A soft-output polar code decoding method based on symbol likelihood

Abstract

The application is a kind of soft output polar code decoding method based on symbol likelihood, which firstly generates candidate paths and performs cyclic redundancy check (CRC) by using the existing serial cancellation list (SCL) decoder based on symbol likelihood, and outputs the hard decision result if the check is passed; otherwise, the system enters the iteration processing stage: the single-time belief propagation decoding based on symbol likelihood is used to transfer the symbol likelihood information on the factor graph to update and enhance the symbol likelihood vector information of each symbol, and then the soft information output by the belief propagation decoding is fed back to the SCL decoder based on symbol likelihood as prior information to re-execute the SCL decoding based on symbol likelihood. The application can effectively handle the intra-symbol bit dependency and generate soft information to support iterative reception, optimize the BLER performance of the system, and under high signal-to-noise ratio (SNR), the computational complexity of the receiving end is close to that of the non-iterative receiver, which is suitable for practical communication applications.

Description

Technical Field

[0001] This invention belongs to the field of channel decoding technology in wireless communication, specifically relating to a serial cancellation list decoding method for noncoherent soft-output polar codes based on symbol likelihood for single-input multiple-output antenna transmission systems. Background Technology

[0002] In short data packet transmission in wireless communication, pilot signals often occupy a large amount of time-frequency resources. If traditional coherent detection is used, the pilot overhead may exceed the actual data volume, leading to a significant decrease in spectral efficiency. Simultaneously, in high-mobility scenarios, the channel state changes rapidly, making it difficult for the receiver to accurately estimate the channel before the change. To cope with rapidly changing channel environments without relying on real-time channel estimation, incoherent transmission technology has become a key choice. Although incoherent transmission has the advantages of low overhead and low latency, its performance is generally weaker than coherent detection because it loses channel phase information during demodulation. Single-Input Multiple-Output (SIMO) antenna transmission systems utilize multiple receiving antennas at the receiver to obtain spatial diversity gain and leverage multi-antenna combining technology to effectively combat multipath fading in the wireless channel, ensuring extremely high link robustness under incoherent conditions.

[0003] Polar codes, due to their excellent Block Error Ratio (BLER) performance with short code lengths, have been adopted as the standard coding scheme for the New Radio Control Channel (NRC) of 5G mobile communication technology. In practical systems, successive cancellation list (SCL) decoding based on bit-level likelihood is currently the most commonly used polar code decoding method, effectively improving decoding reliability by retaining multiple candidate paths. However, in typical scenarios such as uplink control for 5G / 6G mobile communication technology, existing SCL decoding schemes have the following limitations when dealing with bit dependencies and iterative reception requirements under high-order modulation incoherent transmission.

[0004] On the one hand, traditional bit-likelihood-based decoding methods (such as bit-likelihood-based SCL decoding and bit-likelihood-based soft output list polar code decoding) struggle to handle bit dependencies under higher-order modulation. These methods typically rely on the "bit independence" assumption, demodulating the received signal into independent log-likelihood ratio (LLR) sequences. However, under higher-order modulation, a single modulation symbol often carries multiple coded bits, which exhibit high statistical correlation. Bit-likelihood-based decoding methods forcibly treat bits independently, ignoring the joint probability constraints between bits within a symbol. This results in the generated bit-level LLR failing to reflect the overall likelihood characteristics of the symbol, leading to computational biases in the decoding path metric and path pruning errors, thus limiting the BLER performance of polar codes under higher-order modulation.

[0005] On the other hand, existing SCL decoding schemes struggle to achieve a balance between soft information output and symbol likelihood feature extraction when dealing with the iterative reception requirements of high-order modulation. Although bit-likelihood-based soft-output list polar code decoding can achieve iterative reception by introducing a soft-output mechanism, it is still constrained by the bit independence assumption. In incoherent transmission scenarios, the extracted soft information often suffers from confidence bias due to neglecting the joint probability features of symbols, resulting in limited gain during the iteration process. While existing symbol-likelihood-based SCL decoding schemes can effectively utilize symbol likelihood features to improve decision accuracy, they are essentially hard-decision output architectures, unable to provide necessary external information feedback to the front-end detector, thus cutting off the iterative correction loop of the receiving system. This performance gap between schemes makes it difficult for existing polar code reception technologies to fully utilize the gains brought by iterative processing, limiting the BLER performance of the system in complex channel environments.

[0006] Based on the aforementioned problems, this invention proposes a noncoherent soft-output SCL decoding method based on symbol likelihood for incoherent polar code-coded SIMO transmission systems. This method combines the advantages of handling intra-symbol bit dependencies and soft-input soft-output iterative decoding. Compared to existing symbol likelihood-based SCL decoding, bit likelihood-based SCL decoding, and bit likelihood-based soft-output list polar code decoding, this invention effectively utilizes bit dependencies under higher-order modulation while achieving integration with iterative receiving systems, improving the system's BLER performance. Furthermore, at high signal-to-noise ratios, the receiver's computational complexity is close to that of a non-iterative receiver, making it suitable for practical communication applications. Summary of the Invention

[0007] Purpose of the invention: To address the shortcomings of the aforementioned technologies, this invention proposes a soft-output polar code decoding method based on symbol likelihood for incoherent polar code encoded SIMO transmission systems. This method can effectively handle intra-symbol bit dependencies and generate soft information to support iterative reception, thus optimizing the BLER performance of the system. Furthermore, under high signal-to-noise ratio conditions, the computational complexity at the receiver is close to that of a non-iterative receiver, making it suitable for practical communication applications.

[0008] Technical Solution: The present invention provides a soft-output polar code decoding method based on symbolic likelihood. First, it utilizes an existing serial cancellation list (SCL) decoder based on symbolic likelihood to generate candidate paths and performs cyclic redundancy check (CRC). If the check passes, a hard decision result is output; otherwise, the system enters the iterative processing stage: using single-belief propagation decoding based on symbolic likelihood, symbolic likelihood information is transmitted on the factor graph to update and enhance the symbolic likelihood vector information of each symbol. Subsequently, the soft information output by the belief propagation decoding is fed back as prior information to the SCL decoder based on symbolic likelihood, and the SCL decoding based on symbolic likelihood is re-executed.

[0009] The polar code mentioned above has a code length of The parameters are preset, and their values ​​satisfy the following conditions: ,in ;make Indicates bitrate, The length of the information bits is ;make This represents the input bit sequence of the polar code encoder, where Indicates all lengths of The set of binary vectors, for Perform serial-to-parallel conversion to obtain The size is The bit subsequence, denoted as ,in , ,satisfy ,Right now ;make express The set of locations of the information bits contained therein, based on the set of information bit locations Determine the first Subsequences The set of positions of the information bits contained therein, k=1,2,…K, is denoted as Based on this, calculation The set of possible values ​​is: , in Represents a set and The difference set, that is, all sets belonging to But not belonging to A set consisting of elements; The generated codeword bit sequence after polarization coding Represented as: , in Represented as the transpose of a matrix or vector. This is the generator matrix of the polar code. For Kronecker product, It is a two-dimensional binary kernel matrix. Represents a logarithmic function base 2; a sequence of intermediate variables. express With matrix The bit sequence obtained after multiplication is represented as ,in yes The The size is Bit subsequence, codeword bit sequence Represented as ,in yes The first in The size is codeword subsequence, Represented as An identity matrix of order 1. Represented as An identity matrix of order 1; Each codeword subsequence is mapped using a gray-bit to symbol-like mapping. Mapping to symbols ,in It is a length of A complex field vector, where Indicates the number of subcarriers; Taken from size A collection of constellation symbols And satisfy , Denote the Frobenius norm; let Indicates the number of receiving antennas. The received signal is represented as: , in The additive white Gaussian noise matrix is ​​of size . Complex field matrix, Indicates the first The size corresponding to this transmission is The channel gain vector.

[0010] The decoding method described above employs a non-coherent transmission mechanism, a transmission method that can perform signal detection and decoding without acquiring channel state information; neither the transmitting nor receiving end acquires the channel gain vector. The instantaneous value of the received signal is used for signal processing only, utilizing its statistical distribution characteristics; all decoding operations are based on the received signal. The statistical correlation between the candidate transmission symbols and the target symbols has been completed.

[0011] The decoding method described above employs incoherent polar code encoding of the SIMO transmission system and includes the following steps: Step 1: Order Represents a set of symbols The The initial symbol metric is calculated using the following formula: , in It is the size of The initial symbolic metric matrix, Represents the initial symbolic metric matrix The Middle Line number Column elements, Represents the conjugate transpose of a matrix or vector; Step 2: Set the current iteration number And define the maximum number of iterations as Its value is determined based on simulation. Step 3: Perform symbol-by-symbol SCL decoding. This decoding process is similar to traditional bit-by-bit SCL decoding, but the basic processing unit is expanded from a single bit to a length of... The subsequence; specifically, symbol-by-symbol SCL decoding, within the framework of a factor graph, utilizes its inherent butterfly structure to transfer symbol metrics, which is composed of... The decoder consists of a layered butterfly structure. In each layer, each butterfly structure receives two sets of input symbol metrics in parallel and outputs two updated metrics. The decoder maintains a length of... A list of paths, each path corresponding to a set of decoding hard decision results; in processing the first... When there are multiple subsequences, since the subsequence consists of... It consists of bits, and all possible binary bit sequences can take a total of values. Seed; at each subsequence position, the decoder passes through functions and The function calculates the symbol metric value corresponding to each binary bit sequence and updates the cumulative path metric for each path; after completing the first step... After processing each subsequence, retain the one with the largest path metric value. The path to the first Decoding a subsequence, when After all subsequences have been decoded, the path with the largest path metric value is selected as the [path]. The decoding result; Step 4: Perform single-symbol-by-symbol belief propagation decoding to generate the decoder's external information. This step includes the following process: Step 4.1: Output the external information matrix , It is the size of The real field matrix; this external information This reflects the final confidence level of symbol-by-symbol SCL confidence propagation decoding for each binary bit sequence; let The size generated during the symbol-by-symbol SCL confidence propagation decoding process is... The symbolic metric matrix, the specific calculation process starts from the first... Starting from the first layer, the metric is recursively applied layer by layer based on the factor graph of the polar code, reaching the 1st layer. Layer to the first In the recursion of the layers, for each pair of related metrics, the first... The layer's metric value is calculated using the following formula: , , And there are: , in , , They represent lengths of The binary bit sequence, , , These are their corresponding decimal index values; and The index of the node participating in the computation at the current layer, whose value satisfies: , In the above formula, This is the node block index at the current level, and its value range is... , This is the offset within the block, and its value range is... ;also, , and All are sets The elements in the table, when combined, constitute the complete node index for the current layer participating in the computation; express The The element represents the element at the th position. Layer, First The nodes are at index 1 The symbolic measurement value at that time; This represents the bitwise XOR operation on a binary bit sequence. This indicates the operation of retrieving the maximum value. intermediate decoding state matrix The Line number Column elements, , External information matrix The Middle Line number The elements of the column are matrices. The first in One element; For the first Subsequences The set of locations of the information bits contained therein for The set of possible values, Indicates the size of a set or vector. Indicates negative infinity; Step 4.2: Introduce feedback gain coefficient Update the symbolic metric matrix This matrix records the sign likelihood value for each symbol; when When the value is too large, it will introduce errors in belief propagation decoding, leading to performance degradation; when If the size is too small, the correction effect is insufficient; the aforementioned The optimal value was determined offline through a large number of Monte Carlo simulation experiments: in a noncoherent polar code encoded SIMO transmission system, for various code lengths and code rates, iterative... Candidate values ​​were selected, and the block error rate (BLER) under different signal-to-noise ratios was statistically analyzed. The value that minimizes the overall BLER of the system was chosen. As a parameter, its typical values ​​are 0.23, 0.24, 0.25, 0.26, and 0.27; the updated metric matrix for: , Step 4.3: Update the current iteration count. ,like Then the updated metric matrix obtained in step 4.2 will be used. As new input, return to step 3 and re-execute symbol-by-symbol SCL decoding; otherwise, end the iteration process and output the optimal path obtained from the last symbol-by-symbol SCL decoding as the final decoding result.

[0012] The aforementioned functions and The function is one of the two basic units in the symbol-by-symbol SCL decoding process, defined as follows: function: , function: , in, For the first The first path The intermediate decoding state matrix obtained from all butterfly structure operations in the layer is used not only for the recursive calculation within the symbol-by-symbol SCL, but also for subsequent symbol-by-symbol SCL confidence propagation decoding. Indicates the current level, i.e., the [number]th level. Sub-bit vectors of the layer and Indicates the next level, i.e., the first Two associated sub-bit vectors of the layer; , , These represent the specific binary sequence values ​​taken by the above vectors during calculation; in the recursive calculation, formula (5) is used to calculate... Path metric; Formula (6) in known Under the premise of using constraint relationships renew The path metric is then passed to the matrix. middle; This represents the bitwise XOR operation on a binary bit sequence. This indicates the operation of retrieving the maximum value. Indicates all lengths of A set of binary vectors.

[0013] In the symbol-by-symbol SCL decoding, the path metric is a numerical index calculated and maintained for each candidate decoding path. It is used to quantify the likelihood probability of the path relative to the received signal at the current decoding stage. The larger the value, the more likely the path is to be the correct transmission sequence. The calculation formula is as follows: , in, Indicates the first The path metric of the candidate paths, Representing a subsequence The corresponding binary sequence value under the current path Indicates the first Symbol values ​​stored in the layer for The sign likelihood value at time; In the symbol-by-symbol SCL decoding process, all intermediate decoding state matrices generated during the decoding process are saved, denoted as... ,in , ;gather This will be used for subsequent symbol-by-symbol SCL confidence propagation decoding; For the A sequence of codes to be decoded Its value is limited by the input bit subsequence. The set of values ,because Define subsequence The set of possible values ​​is: , After symbol-by-symbol SCL decoding is completed, the remaining L candidate paths are denoted as... ,in , Representative at the Subsequences under each path Hard decision estimation; subsequently, based on the path metric... The candidate paths are reordered in descending order, and the sorted sequence of metrics is denoted as follows: To satisfy: ,in This corresponds to the path metric value of the l-th path after sorting; a larger path metric value indicates fewer errors in the path, and a greater likelihood that it is a correct path; based on this criterion, the l-th path after sorting... The first path is determined to be the current optimal path, and the decoder will prioritize its subsequent processing. This involves extracting the saved intermediate bit sequence from this path and then inversely transforming it into the input bit sequence. Specifically, for the first path... Path, using The intermediate bit sequence is inversely transformed into the input bit sequence to obtain... The hard verdict for: , Based on all the calculated subsequences, we obtain The complete estimated sequence is For these L candidate paths The estimated sequence is subjected to CRC check, and the decision and output rules are as follows: If a path that passes the check exists, the path corresponding to that path is directly output. The final decoding result is used, and subsequent processing is terminated; if all L candidate paths fail the verification, decoding failure is determined, and the sorted Lth path is directly selected. The system identifies a path and uses the intermediate decoding state matrix corresponding to that path as the final output for subsequent processing steps.

[0014] Beneficial Effects: The noncoherent soft-output SCL decoding method based on symbol likelihood proposed in this invention achieves a significant improvement in BLER performance compared to traditional symbol likelihood-based SCL decoding, bit likelihood-based SCL decoding, and bit likelihood-based soft-output list polar code decoding, with a performance gain of at least 0.45 dB. At high signal-to-noise ratios, the computational complexity of the proposed noncoherent soft-output SCL decoding method based on symbol likelihood is close to that of traditional symbol likelihood-based SCL decoding methods. Attached Figure Description

[0015] Figure 1 This is a block diagram of a noncoherent polar code encoded SIMO transmission system, in which... Indicates multiplication operation. This represents the addition operation.

[0016] Figure 2 This is a factor graph of the symbol-by-symbol SCL decoder in the method of this invention, wherein ( ) represents a butterfly-shaped structure.

[0017] Figure 3 This is the factor graph of the symbol-by-symbol confidence propagation decoder in the method of this invention.

[0018] Figure 4 This invention relates to different soft information feedback coefficients The BLER performance results are as follows.

[0019] Figure 5 This is a comparison of the BLER performance of the present invention (noncoherent iterative symbol-by-symbol SCL decoding) and existing noncoherent non-iterative symbol-by-symbol SCL decoding, noncoherent interleaved iterative bit-level SCL decoding, noncoherent interleaved non-iterative bit-level SCL decoding, pilot-based coherent interleaved iterative bit-level SCL decoding, and pilot-based coherent interleaved non-iterative bit-level SCL decoding under different signal-to-noise ratios.

[0020] Figure 6 This represents the average number of iterations of the invention under different signal-to-noise ratios. Detailed Implementation

[0021] by Figure 1 The specific implementation of the method of the present invention will be described using an example of a noncoherent polar code encoded SIMO transmission system, wherein the number of transmit antennas is 1 and the number of receive antennas is... , the number of subcarriers The total code length of the polar code is set to be... bitrate Therefore, the number of information bits is 32. The length of the encoded input is... The bit sequence is converted from serial to parallel to obtain... A length of A subsequence of bits. This is an existing set of normalized multidimensional Reid-Muller-Glassman constellation symbols suitable for incoherent transmission, containing 256 constellation points. Additionally, the CRC bit count is 6, and the polar code decoding list size is... Maximum number of iterations Soft information feedback coefficient .

[0022] In this invention, the code length of the polar code is... The parameters are preset, and their values ​​satisfy the following conditions: ,in .make Indicates bitrate, The length of the information bits is .make This represents the input bit sequence of the polar code encoder, where Indicates all lengths of A set consisting of binary vectors. Perform serial-to-parallel conversion to obtain The size is The bit subsequence, denoted as ,in , ,satisfy ,Right now .make express The set of locations of the information bits contained therein. It can be determined that the first ( ) subsequences The set of locations of the information bits contained herein is denoted as Based on this, the calculation The set of possible values ​​is: , in Represents a set and The difference set, that is, all sets belonging to But not belonging to A set consisting of elements; The generated codeword bit sequence after polarization coding It can be represented as: , in Represented as the transpose of a matrix or vector. This is the generator matrix of the polar code. For Kronecker product, It is a two-dimensional binary kernel matrix. Represents a logarithmic function to the base 2. Intermediate variable sequence. express With matrix The resulting bit sequence after multiplication can be represented as: ,in yes The The size is The bit subsequence. Codeword bit sequence. It can be represented as ,in yes The first in The size is The codeword subsequence. Represented as An identity matrix of order 1. Represented as An identity matrix of order 1.

[0023] Subsequently, each codeword subsequence is mapped using a graybit-to-symbol mapping. Mapping to symbols ,in It is a length of A complex field vector, where This indicates the number of subcarriers. Taken from size A collection of constellation symbols And satisfy , Let represent the Frobenius norm. Indicates the number of receiving antennas. The received signal is represented as: , in The additive white Gaussian noise matrix is ​​of size . Complex field matrix, Indicates the first The size corresponding to this transmission is The channel gain vector.

[0024] This invention employs a non-coherent transmission mechanism, where neither the transmitting nor receiving end acquires the channel gain vector. The instantaneous value is used for signal processing only, utilizing its statistical distribution characteristics. All decoding operations are based on the received signal. Statistical correlation with candidate transmitted symbols is completed without channel estimation or feedback.

[0025] Based on the aforementioned incoherent polar code encoded SIMO transmission system, the incoherent soft-output SCL decoding method based on symbol likelihood proposed in this invention includes the following steps: Step 1: Order Represents a set of symbols The The initial symbol metric is calculated using the following formula: ,

[0026] in It is the size of The initial symbolic metric matrix, Represents the initial symbolic metric matrix The Middle Line number Column elements, Represents the conjugate transpose of a matrix or vector.

[0027] The steps described above are explained in detail below: A dimension is obtained through formula (17). Initial symbolic metric matrix And it serves as the input to the symbol-by-symbol SCL decoder.

[0028] Step 2: Set the current iteration number And define the maximum number of iterations as Its value is determined based on simulation.

[0029] Step 3: Perform symbol-by-symbol SCL decoding. This decoding process is similar to traditional bit-by-bit SCL decoding, but the basic processing unit is expanded from a single bit to a length of... The subsequence. Specifically, symbol-by-symbol SCL decoding, within the framework of a factor graph, utilizes its inherent butterfly structure to transfer symbol metrics. This factor graph is composed of... The decoder consists of a layered butterfly structure. In each layer, each butterfly structure receives two sets of input symbol metrics in parallel and outputs two updated metrics. The decoder maintains a length of... A list of paths, each path corresponding to a set of hard-decision decoding results. In processing the... When there are multiple subsequences, since the subsequence consists of... It consists of bits, and all possible binary bit sequences can take a total of values. At each subsequence position, the decoder passes through... functions and The function calculates the symbol metric value corresponding to each binary bit sequence and updates the cumulative path metric for each path. After completing the... After processing each subsequence, retain the one with the largest path metric value. The path to the first Decoding a subsequence, when After all subsequences have been decoded, the path with the largest path metric value is selected as the [path]. The decoding result. Here, the symbol-by-symbol SCL decoding process... functions and The function is defined as follows: function: , function: , in, For the first The first path The intermediate decoding state matrix obtained from all butterfly structure operations in the layer is used not only for recursive calculations within the SCL, but also for subsequent symbol-by-symbol confidence propagation decoding. Indicates the current level (the first level) Sub-bit vectors of (layer), and Indicates the next level (the first level) Two associated sub-bit vectors of the layer. , , These represent the specific binary sequence values ​​taken by the above vectors during calculation. In the recursive calculation, formula (18) is used to calculate... Path metric; Formula (19) in the known Under the premise of using constraint relationships renew The path metric is then passed to the matrix. middle. This represents the bitwise XOR operation on a binary bit sequence. This indicates the operation of retrieving the maximum value. Indicates all lengths of A set of binary vectors.

[0030] The path metric is calculated using the following formula during the decoding process: , in, Indicates the first The path metric for each candidate path. Representing a subsequence The specific binary sequence value corresponding to the current path. Indicates the first Symbol values ​​stored in the layer for The sign likelihood value at time.

[0031] During the decoding process, all intermediate decoding state matrices generated during decoding are saved, denoted as... ,in , .gather This will be used for subsequent symbol-by-symbol belief propagation decoding.

[0032] In the symbol-by-symbol SCL decoding process, for the first... A sequence of codes to be decoded Its value is limited by the input bit subsequence. The set of values .because Define subsequence The set of possible values ​​is: , After symbol-by-symbol SCL decoding is completed, the remaining data will be... The candidate paths are denoted as ,in , Representative at the Subsequences under each path Hard decision estimation. Then, based on the path metric, this... The candidate paths are reordered in descending order, and the sorted sequence of metrics is denoted as follows: To satisfy: ,in After sorting, the first The path metric value of each path. A higher path metric value indicates fewer errors and a greater likelihood that the path is correct. Based on this criterion, the sorted path... The path is determined to be the current optimal path, and the decoder will prioritize its subsequent processing, that is, extract the saved intermediate bit sequence from this path, and then inversely transform this sequence into the input bit sequence. Specifically, for the path... Path, using The intermediate bit sequence is inversely transformed into the input bit sequence to obtain... The hard verdict for: , Based on all the calculated subsequences, we obtain The complete estimated sequence is Regarding this strip The estimated sequence is subjected to CRC check, and the decision and output rules are as follows: If a path that passes the check exists, the path corresponding to that path is directly output. This serves as the final decoding result, terminating subsequent processing; if all If none of the paths pass the verification, a decoding failure is determined. In this case, the sorted path is directly selected. The process involves identifying a path and using the intermediate decoding state matrix corresponding to that path as the final output for the fourth step of processing.

[0033] The above steps are explained in detail below: Based on the simulation results, the maximum number of iterations in this invention... .like Figure 2 In the embodiments used in this invention, the factor graph has a total of three layers. Starting with the layer, proceed first. , , , Structure The calculation yields and The symbolic metric vector is input, and then... and Structure The calculation yields Input the symbolic metric vector, and then perform... Structure The calculation yields The symbolic metric vector, and obtain Reference hard decision vector Used in judgment That is, to carry out Structure The calculation yields Reference hard decision vector Then in Through the layer and Get and Structural progress The required reference hard decision vector is then processed. The calculation yields Structure The symbolic metric vector of the operation is input, and then... Structure The calculation yields The symbolic metric vector, and obtain Reference hard decision vector Used in judgment That is, to carry out Structure The calculation yields Reference hard decision vector At this point, the upper half of the factor graph has been fully calculated, and we return to... Get from layer , , , The reference hard decision vector required by the structure is used for Calculation, to obtain and The symbolic metric vector is input and then sequentially passed through... and The structure is obtained , , , The decoding process ends with the determination of the symbol metric vector and the reference hard decision vector. All operations in the above steps involve operations of size [value missing]. Operations are performed using the symbolic metric vector as the unit.

[0034] Step 4: Perform single-symbol-by-symbol belief propagation decoding to generate the decoder's external information. This step includes the following process: Step 4.1: Output the external information matrix , It is the size of The real field matrix; this external information This reflects the final confidence level of symbol-by-symbol SCL confidence propagation decoding for each binary bit sequence; let The size generated during the symbol-by-symbol SCL confidence propagation decoding process is... The symbolic metric matrix, the specific calculation process starts from the first... Starting from the first layer, the metric is recursively applied layer by layer based on the factor graph of the polar code, reaching the 1st layer. Layer to the first In the recursion of the layers, for each pair of related metrics, the first... The layer's metric value is calculated using the following formula: , , And there are: , in , , They represent lengths of The binary bit sequence, , , These are their corresponding decimal index values; and The index of the node participating in the computation at the current layer, whose value satisfies: , In the above formula, This is the node block index at the current level, and its value range is... , This is the offset within the block, and its value range is... ;also, , and All are sets The elements in the table, when combined, constitute the complete node index for the current layer participating in the computation; express The The element represents the element at the th position. Layer, First The nodes are at index 1 The symbolic measurement value at that time; This represents the bitwise XOR operation on a binary bit sequence. This indicates the operation of retrieving the maximum value. intermediate decoding state matrix The Line number Column elements, , External information matrix The Middle Line number The elements of the column are matrices. The first in One element; For the first Subsequences The set of locations of the information bits contained therein for The set of possible values, Indicates the size of a set or vector. Indicates negative infinity; Step 4.2: Introduce feedback gain coefficient Update the symbolic metric matrix .when When the value is too large, it will introduce errors in belief propagation decoding, leading to performance degradation; when If the size is too small, the correction effect will be insufficient. The optimal value was determined offline through a large number of Monte Carlo simulation experiments: Under the above-mentioned incoherent polar code encoded SIMO transmission system, for various code lengths and code rates, the optimal value was determined by traversing... Candidate values ​​are selected, and the BLER under different signal-to-noise ratios is statistically analyzed. The value that minimizes the overall BLER of the system is chosen. As a parameter, its typical values ​​are 0.23, 0.24, 0.25, 0.26, and 0.27. The updated metric matrix. for: , Step 4.3: Update the current iteration count. .like Then the optimized metric matrix obtained in step 4.2 will be used. As new input, return to step 3 and re-execute symbol-by-symbol SCL decoding; otherwise, end the iteration process and output the optimal path obtained from the last symbol-by-symbol SCL decoding as the final decoding result.

[0035] The above steps are explained in detail below: Figure 3 For example, in symbol-by-symbol confidence propagation decoding, formulas (23) and (24) are used to obtain... Layer-by-layer calculation The layer obtains the external information matrix. In formula (23), with For example, at this time , , The solid lines represent the inputs, and the three inputs are as follows: , , The dashed line represents the output, and the output is... In formula (24), with For example, at this time , , The solid lines represent the inputs, and the three inputs are as follows: , , The dashed line represents the output, and the output is... The soft information feedback gain coefficient is based on... Figure 4 Different soft information feedback coefficients The changes in BLER can be used to determine that, after multiple Monte Carlo simulations, when When the value is between 0.25 and 0.75, BLER does not change significantly; therefore, in this invention, the value is... .

[0036] The proposed method is compared with existing noncoherent non-iterative symbol-by-symbol SCL decoding, noncoherent interleaved iterative bit-level SCL decoding, noncoherent interleaved non-iterative bit-level SCL decoding, pilot-based coherent interleaved iterative bit-level SCL decoding, and pilot-based coherent interleaved non-iterative bit-level SCL decoding at different signal-to-noise ratios (SNRs). To ensure fairness in the comparison, the spectral efficiency of each comparison scheme must be consistent. Specifically, for the pilot-based coherent scheme, the number of subcarriers is set... The number of pilot symbols is The number of data symbols is bitrate and adopt Quadrature amplitude modulation. By setting the above parameters, the coherent comparison scheme and the scheme of this invention are compared in BLER performance at the same spectral efficiency, and the results are as follows: Figure 5 As shown. Figure 5 The results show that the method proposed in this invention has a performance improvement of 0.45dB compared with existing noncoherent non-iterative symbol-by-symbol SCL decoding. The performance gain is more significant compared with noncoherent interleaved iterative bit-level SCL decoding, noncoherent interleaved non-iterative bit-level SCL decoding, pilot-based coherent interleaved iterative bit-level SCL decoding, and pilot-based coherent interleaved non-iterative bit-level SCL decoding, thus verifying the effectiveness of the method of this invention. Figure 6 This demonstrates that, under high signal-to-noise ratio conditions, the computational complexity of the proposed noncoherent soft-output SCL decoding method based on symbol likelihood is close to that of the traditional SCL decoding method based on symbol likelihood.

[0037] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. A soft-output polar code decoding method based on symbolic likelihood, characterized in that, This method first uses an existing serial cancellation list (SCL) decoder based on symbol likelihood to generate candidate paths and performs cyclic redundancy check (CRC). If the check passes, a hard decision result is output. Otherwise, the system enters the iterative processing stage: using single-belief propagation decoding based on symbolic likelihood, symbolic likelihood information is transmitted on the factor graph to update and enhance the symbolic likelihood vector information of each symbol. Subsequently, the soft information output by the belief propagation decoding is fed back as prior information to the symbolic likelihood-based SCL decoder, and the symbolic likelihood-based SCL decoding is re-executed.

2. The soft-output polar code decoding method based on symbolic likelihood according to claim 1, characterized in that, The polar code mentioned above has a code length of The parameters are preset, and their values ​​satisfy the following conditions: ,in ;make Indicates bitrate, The length of the information bits is ;make This represents the input bit sequence of the polar code encoder, where Indicates all lengths of The set of binary vectors, for Perform serial-to-parallel conversion to obtain The size is The bit subsequence, denoted as ,in , ,satisfy ,Right now ;make express The set of locations of the information bits contained therein, based on the set of information bit locations Determine the first Subsequences The set of positions of the information bits contained therein, k=1,2,…K, is denoted as Based on this, calculation The set of possible values ​​is: ， in Represents a set and The difference set, that is, all sets belonging to But not belonging to A set consisting of elements; The generated codeword bit sequence after polarization coding Represented as: ， in Represented as the transpose of a matrix or vector. This is the generator matrix of the polar code. For Kronecker product, It is a two-dimensional binary kernel matrix. Represents a logarithmic function base 2; a sequence of intermediate variables. express With matrix The bit sequence obtained after multiplication is represented as ,in yes The The size is Bit subsequence, codeword bit sequence Represented as ,in yes The first in The size is codeword subsequence, Represented as An identity matrix of order 1. Represented as An identity matrix of order 1; Each codeword subsequence is mapped using a gray-bit to symbol-like mapping. Mapping to symbols ,in It is a length of A complex field vector, where Indicates the number of subcarriers; Taken from size A collection of constellation symbols And satisfy , Denote the Frobenius norm; let Indicates the number of receiving antennas. The received signal is represented as: ， in The additive white Gaussian noise matrix is ​​of size . Complex field matrix, Indicates the first The size corresponding to this transmission is The channel gain vector.

3. The soft-output polar code decoding method based on symbolic likelihood according to claim 2, characterized in that, The decoding method described above employs a non-coherent transmission mechanism, a transmission method that can perform signal detection and decoding without acquiring channel state information; neither the transmitting nor receiving end acquires the channel gain vector. The instantaneous value of the received signal is used for signal processing only, utilizing its statistical distribution characteristics; all decoding operations are based on the received signal. The statistical correlation between the candidate transmission symbols and the target symbols has been completed.

4. The soft-output polar code decoding method based on symbolic likelihood according to claim 3, characterized in that, The decoding method described above employs incoherent polar code encoding of the SIMO transmission system and includes the following steps: Step 1: Order Represents a set of symbols The The initial symbol metric is calculated using the following formula: ， in It is the size of The initial symbolic metric matrix, Represents the initial symbolic metric matrix The Middle Line number Column elements, Represents the conjugate transpose of a matrix or vector; Step 2: Set the current iteration number And define the maximum number of iterations as Its value is determined based on simulation. Step 3: Perform symbol-by-symbol SCL decoding. This decoding process is similar to traditional bit-by-bit SCL decoding, but the basic processing unit is expanded from a single bit to a length of... The subsequence; specifically, symbol-by-symbol SCL decoding, within the framework of a factor graph, utilizes its inherent butterfly structure to transfer symbol metrics, which is composed of... The decoder consists of a layered butterfly structure. In each layer, each butterfly structure receives two sets of input symbol metrics in parallel and outputs two updated metrics. The decoder maintains a length of... A list of paths, each path corresponding to a set of decoding hard decision results; in processing the first... When there are multiple subsequences, since the subsequence consists of... It consists of bits, and all possible binary bit sequences can take a total of values. Seed; at each subsequence position, the decoder passes through functions and The function calculates the symbol metric value corresponding to each binary bit sequence and updates the cumulative path metric for each path; after completing the first step... After processing each subsequence, retain the one with the largest path metric value. The path to the first Decoding a subsequence, when After all subsequences have been decoded, the path with the largest path metric value is selected as the [path]. The decoding result; Step 4: Perform single-symbol-by-symbol belief propagation decoding to generate the decoder's external information. This step includes the following process: Step 4.1: Output the external information matrix , It is the size of The real field matrix; this external information This reflects the final confidence level of symbol-by-symbol SCL confidence propagation decoding for each binary bit sequence; let The size generated during the symbol-by-symbol SCL confidence propagation decoding process is... The symbolic metric matrix, the specific calculation process starts from the first... Starting from the first layer, the metric is recursively applied layer by layer based on the factor graph of the polar code, reaching the 1st layer. Layer to the first In the recursion of the layers, for each pair of related metrics, the first... The layer's metric value is calculated using the following formula: ， ， And there are: ， in , , They represent lengths of The binary bit sequence, , , These are their corresponding decimal index values; and The index of the node participating in the computation at the current layer, whose value satisfies: ， In the above formula, This is the node block index at the current level, and its value range is... , This is the offset within the block, and its value range is... ;also, , and All are sets The elements in the table, when combined, constitute the complete node index for the current layer participating in the computation; express The The element represents the element at the th position. Layer, First The nodes are at index 1 The symbolic measurement value at that time; This represents the bitwise XOR operation on a binary bit sequence. This indicates the operation of retrieving the maximum value. intermediate decoding state matrix The Line number Column elements, , External information matrix The Middle Line number The elements of the column are matrices. The first in One element; For the first Subsequences The set of locations of the information bits contained therein for The set of possible values, Indicates the size of a set or vector. Indicates negative infinity; Step 4.2: Introduce feedback gain coefficient Update the symbolic metric matrix This matrix records the sign likelihood value for each symbol; when When the value is too large, it will introduce errors in belief propagation decoding, leading to performance degradation; when If the size is too small, the correction effect is insufficient; the aforementioned The optimal value was determined offline through a large number of Monte Carlo simulation experiments: in a noncoherent polar code encoded SIMO transmission system, for various code lengths and code rates, iterative... Candidate values ​​were selected, and the block error rate (BLER) under different signal-to-noise ratios was statistically analyzed. The value that minimizes the overall BLER of the system was chosen. As a parameter, its typical values ​​are 0.23, 0.24, 0.25, 0.26, and 0.27; the updated metric matrix for: ， Step 4.3: Update the current iteration count. ,like Then the updated metric matrix obtained in step 4.2 will be used. As new input, return to step 3 and re-execute symbol-by-symbol SCL decoding; otherwise, end the iteration process and output the optimal path obtained from the last symbol-by-symbol SCL decoding as the final decoding result.

5. The soft-output polar code decoding method based on symbolic likelihood according to claim 4, characterized in that, The aforementioned functions and The function is one of the two basic units in the symbol-by-symbol SCL decoding process, defined as follows: function: ， function: ， in, For the first The first path The intermediate decoding state matrix obtained from all butterfly structure operations in the layer is used not only for the recursive calculation within the symbol-by-symbol SCL, but also for subsequent symbol-by-symbol SCL confidence propagation decoding. Indicates the current level, i.e., the [number]th level. Sub-bit vectors of the layer and Indicates the next level, i.e., the first Two associated sub-bit vectors of the layer; , , These represent the specific binary sequence values ​​taken by the above vectors during calculation; in the recursive calculation, formula (5) is used to calculate... Path metric; Formula (6) in known Under the premise of using constraint relationships renew The path metric is then passed to the matrix. middle; This represents the bitwise XOR operation on a binary bit sequence. This indicates the operation of retrieving the maximum value. Indicates all lengths of A set of binary vectors.

6. The soft-output polar code decoding method based on symbolic likelihood according to claim 5, characterized in that, In the symbol-by-symbol SCL decoding, the path metric is a numerical index calculated and maintained for each candidate decoding path. It is used to quantify the likelihood probability of the path relative to the received signal at the current decoding stage. The larger the value, the more likely the path is to be the correct transmission sequence. The calculation formula is as follows: ， in, Indicates the first The path metric of the candidate paths, Representing a subsequence The corresponding binary sequence value under the current path Indicates the first Symbol values ​​stored in the layer for The sign likelihood value at time; In the symbol-by-symbol SCL decoding process, all intermediate decoding state matrices generated during the decoding process are saved, denoted as... ,in , ;gather This will be used for subsequent symbol-by-symbol SCL confidence propagation decoding; For the A sequence of codes to be decoded Its value is limited by the input bit subsequence. The set of values ,because Define subsequence The set of possible values ​​is: ， After symbol-by-symbol SCL decoding is completed, the remaining L candidate paths are denoted as... ,in , Representative at the Subsequences under each path Hard decision estimation; subsequently, based on the path metric... The candidate paths are reordered in descending order, and the sorted sequence of metrics is denoted as follows: To satisfy: ,in This corresponds to the path metric value of the l-th path after sorting; a larger path metric value indicates fewer errors in the path, and a greater likelihood that it is a correct path; based on this criterion, the l-th path after sorting... The first path is determined to be the current optimal path, and the decoder will prioritize its subsequent processing. This involves extracting the saved intermediate bit sequence from this path and then inversely transforming it into the input bit sequence. Specifically, for the first path... Path, using The intermediate bit sequence is inversely transformed into the input bit sequence to obtain... The hard verdict for: ， Based on all the calculated subsequences, we obtain The complete estimated sequence is For these L candidate paths The estimated sequence is subjected to CRC check, and the decision and output rules are as follows: If a path that passes the check exists, the path corresponding to that path is directly output. The final decoding result is used, and subsequent processing is terminated; if all L candidate paths fail the verification, decoding failure is determined, and the sorted Lth path is directly selected. The system identifies a path and uses the intermediate decoding state matrix corresponding to that path as the final output for subsequent processing steps.

Images