown in this embodiment, the polar code confidence propagation decoding and stopping method based on soft information evolution disclosed in this embodiment has the following specific implementation steps:

[0072] Step 1: Construct a polar code encoding and channel transmission model to obtain the received signal;

[0073] The sending end generates the original information sequence Information bit index set With frozen bit index set Determined by the Baptiste construction method; for any ,have ; after the code rate After polar code encoding, the codeword is obtained. The generating matrix The codewords are modulated using BPSK to obtain the transmitted symbol vector. After the transmitted symbol vector is transmitted through the fading channel, the receiving end obtains the received signal.

[0074]

[0075] in, This is the channel fading coefficient vector. For Hadamard product, Let be a Gaussian noise vector, and satisfy... Fading coefficients They are independent of each other, and in this embodiment they follow a Nakagami-m distribution with a probability density function of:

[0076]

[0077] in, This represents the average power, and m=2 represents the shape parameter.

[0078] Step 2: Determine the channel prior probability based on the received signal obtained in Step 1; initialize the confidence propagation decoding message based on the polar code factor diagram;

[0079] A confidence propagation decoding factor graph is constructed based on the recursive structure of polar codes. For a polar code of length N, the factor graph contains 10 levels, each containing 512 processing units. Let the node be [node number missing] in the t-th iteration. The right-to-left message at the location is denoted as Messages from left to right are denoted as Each message is represented as a bit value. The probability pairs; the receiver initializes the channel prior probability of the rightmost node based on the channel observations; the channel prior probability corresponding to the j-th symbol is...

[0080]

[0081] make For the prior message on the left, if the j-th bit corresponds to an information bit, then initialize it as follows: If the j-th bit corresponds to a frozen bit, then initialize it as follows: .

[0082] Step 3: Based on the prior channel probability obtained in Step 2, perform iterative message updates on the polarization code factor graph, calculate the posterior probability of each code element, and obtain the hard decision codeword vector and information bit estimation results.

[0083] In the t-th iteration, the messages of each node are updated according to the following rules.

[0084]

[0085] In the formula, the operator and These represent probability domain convolution and probability domain multiplication operations, respectively, and their specific calculation methods are as follows:

[0086]

[0087] After completing the t-th iteration message update, calculate the posterior probability of each symbol based on the updated left and right propagation messages:

[0088]

[0089] The hard-decision codeword vector for the current iteration is obtained based on the posterior probability. ,in:

[0090]

[0091] And generate matrices and vectors based on polar codes. Recover the information bit estimation results of the current iteration. .

[0092] Step 4: Construct a soft information indicator function based on the posterior probability obtained in Step 3, and construct an adjacent iteration difference vector based on the hard decision codeword vector obtained in Step 3.

[0093] After the t-th iteration, a soft information indicator function is constructed based on the posterior probability of each symbol. :

[0094]

[0095] In the formula, This indicates that the j-th symbol takes the value in the t-th iteration. The posterior probability, the soft information indication function It represents the average of the maximum posterior probabilities of all symbols.

[0096] Construct the hard decision difference vector between the t-th iteration and the (t-1)-th iteration. ,in

[0097]

[0098] In the formula, This represents modulo-2 addition; when , indicating that the hard decision result of the j-th symbol is flipped in two adjacent iterations; when When this occurs, it indicates that the hard decision result for that code element has not changed.

[0099] Step 5: When the soft information indicator function is less than the switching threshold after the t-th iteration, perform low-reliability region error convergence detection and stop early;

[0100] After the t-th iteration, the soft information indicator function satisfies When the current decoding process enters a low-reliability region, the change in the soft information indicator function between the t-th iteration and the (t-1)-th iteration is calculated.

[0101]

[0102] If satisfied If the change in the soft information indicator function during the current iteration is considered to be below the preset tolerance range, it indicates that the decoding process tends to stabilize in the low reliability region; at this point, the error convergence counter is updated to...

[0103]

[0104] like Then reset the error convergence counter to ;when When the current confidence propagation decoding process enters a low-reliability error convergence state, the low-reliability stop flag is set. If the value is 1, the current decoding iteration process is terminated early, and the information bit estimation result corresponding to the current iteration is output.

[0105] Step 6: When the soft information indication function is greater than or equal to the switching threshold after the t-th iteration, perform a high-reliability region dual-threshold comprehensive verification to stop the decision and retain the candidate output results;

[0106] After the t-th iteration, when the soft information indicator function satisfies When the current decoding process enters a high-reliability region, it is determined that the current decoding process has entered a high-reliability region; within the high-reliability region, the current hard-decision codeword vector is processed. Perform comprehensive verification; for the parity check matrix of polar codes The comprehensive vector corresponding to the t-th iteration is

[0107]

[0108] when If the current hard decision codeword is valid, then the current hard decision codeword is determined to be invalid; otherwise, the current hard decision codeword is determined to be invalid, the iteration count is incremented by 1, and the process returns to step three for the next iteration message update.

[0109] For cases where the codeword is determined to be valid, when When the decoding result corresponding to the current valid codeword is determined to have reached a stable and highly reliable state, then, Set to high threshold; at this time, set the high reliability stop flag. The value is 1, and the information bit estimation result corresponding to the current iteration is used as the final output result; when When the current valid codeword is determined to be a transient valid output, the iteration count is incremented by 1, step three is continued, and the optimal candidate reliability value is set. and the corresponding optimal candidate information bit estimation results When the current soft information indicator function is greater than Update and .

[0110] Step 7: Incrementally update the composite vector based on the adjacent iteration difference vector obtained in Step 4, and output the final decoding result according to the stopping decision result or the maximum number of iterations in Steps 5 and 6.

[0111] Based on the hard decision difference vector between the t-th iteration and the (t-1)-th iteration The current hard decision codeword is represented as

[0112]

[0113] According to the definition of a composite vector, the composite vector in the t-th iteration satisfies

[0114]

[0115] Since the synthesis operation satisfies a linear superposition relationship over the binary field of the linear code, the incremental update formula for the synthesis vector can be obtained.

[0116]

[0117] Furthermore, let the check matrix be... The j-th column is The set of bit positions where a hard decision flip occurs is denoted as Then the incremental update formula for the composite vector can be rewritten as follows:

[0118]

[0119] Therefore, by simply accumulating and updating the corresponding column vectors for the bit positions that are flipped between two adjacent iterations, the synthesized vector for the current iteration can be obtained without repeating the complete matrix multiplication operation, thus reducing the complexity of the synthesis verification in the high-reliability region. Throughout the decoding process, if the low-reliability stop flag in step five... Or the high-reliability stop flag in step six. Then terminate the belief propagation decoding iteration and output the currently saved information bit estimation result.

[0120] If the current iteration count reaches the preset maximum iteration count And not satisfied and Then output the optimal candidate reliability value. The corresponding optimal candidate information bit estimation result As the final decoded output; if the current iteration count has not yet reached the preset maximum iteration count, and the condition is not met. and If the iteration count is not met, the iteration count is incremented by 1, and the process returns to step three to perform the next iteration message update, posterior probability calculation, hard decision output, and stop decision, until the stop condition is met or the maximum number of iterations is reached.

[0121] The polar code confidence propagation decoding stopping method based on soft information evolution in this embodiment achieves adaptive stopping for polar code confidence propagation decoding by performing error convergence detection in the low reliability region, performing dual-threshold comprehensive verification stopping decision in the high reliability region, and combining it with an incremental comprehensive update mechanism. This reduces unnecessary iterations, lowers decoding latency, and reduces computational complexity while ensuring decoding performance.

[0122] To verify the ability of the soft information indicator function described in this invention to represent different decoding states, Figure 3 The probabilistic statistics of different received frame types under different signal-to-noise ratios are presented under the condition of a Bavarian polar code (1024, 512) and a Nakagami-m fading channel parameter m=2. Combining the soft information indicator function and its iterative evolution characteristics during the decoding process, the received frames can be divided into three categories: undecodable frames correspond to a low-reliability error convergence state in the decoding process; oscillating frames correspond to repeated changes in soft information and hard decision results between adjacent iterations during the decoding process, without yet achieving stable convergence; and decodable frames correspond to a stable, high-reliability convergence state that is ultimately achieved in the decoding process. Figure 3 It is evident that as the signal-to-noise ratio (SNR) increases, the dominant received frame type shifts from undecodable frames to oscillating frames and then back to decodable frames. Specifically, undecodable frames dominate in low SNR regions, oscillating frames increase in proportion in medium SNR regions, and decodable frames gradually become dominant in high SNR regions. This statistical result demonstrates that the stopping mechanism constructed based on soft information evolution in this invention can effectively reflect the changing patterns of decoding states under different channel conditions, providing support for error convergence detection in low-reliability regions and stopping decisions in high-reliability regions.

[0123] Simulation analysis was performed on the code pattern of this embodiment to measure the block error rate and average number of iterations. The impact of setting three threshold parameters on decoding performance was observed. Simulation results for some parameters are shown below. Figure 4 and Figure 5 As shown, taking the Babbitt polar code (1024, 512) as an example, under the condition that the Nakagami-m fading channel parameter m=2, the block error rate performance and average iteration count performance of the stopping decision method proposed in this embodiment under different parameter settings were simulated and analyzed. The maximum number of iterations was set to... Switch threshold In the simulation, the tolerance threshold for variation was... Continuous counting threshold and high threshold Different combinations of settings were implemented and compared with the fixed maximum number of iterations BP decoding method without early stopping mechanism.

[0124] like Figure 4As shown, the overall block error rate (BRR) of the decoding method based on the stopping decision method of this embodiment is better than that of the decoding method based on the generator matrix stopping criterion. In the low signal-to-noise ratio (SNR) region, under certain parameter settings, the BRR performance of this embodiment is basically consistent with the benchmark method; under certain parameter settings, such as when the parameter value is set to a certain value, a performance gain of approximately 0.01 dB can be obtained. In the high SNR region, this embodiment achieves a performance advantage of approximately 0.1 dB compared to the decoding method based on the generator matrix stopping criterion under different parameter settings. Different parameter settings have a certain impact on the BRR performance, among which the high threshold... The impact on block error rate performance is quite significant. When the value is appropriately increased, the decoding reliability under high signal-to-noise ratio conditions can be improved to a certain extent.

[0125] like Figure 5 As shown, under low to medium signal-to-noise ratio (SNR) conditions, the decoding method based on the stopping decision method of this embodiment significantly reduces the average number of iterations compared to the decoding method based on the generator matrix stopping criterion. This indicates that the proposed method can promptly identify and terminate invalid iterations in low-reliability error convergence states, thereby significantly reducing system processing latency. In the low SNR region, the average number of iterations can be reduced by 82.90% to 92.87%; in the high SNR region, the average number of iterations of the proposed method converges to approximately 4, which is at most 0.6 iterations less than the decoding method based on the generator matrix stopping criterion.

[0126] For the code type of this embodiment, when At that time, parameters Take a value of 0.001 to 0.004. Take 3 to 5. When the value is between 0.99 and 0.9999, the decoder exhibits good overall performance. Reducing... or increase This will make the stopping decision more conservative, thus increasing the average number of iterations but slightly improving the error rate; increasing This makes the stopping decision more stringent under high signal-to-noise ratio conditions, resulting in a slight increase in the average number of iterations but better block error rate performance. Considering both block error rate and average number of iterations, the code type used in this embodiment can be selected as follows: , , As the preferred parameter setting.

[0127] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A polar code confidence propagation decoding and stopping method based on soft information evolution, characterized in that: Includes the following steps, Step 1: Construct a polar code encoding and channel transmission model to obtain the received signal; Step 2: Determine the channel prior probability based on the received signal obtained in Step 1; initialize the confidence propagation decoding message based on the polar code factor diagram; Step 3: Based on the prior channel probability obtained in Step 2, perform iterative message updates on the polarization code factor graph, calculate the posterior probability of each code element, and obtain the hard decision codeword vector and information bit estimation results. Step 4: Construct a soft information indicator function based on the posterior probability obtained in Step 3, and construct an adjacent iteration difference vector based on the hard decision codeword vector obtained in Step 3. Step 5: When the soft information indicator function is less than the switching threshold after the t-th iteration, perform low-reliability region error convergence detection and stop early; Step 6: When the soft information indication function is greater than or equal to the switching threshold after the t-th iteration, perform a high-reliability region dual-threshold comprehensive verification to stop the decision and retain the candidate output results; Step 7: Based on the adjacent iteration difference vector obtained in Step 4, incrementally update the comprehensive vector, and output the final decoding result according to the stopping decision result or the maximum number of iterations in Steps 5 and 6.

2. The method as described in claim 1, characterized in that: The implementation method for step one is as follows: The sending end generates the original information sequence Where N is the code length, and the information bit index set is... And the number of information bits is K, and the set of frozen bit indices is And for any ,have ; after the code rate After polar code encoding, the codeword is obtained. The generating matrix , For the kernel matrix, It is an nth-order Kronecker power, and ; The codeword is modulated using binary phase shift keying (BPSK) to obtain the transmitted symbol vector. ; After the transmitted symbol vector is transmitted through the fading channel, the receiving end obtains the received signal. in, This is the channel fading coefficient vector. For Hadamard product, Let be a Gaussian noise vector, and satisfy... .

3. The method as described in claim 1, characterized in that: The implementation method for step two is as follows: Construct a confidence propagation decoding factor graph based on the recursive structure of polar codes; for a polar code of length N, its factor graph contains n levels, each containing N / 2 processing units; let the node at the t-th iteration be... The right-to-left message at the location is denoted as Messages from left to right are denoted as Each message is represented as a bit value. The probability pairs; the receiver initializes the channel prior probability of the rightmost node based on the channel observations; the channel prior probability corresponding to the j-th symbol is... make ; For the prior message on the left, if the j-th bit corresponds to an information bit, then initialize it as follows: If the j-th bit corresponds to a frozen bit, then initialize it as follows: .

4. The method as described in claim 1, characterized in that: The implementation method for step three is as follows: In the t-th iteration, the messages of each node are updated according to the following rules. In the formula, the operator and Let represent the convolution operation in the probability domain and the multiplication operation in the probability domain, respectively; after completing the message update in the t-th iteration, calculate the posterior probability of each symbol based on the updated left and right propagation messages: The hard-decision codeword vector for the current iteration is obtained based on the posterior probability. ,in: And generate matrices and vectors based on polar codes. Recover the information bit estimation results of the current iteration. .

5. The method as described in claim 1, characterized in that: The soft information indication function mentioned in step four is, After the t-th iteration, a soft information indicator function is constructed based on the posterior probability of each symbol. : In the formula, This indicates that the j-th symbol takes the value in the t-th iteration. The posterior probability, the soft information indication function It represents the average of the maximum posterior probabilities of all symbols.

6. The method as described in claim 1, characterized in that: The adjacent iteration difference vector mentioned in step four is, Construct the hard decision difference vector between the t-th iteration and the (t-1)-th iteration. ,in In the formula, This represents modulo-2 addition; when , indicating that the hard decision result of the j-th symbol is flipped in two adjacent iterations; when When this occurs, it indicates that the hard decision result for that code element has not changed.

7. The method as described in claim 1, characterized in that: The detection method described in step five is as follows: After the t-th iteration, the soft information indicator function satisfies When the current decoding process is determined to have entered a low-reliability region, then... To set the switching threshold, the change in the soft information indicator function between the t-th iteration and the (t-1)-th iteration is defined as follows: If satisfied If the change in the soft information indicator function in the current iteration is considered to be below the preset tolerance range, it indicates that the decoding process tends to stabilize in the low reliability region. The tolerance threshold is changed; at this point, the error convergence counter is updated to... like Then reset the error convergence counter to ;when When the current confidence propagation decoding process enters a low-reliability error convergence state, it is determined that the current confidence propagation decoding process has entered a low-reliability error convergence state. This is the continuous counting threshold; at this time, the reliable stop flag is set low. If the value is 1, the current decoding iteration process is terminated early, and the information bit estimation result corresponding to the current iteration is output.

8. The method as described in claim 1, characterized in that: Step six is ​​implemented as follows: After the t-th iteration, when the soft information indicator function satisfies When the current decoding process enters a high-reliability region, it is determined that the current decoding process has entered a high-reliability region; within the high-reliability region, the current hard-decision codeword vector is processed. Perform comprehensive verification; let the parity-check matrix of the polar code be... Then the comprehensive vector corresponding to the t-th iteration is when If the current hard decision codeword is valid, then the current hard decision codeword is invalid; otherwise, the current hard decision codeword is invalid, the iteration count is incremented by 1, and the process returns to step three for the next iteration message update. For cases where the codeword is determined to be valid, when When the decoding result corresponding to the current valid codeword is determined to have reached a stable and highly reliable state, then, Set to high threshold; at this time, set the high reliability stop flag. The value is 1, and the information bit estimation result corresponding to the current iteration is used as the final output result; when When the current valid codeword is determined to be a transient valid output, the iteration count is incremented by 1, step three is continued, and the optimal candidate reliability value is set. and the corresponding optimal candidate information bit estimation results When the current soft information indicator function is greater than Update and .

9. The method as described in claim 1, characterized in that: The incremental update method for the comprehensive vector described in step seven is as follows: Based on the hard decision difference vector between the t-th iteration and the (t-1)-th iteration The current hard decision codeword is represented as According to the definition of a composite vector, the composite vector in the t-th iteration satisfies Since the synthesis operation satisfies a linear superposition relationship over the binary field of the linear code, the incremental update formula for the synthesis vector is obtained. Set the check matrix The j-th column is The set of bit positions where a hard decision flip occurs is denoted as Then the incremental update formula for the composite vector can be rewritten as follows:

10. The method as described in claim 1, characterized in that: The method for outputting the final decoding result in step seven is as follows: If the current iteration count reaches the preset maximum iteration count And not satisfied and Then output the optimal candidate reliability value. The corresponding optimal candidate information bit estimation result As the final decoded output; If the current iteration count has not yet reached the preset maximum iteration count And not satisfied and If the iteration count is not met, the iteration count is incremented by 1, and the process returns to step three to perform the next iteration message update, posterior probability calculation, hard decision output, and stop decision until the stop condition is met or the maximum number of iterations is reached, at which point the final decoding result is output.

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