An interleaved cyclic redundancy check polar code encoding and decoding method and system based on code weight redistribution optimization

Abstract

The application relates to the technical field of channel coding, and discloses an interleaving cyclic redundancy check polar code encoding and decoding method and system based on code weight distribution optimization, the method comprising the following steps: a sending end converts a CRC check matrix into an equivalent ladder type matrix by adopting a ladder algorithm, and determines an optimal insertion position scheme of CRC bits corresponding to optimal code weight distribution according to the equivalent ladder type matrix; the information sequence is subjected to interleaving CRC coding according to the equivalent ladder type matrix and the optimal insertion position scheme, so that an extended information sequence is obtained; the extended information sequence is subjected to polar coding, so that a polar coding code word is obtained; and a receiving end subjects the polar coding code word after transmission through a channel to interleaving CA-SCL decoding, so that an optimal information sequence estimation is obtained. The optimal CRC insertion position scheme is determined based on code weight distribution optimization, the error correction performance of the CRC-Polar code is improved, early detection termination of error decoding is realized, and the average decoding delay is reduced.

Description

Technical Field

[0001] This invention relates to the field of channel coding technology, and in particular to an interleaved cyclic redundancy check polar code encoding and decoding method and system based on code redundancy distribution optimization. Background Technology

[0002] By concatenating CRC (Cyclic Redundancy Check) codes as outer codes to Polar code information bits, the correct decoding path can be selected using the CRC check information, thus significantly improving the BLER (Block Error Ratio) performance of SCL (Successive Cancellation List) decoding. This type of CRC-Polar coding scheme, which adds a CRC sequence to the end of the information sequence, has been adopted in 5G standards. However, the tail-end CRC-Polar coding scheme requires decoding the entire information sequence to determine if a valid path exists, leading to wasted computational resources and high decoding latency. To introduce an early termination mechanism in SCL decoders to reduce latency, existing research has proposed several distributed CRC-Polar coding schemes, including segmented CRC-Polar coding schemes, which divide a long CRC sequence into several short CRC sequences of fixed length and protect the information sequence by segmenting them at equal intervals; and simple interleaved CRC-Polar coding schemes, which directly insert CRC bits after the last information bit they depend on, thereby eliminating erroneous paths that do not meet the CRC check in real time during SCL decoding and improving the error correction performance of CRC-Polar codes.

[0003] However, most existing studies use relatively fixed CRC concatenation structures. Although this can achieve early detection and termination of error decoding, it does not perform targeted structural design for the CRC insertion position based on optimal error correction performance, resulting in insufficient error correction performance of CRC-Polar codes.

[0004] Therefore, existing technologies still need to be improved and developed. Summary of the Invention

[0005] The main objective of this invention is to provide an interleaved cyclic redundancy check polar code encoding and decoding method and system based on code redundancy optimization, aiming to solve the problem that existing CRC-Polar encoding schemes do not have targeted structural design for the CRC insertion position based on optimal error correction performance, resulting in insufficient error correction performance of CRC-Polar codes.

[0006] To achieve the above-mentioned objective, this invention provides an interleaved cyclic redundancy check (CRC) polar code encoding and decoding method based on code redundancy distribution optimization. The method includes:

[0007] The sending end acquires the information sequence and CRC check matrix, uses a laddering algorithm to convert the CRC check matrix into an equivalent ladder matrix, and determines the optimal insertion position scheme of the CRC bits corresponding to the optimal code redistribution based on the equivalent ladder matrix.

[0008] The transmitting end performs interleaved CRC encoding on the information sequence according to the equivalent ladder matrix and the optimal insertion position scheme to obtain the extended information sequence;

[0009] The transmitting end performs polar coding on the extended information sequence to obtain polar coded codewords, and transmits the polar coded codewords to the receiving end through the channel;

[0010] The receiving end performs interleaved CA-SCL decoding on the polarized codewords transmitted through the channel to obtain the optimal information sequence estimate.

[0011] Optionally, the step of using a step-based algorithm to convert the CRC check matrix into an equivalent step-based matrix specifically includes:

[0012] The number of rows and columns of the CRC check matrix are set to correspond to the number of information bits and the number of CRC bits, respectively;

[0013] Construct a row index set and a column index set for the CRC check matrix, wherein the row index set and the column index set record the row index of the processed row and the column index of the processed column in the CRC check matrix, respectively;

[0014] The unprocessed column with the fewest elements of value 1 in the unprocessed column of the CRC check matrix is ​​taken as the priority column. The rows with unprocessed values ​​of 1 in the priority column are extracted, and the row index of the row is recorded in the row index set. The column index of the priority column is also recorded in the column index set.

[0015] Repeatedly update the row index set and the column index set until the row indexes of all rows of the CRC check matrix have been recorded in the row index set. Then, record the column indexes of the columns that have not yet been processed in the CRC check matrix into the column index set in the original order of the columns that have not yet been processed.

[0016] The CRC check matrix is ​​rearranged according to the order of the row indices in the row index set and the order of the column indices in the column index set to obtain an equivalent ladder matrix that satisfies the row-column progressive structure.

[0017] Optionally, the step of determining the optimal insertion position scheme of the CRC bits corresponding to the optimal code redistribution based on the equivalent ladder matrix specifically includes:

[0018] Based on the dependency relationship between each CRC bit and the information bit reflected in the equivalent ladder matrix and the order of each CRC bit in the equivalent ladder matrix, the set of candidate insertion positions for each CRC bit is determined.

[0019] Based on the candidate insertion position set of each CRC bit, multiple candidate insertion position schemes for all CRC bits are obtained;

[0020] Calculate the code weight distribution of the interleaved cyclic redundancy check polar code corresponding to each of the candidate insertion position schemes, and take the candidate insertion scheme corresponding to the optimal code weight distribution among the multiple code weight distributions as the optimal insertion position scheme for all CRC bits.

[0021] Optionally, determining the set of candidate insertion positions for each CRC bit based on the dependency relationship between each CRC bit and the information bit reflected in the equivalent echelon matrix and the order of each CRC bit in the equivalent echelon matrix specifically includes:

[0022] The CRC bits are processed one by one according to their order in the equivalent ladder matrix;

[0023] For the currently processed CRC bit, the information bit on which the CRC bit depends is determined based on the dependency relationship between the CRC bit and the information bit reflected by the equivalent ladder matrix.

[0024] The positions that satisfy the constraint conditions among all positions after the last information bit in the information bits are taken as candidate insertion positions of the CRC bits, thus obtaining the set of candidate insertion positions of the CRC bits.

[0025] The constraints include the insertion position of the processed CRC bit before the candidate insertion position of the currently processed CRC bit and the insertion position of the unprocessed CRC bit after the candidate insertion position of the currently processed CRC bit.

[0026] Optionally, the step of calculating the code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes, and taking the candidate insertion scheme corresponding to the optimal code weight distribution among the multiple code weight distributions as the optimal insertion position scheme for all CRC bits, specifically includes:

[0027] The code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes is calculated using the Polar code distance spectrum analysis method. The code weight distribution includes the number of codewords with the minimum code weight and the number of codewords with a code weight lower than a set threshold.

[0028] The candidate insertion scheme corresponding to the optimal code redistribution among the multiple code redistributions is taken as the optimal insertion position scheme for all CRC bits.

[0029] The optimal insertion position scheme includes the optimal insertion position for each of the CRC bits.

[0030] Optionally, the transmitting end performs interleaved CRC encoding on the information sequence according to the equivalent ladder matrix and the optimal insertion position scheme to obtain an extended information sequence, specifically including:

[0031] The transmitting end inputs the information sequence into the interleaved CRC encoder, and obtains the CRC sequence based on the information sequence and the equivalent ladder matrix corresponding to the interleaved CRC encoder, wherein the information sequence includes information bits and the CRC sequence includes CRC bits;

[0032] The transmitting end inserts the CRC bits from the CRC sequence into the information sequence according to the optimal insertion position scheme to obtain the extended information sequence.

[0033] Optionally, the transmitting end performs polar coding on the extended information sequence to obtain polar coded codewords, and transmits the polar coded codewords to the receiving end through the channel, specifically including:

[0034] The transmitting end fills the extended information sequence into the information bits in the input bit set of the polarization encoder;

[0035] The transmitting end sets the frozen bits in the input bit set to fixed values ​​to obtain the first input bit sequence of the polarization encoder;

[0036] The transmitting end performs a polarization transformation on the first input bit sequence using a polarization coding process to obtain a polarized codeword of a preset code length.

[0037] The transmitting end transmits the polarization-coded codeword to the receiving end through the channel.

[0038] Optionally, the receiving end performs interleaved CA-SCL decoding on the polar-coded codewords transmitted through the channel to obtain an optimal information sequence estimate, specifically including:

[0039] The receiving end uses the polarized codeword transmitted through the channel as the second input bit sequence of the interleaved CA-SCL decoder.

[0040] The receiving end decodes each input bit in the second input bit sequence in sequence. If the input bit corresponds to a frozen bit, the input bit is assigned a value of 0 on each candidate path. If the input bit corresponds to an information bit, each candidate path is expanded into two candidate branches, 0 and 1, and the metric value of the candidate path is updated. The candidate path with the best metric value is retained, and the remaining candidate paths are eliminated.

[0041] When the decoding process reaches the CRC bit, the receiving end performs CRC verification based on the set of information bits that the CRC bit depends on.

[0042] After all input bits have been decoded, the receiver takes the candidate path with the smallest metric value and that passes the CRC check as the final output path, and uses the output result of the final output path as the optimal extended information sequence estimate.

[0043] The receiving end performs deinterleaving and CRC stripping on the optimal extended information sequence estimate to obtain the optimal information sequence estimate.

[0044] Optionally, when the decoding process reaches the CRC bit, the receiving end performs CRC verification based on the set of information bits that the CRC bit depends on, specifically including:

[0045] When the decoding process reaches the CRC bit, the receiving end performs CRC verification on the associated information bit sequence corresponding to the information bit set on the candidate path based on the information bit set to which the CRC bit depends.

[0046] If the associated information bit sequence passes the CRC check, the candidate path is retained and the candidate path is extended.

[0047] If the associated information bit sequence fails the CRC check, the candidate path is eliminated.

[0048] To achieve the above-mentioned objectives, the present invention also provides an interleaved cyclic redundancy check (CRC) polar code encoding and decoding system based on code weight distribution optimization, the system comprising a transmitter and a receiver:

[0049] The transmitting end is used to acquire the information sequence and the CRC check matrix, and uses a laddering algorithm to convert the CRC check matrix into an equivalent ladder matrix. Based on the equivalent ladder matrix, it determines the optimal insertion position scheme for the CRC bits corresponding to the optimal code redistribution. Based on the equivalent ladder matrix and the optimal insertion position scheme, it performs interleaved CRC encoding on the information sequence to obtain an extended information sequence. It then performs polar encoding on the extended information sequence to obtain polar encoded codewords, and transmits the polar encoded codewords to the receiving end through the channel.

[0050] The receiving end is used to perform interleaved CA-SCL decoding on the polarized codewords transmitted through the channel to obtain the optimal information sequence estimate.

[0051] In this invention, the transmitting end acquires an information sequence and a CRC check matrix, uses a laddering algorithm to convert the CRC check matrix into an equivalent ladder matrix, and determines the optimal insertion position scheme for the CRC bits corresponding to the optimal code redistribution based on the equivalent ladder matrix. The transmitting end performs interleaved CRC encoding on the information sequence based on the equivalent ladder matrix and the optimal insertion position scheme to obtain an extended information sequence. The transmitting end performs polar encoding on the extended information sequence to obtain polar encoded codewords, and transmits the polar encoded codewords to the receiving end through a channel. The receiving end performs interleaved CA-SCL decoding on the polar encoded codewords transmitted through the channel to obtain an optimal information sequence estimate. This invention effectively improves the error correction performance of CRC-Polar codes by maximizing the minimum code distance of concatenated codes and reducing low-weight codewords, resulting in a lower block error rate compared to fixed-segmentation or simple interleaving CRC-Polar codes. By distributing CRC bits throughout the information sequence, CRC checks can be performed multiple times during the decoding process to achieve early detection and termination of error decoding. Compared to traditional tail-based CRC-Polar codes, this significantly reduces the exploration of invalid paths and lowers the average decoding delay. Attached Figure Description

[0052] Figure 1 This is a flowchart of a preferred embodiment of the interleaved cyclic redundancy check polar code encoding and decoding method based on code redundancy optimization of the present invention;

[0053] Figure 2 This is another flowchart of a preferred embodiment of the interleaved cyclic redundancy check polar code encoding and decoding method based on code redistribution optimization of the present invention;

[0054] Figure 3 This is a structural diagram of a preferred embodiment of the interleaved cyclic redundancy check polar code encoding and decoding system based on code redundancy distribution optimization of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0056] Polar codes can approximate channel capacity with asymptotically large block lengths, but with finite code lengths, especially in Successive Cancellation (SC) decoding, their performance is inferior to established coding schemes such as Low-Density Parity-Check (LDPC) or Turbo codes. Subsequent successive cancellation list decoding significantly improved the finite-length error correction performance of Polar codes by retaining multiple candidate paths. Furthermore, by concatenating CRC codes as outer codes to the Polar code information bits, the correct decoding path can be selected using CRC check information, thus significantly improving the BLER performance of SCL decoding. This type of CRC-Polar coding scheme, which adds a CRC sequence to the end of the information sequence, has been adopted in 5G standards. However, the tail-based CRC-Polar coding scheme requires decoding the entire information sequence to determine the existence of a valid path, leading to wasted computational resources and high decoding latency. To introduce an early termination mechanism in SCL decoders to reduce latency, existing research has proposed several distributed CRC-Polar coding schemes, including segmented CRC-Polar coding schemes, which divide a long CRC sequence into several short CRC sequences of fixed length and protect the information sequence by segmenting them at equal intervals; and simple interleaved CRC-Polar coding schemes, which directly insert CRC bits after the last information bit they depend on, thereby eliminating erroneous paths that do not meet the CRC check in real time during SCL decoding and improving the error correction performance of CRC-Polar codes.

[0057] However, most existing studies employ relatively fixed CRC concatenation structures. While these can achieve early detection and termination of error decoding, they do not involve targeted structural design of the CRC insertion position based on optimal error correction performance, resulting in insufficient error correction performance of CRC-Polar codes. Therefore, further exploring the optimization potential of CRC bit insertion position for CRC-Polar code error correction performance while maintaining the advantage of early error detection has become an urgent problem to be solved in this field. Therefore, the technical problem to be solved by this invention is: optimizing the insertion position of CRC bits in the information bit block of the CRC-Polar code, improving the codeword weight distribution of the CRC-Polar code while ensuring the early termination mechanism of error decoding, and theoretically approaching a better maximum likelihood decoding performance.

[0058] To address the aforementioned technical problems, this invention provides an interleaved cyclic redundancy check (CRC) polar code encoding and decoding method based on code redundancy distribution optimization. The transmitting end acquires an information sequence and a CRC check matrix, and uses a stepwise transformation algorithm to convert the CRC check matrix into an equivalent stepwise matrix. Based on the equivalent stepwise matrix, it determines the optimal insertion position scheme for the CRC bits corresponding to the optimal code redundancy distribution. The transmitting end performs interleaved CRC encoding on the information sequence according to the equivalent stepwise matrix and the optimal insertion position scheme to obtain an extended information sequence. The transmitting end performs polar encoding on the extended information sequence to obtain polar encoded codewords, and transmits the polar encoded codewords to the receiving end through a channel. The receiving end performs interleaved CA-SCL decoding on the polar encoded codewords transmitted through the channel to obtain an estimate of the optimal information sequence. This invention effectively improves the error correction performance of CRC-Polar codes by maximizing the minimum code distance of concatenated codes and reducing low-weight codewords. Compared with fixed-segmentation or simple interleaving CRC-Polar codes, it has a lower block error rate. By distributing CRC bits into the information sequence, CRC checks can be performed multiple times during the decoding process to achieve early detection and termination of error decoding. Compared with traditional tail CRC-Polar codes, it can significantly reduce the exploration of invalid paths, reduce the consumption of computing resources, and reduce the average decoding delay.

[0059] The application content will be further explained below with reference to the accompanying drawings and the description of the embodiments.

[0060] A preferred embodiment of the interleaved cyclic redundancy check polar code encoding and decoding method based on code redundancy distribution optimization of the present invention is as follows: Figure 1 and Figure 2 As shown, it specifically includes:

[0061] S1. The sending end obtains the information sequence and CRC check matrix, uses a laddering algorithm to convert the CRC check matrix into an equivalent ladder matrix, and determines the optimal insertion position scheme of the CRC bits corresponding to the optimal code redistribution based on the equivalent ladder matrix.

[0062] In one implementation of this embodiment, the step of using a step-based algorithm to convert the CRC check matrix into an equivalent step-based matrix specifically includes:

[0063] The number of rows and columns of the CRC check matrix are set to correspond to the number of information bits and the number of CRC bits, respectively;

[0064] Construct a row index set and a column index set for the CRC check matrix, wherein the row index set and the column index set record the row index of the processed row and the column index of the processed column in the CRC check matrix, respectively;

[0065] The unprocessed column with the fewest elements of value 1 in the unprocessed column of the CRC check matrix is ​​taken as the priority column. The rows with unprocessed values ​​of 1 in the priority column are extracted, and the row index of the row is recorded in the row index set. The column index of the priority column is also recorded in the column index set.

[0066] Repeatedly update the row index set and the column index set until the row indexes of all rows of the CRC check matrix have been recorded in the row index set. Then, record the column indexes of the columns that have not yet been processed in the CRC check matrix into the column index set in the original order of the columns that have not yet been processed.

[0067] The CRC check matrix is ​​rearranged according to the order of the row indices in the row index set and the order of the column indices in the column index set to obtain an equivalent ladder matrix that satisfies the row-column progressive structure.

[0068] Specifically, assuming the sender uses a code length of... The number of information bits is The Polar code, the information sequence is represented as The CRC sequence length is bits (i.e., the number of CRC bits) The original CRC generation matrix is The CRC sequence is represented as The interleaved CRC-Polar code proposed in this invention is transmitted through the channel after interleaved CRC encoding and polarization encoding at the transmitting end. At the receiving end, it is decoded by executing a CRC-aided SCL (CA-SCL, CRC-aided SCL, Cyclic Redundancy Check Assisted Continuous Elimination List) algorithm (i.e., interleaved CA-SCL decoding). The specific process of interleaved CRC encoding (referring to interleaved CRC encoding in a broad sense, including preprocessing and interleaved CRC encoding in a narrow sense) includes: stepwise transformation of the original CRC check matrix, determination of the optimal CRC insertion position for code redistribution, and interleaved CRC encoding (interleaved CRC encoding in the narrow sense).

[0069] The specific process of stepping the original CRC check matrix (i.e., the CRC check matrix mentioned above) includes: Under normal circumstances, the CRC encoder can use a fixed generator matrix. This generator matrix can be divided into two parts: the left side is a matrix of size... The identity matrix represents the transmission relationship of information bits; the right side is a matrix of size . The CRC check matrix is ​​constructed such that each column corresponds to a CRC bit. The positions of '1's in each column indicate which information bits each CRC bit is derived from. To ensure that the earlier CRC bits depend only on the earlier information bits, thus enabling step-by-step verification, this invention employs a step-by-step algorithm to transform the original CRC check matrix... This can be converted into an equivalent echelon matrix (i.e., the equivalent echelon matrix mentioned earlier). This structure resembles an upper triangular matrix, where the checksum relationships corresponding to each CRC bit are arranged in a progressive order along the row and column indices, which is helpful for subsequent encoding dependency analysis. The processing algorithm steps are as follows: First, set the number of rows and columns of the current CRC checksum matrix, corresponding to the number of information bits, respectively. and the number of CRC check bits Two index sets (row index set and column index set) are initialized to record the processed row and column numbers (i.e., indices). During execution, in each round, the column with the fewest "1"s from the currently unprocessed columns of the CRC check matrix is ​​selected as the priority column. Then, all rows with a value of "1" that have not yet been processed are extracted from the selected column, considered as valid information bits in the current dependency path, and their numbers are recorded in the row index set. Simultaneously, the column number is recorded in the column index set. This process is repeated until all rows containing information bits have been included in the processing scope (it should be noted that recording the row or column index in the row or column index set indicates that the column or row has been processed and is included in the processing scope, becoming a processed row or column). Subsequently, columns that have not yet participated are added to the column index set according to their original order to ensure the integrity of the entire matrix structure. Finally, based on the row and column index order in the obtained row and column index sets, the original CRC check matrix is ​​rearranged to obtain an equivalent echelon matrix that satisfies the row-column progressive structure. Each column of this equivalent ladder matrix presents a clear information dependency path (i.e., each column represents a CRC bit, the information bit corresponding to the position of "1" in each column is the information bit that the CRC bit depends on, and the set of information bits corresponding to all "1" is the set of information bits that the CRC bit depends on), which facilitates subsequent CRC insertion position analysis and is suitable for the optimization design of dynamic CRC insertion bits.

[0070] Example: Setting the number of information bits CRC bit count The original CRC check matrix corresponding to the interleaved CRC encoder for:

[0071] ;

[0072] After the above step-form transformation, we obtain an equivalent step-form matrix. for:

[0073] ;

[0074] The dependency relationships between CRC bits and information bits can be obtained from this equivalent ladder matrix: the first CRC bit depends on the first, second, and third information bits; the second CRC bit depends on the second, third, fourth, and fifth information bits; the third CRC bit depends on the first, second, fourth, sixth, and seventh information bits; the fourth CRC bit depends on the second, third, fourth, fifth, sixth, and seventh information bits; the fifth CRC bit depends on the second, sixth, seventh, and eighth information bits; the sixth CRC bit depends on the first, third, fourth, fifth, sixth, seventh, and eighth information bits; the seventh CRC bit depends on the fourth, fifth, sixth, and eighth information bits; and the eighth CRC bit depends on the first, fifth, seventh, and eighth information bits.

[0075] In one implementation of this embodiment, the step of determining the optimal insertion position scheme of the CRC bits corresponding to the optimal code redistribution based on the equivalent ladder matrix specifically includes:

[0076] Based on the dependency relationship between each CRC bit and the information bit reflected in the equivalent ladder matrix and the order of each CRC bit in the equivalent ladder matrix, the set of candidate insertion positions for each CRC bit is determined.

[0077] Based on the candidate insertion position set of each CRC bit, multiple candidate insertion position schemes for all CRC bits are obtained;

[0078] Calculate the code weight distribution of the interleaved cyclic redundancy check polar code corresponding to each of the candidate insertion position schemes, and take the candidate insertion scheme corresponding to the optimal code weight distribution among the multiple code weight distributions as the optimal insertion position scheme for all CRC bits.

[0079] Specifically, the process of determining the optimal CRC insertion position for code weight distribution includes: enumerating candidate positions (i.e., determining the set of candidate insertion positions for each CRC bit), and determining the optimal combination of insertion positions based on code weight analysis (i.e., the optimal insertion position scheme for all CRC bits). It should be noted that the set of candidate insertion positions refers to the set of all candidate insertion positions for a single CRC bit, the candidate insertion position scheme is a scheme that includes all candidate insertion positions for all CRC bits, and the optimal insertion position scheme is a scheme that includes the optimal insertion positions for all CRC bits.

[0080] In one implementation of this embodiment, determining the candidate insertion position set for each CRC bit based on the dependency relationship between each CRC bit and the information bit reflected in the equivalent echelon matrix and the order of each CRC bit in the equivalent echelon matrix specifically includes:

[0081] The CRC bits are processed one by one according to their order in the equivalent ladder matrix;

[0082] For the currently processed CRC bit, the information bit on which the CRC bit depends is determined based on the dependency relationship between the CRC bit and the information bit reflected by the equivalent ladder matrix.

[0083] The positions that satisfy the constraint conditions among all positions after the last information bit in the information bits are taken as candidate insertion positions of the CRC bits, thus obtaining the set of candidate insertion positions of the CRC bits.

[0084] The constraints include the insertion position of the processed CRC bit before the candidate insertion position of the currently processed CRC bit and the insertion position of the unprocessed CRC bit after the candidate insertion position of the currently processed CRC bit.

[0085] Specifically, the process of enumerating candidate positions (i.e. determining the set of candidate insertion positions for each CRC bit) includes: after obtaining the staircase CRC check matrix through the aforementioned steps, the present invention further utilizes the causal dependency relationship between the information bits and CRC bits presented by the matrix to finely design the insertion position of each CRC bit in the polar code input sequence, so as to achieve early error detection and better decoding performance.

[0086] Specifically, the calculation of each CRC bit depends on a set of information bits. The index of the last information bit that the CRC bit depends on can be determined using an equivalent ladder matrix. To ensure that the CRC bit is accessed after its dependent information bits during decoding, this invention considers all positions after the last dependent bit as the initial candidate insertion position set for the current CRC bit. Furthermore, to maintain the consistency of the CRC check structure and the correctness of the decoder logic, the relative order of the CRC bits must remain strictly unchanged. That is, during the construction of the insertion position scheme, a later CRC bit cannot be inserted before a preceding CRC bit. For example, if the third CRC bit is determined by the first, second, and fifth information bits, then it can be inserted as early as after the fifth information bit, and must be after the first and second CRC bits, and before the fourth CRC bit (if it exists).

[0087] Therefore, the following strategy is adopted in the actual construction of the candidate insertion position set: 1. Sequential processing: CRC bits are processed one by one in the order of the equivalent ladder matrix to ensure the consistency of the insertion order. 2. Determine the last dependent bit: For the CRC bit being processed, find the one with the largest index in the set of information bits it depends on to determine the last dependent bit. 3. Generate candidate insertion position set: Starting from after the last dependent bit, enumerate all remaining insertable positions (i.e., positions not yet occupied by previous CRC bits) to form the candidate insertion position set. 4. Position constraint maintenance: When inserting, it must be ensured that: (1) the current CRC bit position is after the information bits it depends on; (2) all processed CRC bit insertion positions are before the current CRC bit; (3) all unprocessed CRC bits will be inserted after the current CRC bit. This strategy for constructing the candidate insertion position set not only preserves the correctness of the dependencies, but also provides a legal search space for subsequent selection of the optimal insertion position based on performance indicators (such as minimum code weight), which constitutes the basis of the interleaving optimization algorithm of this invention. The above design allows the CRC bits to be used for path verification and also helps to improve the overall distance characteristics of polar codes, thereby enhancing decoding performance.

[0088] For example: Based on the previous example, for , This refers to a 16-bit interleaved CRC encoder. The first CRC bit must be placed after the third information bit, meaning it can be placed at positions 4 to 9. The second CRC bit can be placed at positions max(7, first CRC bit position + 1) to 10. The third CRC bit can be placed at positions max(10, second CRC bit position + 1) to 11. The fourth CRC bit can be placed at positions max(11, third CRC bit position + 1) to 12. The fifth, sixth, seventh, and eighth CRC bits can only be placed at positions 13, 14, 15, and 16, respectively. This constitutes the set of all candidate insertion positions.

[0089] In one implementation of this embodiment, the step of calculating the code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes, and taking the candidate insertion scheme corresponding to the optimal code weight distribution among the multiple code weight distributions as the optimal insertion position scheme for all CRC bits, specifically includes:

[0090] The code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes is calculated using the Polar code distance spectrum analysis method. The code weight distribution includes the number of codewords with the minimum code weight and the number of codewords with a code weight lower than a set threshold.

[0091] The candidate insertion scheme corresponding to the optimal code redistribution among the multiple code redistributions is taken as the optimal insertion position scheme for all CRC bits.

[0092] The optimal insertion position scheme includes the optimal insertion position for each of the CRC bits.

[0093] Specifically, the process of determining the optimal insertion position combination (i.e., the optimal insertion position scheme for all CRC bits) based on code weight analysis includes: from the information sequence polarized codewords Total Generating Matrix It can be represented as:

[0094] ;

[0095] in, It is the generator matrix corresponding to the interleaved CRC encoder. It is the size of The Kronecker product matrix represents the generator matrix corresponding to the polar encoder. The error probability of maximum likelihood decoding of the polar code under a BI-AWGN (Binary Input-Additive White Gaussian Noise) channel. The upper bound is mainly determined by the total generating matrix. The number of low-code homophones, especially the minimum code homophones, is determined by:

[0096] ;

[0097] in, Indicates code weight is The number of code words, Indicates minimum code weight. Represents the bit energy per unit noise spectral density. Represents bit energy. Represents the noise spectral density. Represents the complementary error function. , Indicates the input parameters. This represents the integral variable.

[0098] As shown in the formula above, the fewer the number of low-level codewords with duplicates, the better the performance of the interleaved CRC-Polar code. The insertion position of the CRC affects... The value of the value affects the total generator matrix. The number of low-weight codewords generated. Therefore, by evaluating the code weight distribution corresponding to all possible CRC bit candidate insertion position schemes, the optimal CRC insertion combination (i.e., the optimal insertion position scheme) is selected. For example, existing Polar code distance spectrum analysis methods can be used to evaluate the overall CRC-Polar code code weight distribution corresponding to all candidate insertion position schemes, especially the number of minimum and low-weight codewords, and finally select the optimal CRC insertion combination. It should be understood that the present invention is not limited to this specific analysis method. Any existing or subsequently developed method that can be used to approximately or effectively evaluate the minimum Hamming distance of codewords and its distribution characteristics can be used in the embodiments of the present invention to assist in the selection of the optimal insertion position.

[0099] For example: Based on the previous example, for , , The CRC-Polar code has the CRC placement positions of the tail CRC-Polar code as [9, 10, 11, 12, 13, 14, 15, 16], and the code weight distribution is as follows. , , The CRC placement positions of the simple interleaved CRC-Polar code are [4, 7, 10, 11, 13, 14, 15, 16], and the code weight distribution is as follows: , , The CRC placement positions of the interleaved CRC-Polar code based on code weight distribution optimization proposed in this invention are [6, 7, 10, 11, 13, 14, 15, 16], and the code weight distribution is as follows: , , The minimum code weight was increased from 8 to 12, and the upper bound of the error probability of maximum likelihood decoding was reduced from 0.0957 for simple interleaving to 0.0807.

[0100] S2. The transmitting end performs interleaved CRC encoding on the information sequence according to the equivalent ladder matrix and the optimal insertion position scheme to obtain the extended information sequence.

[0101] In one implementation of this embodiment, the transmitting end performs interleaved CRC encoding on the information sequence according to the equivalent ladder matrix and the optimal insertion position scheme to obtain an extended information sequence, specifically including:

[0102] The transmitting end inputs the information sequence into the interleaved CRC encoder, and obtains the CRC sequence based on the information sequence and the equivalent ladder matrix corresponding to the interleaved CRC encoder, wherein the information sequence includes information bits and the CRC sequence includes CRC bits;

[0103] The transmitting end inserts the CRC bits from the CRC sequence into the information sequence according to the optimal insertion position scheme to obtain the extended information sequence.

[0104] Specifically, the process of interleaved CRC encoding (in the narrow sense) includes: The information bits (i.e., the information sequence) are applied to the echelonized CRC check matrix (i.e., the equivalent echelon matrix) to generate... The CRC check bits are then used. Then, according to the optimized interleaving scheme (i.e., the optimal insertion position scheme), these... CRC bits are inserted into The optimized position corresponding to the bit information bit forms The extended information sequence of bits.

[0105] For example: Based on the previous example, for , , The interleaved CRC-Polar code based on code redistribution optimization, assuming 8 information bits (i.e., an 8-bit information sequence) are... Then the 8-bit CRC check bits (i.e., the 8-bit CRC sequence) are: Based on the result of the optimal code redistribution (i.e., the optimal insertion position scheme), the information bits are placed sequentially at positions [1, 2, 3, 4, 5, 8, 9, 12], and the CRC bits (i.e., CRC check bits) are placed sequentially at positions [6, 7, 10, 11, 13, 14, 15, 16], resulting in a 16-bit extended information sequence. .

[0106] S3. The transmitting end performs polar coding on the extended information sequence to obtain polar coded codewords, and transmits the polar coded codewords to the receiving end through the channel.

[0107] In one implementation of this embodiment, the transmitting end performs polar coding on the extended information sequence to obtain polar coded codewords, and transmits the polar coded codewords to the receiving end through a channel, specifically including:

[0108] The transmitting end fills the extended information sequence into the information bits in the input bit set of the polarization encoder;

[0109] The transmitting end sets the frozen bits in the input bit set to fixed values ​​to obtain the first input bit sequence of the polarization encoder;

[0110] The transmitting end performs a polarization transformation on the first input bit sequence using a polarization coding process to obtain a polarized codeword of a preset code length.

[0111] The transmitting end transmits the polarization-coded codeword to the receiving end through the channel.

[0112] Specifically, the polar coding process includes: filling the aforementioned extended information sequence into the input bit set of the polar encoder; the filling positions are called "information bits" or "unfrozen bits." Unused positions are filled with fixed values ​​(usually zero) as frozen bits of the polar encoder. Using a standard polar coding process, the input bit sequence is polarized to generate the final encoded sequence (i.e., polar-coded codeword), the length of which is the preset polar code length. The encoded codeword serves as the transmission codeword for the polar code, and through subsequent modulation, physical layer transmission, and other processes, the entire transmission link is completed.

[0113] S4. The receiving end performs CA-SCL interleaving decoding on the polarized codewords transmitted through the channel to obtain the optimal information sequence estimate.

[0114] In one implementation of this embodiment, the step of interleaving and decoding the polar-coded codewords transmitted through the channel to obtain the optimal information sequence estimate specifically includes:

[0115] The receiving end uses the polarized codeword transmitted through the channel as the second input bit sequence of the interleaved CA-SCL decoder.

[0116] The receiving end decodes each input bit in the second input bit sequence in sequence. If the input bit corresponds to a frozen bit, the input bit is assigned a value of 0 on each candidate path. If the input bit corresponds to an information bit, each candidate path is expanded into two candidate branches, 0 and 1, and the metric value of the candidate path is updated. The candidate path with the best metric value is retained, and the remaining candidate paths are eliminated.

[0117] When the decoding process reaches the CRC bit, the receiving end performs CRC verification based on the set of information bits that the CRC bit depends on.

[0118] After all input bits have been decoded, the receiver takes the candidate path with the smallest metric value and that passes the CRC check as the final output path, and uses the output result of the final output path as the optimal extended information sequence estimate.

[0119] The receiving end performs deinterleaving and CRC stripping on the optimal extended information sequence estimate to obtain the optimal information sequence estimate.

[0120] In one implementation of this embodiment, when the decoding process reaches the CRC bit, the receiving end performs CRC verification based on the set of information bits that the CRC bit depends on, specifically including:

[0121] When the decoding process reaches the CRC bit, the receiving end performs CRC verification on the associated information bit sequence corresponding to the information bit set on the candidate path based on the information bit set to which the CRC bit depends.

[0122] If the associated information bit sequence passes the CRC check, the candidate path is retained and the candidate path is extended.

[0123] If the associated information bit sequence fails the CRC check, the candidate path is eliminated.

[0124] Specifically, while maintaining compatibility with traditional CA-SCL decoding, the decoding process incorporates an interleaver design to achieve early error detection, path pruning, and performance improvement. The specific process of interleaved CA-SCL decoding includes:

[0125] 1. Receive soft information sequence: The receiver obtains the polar-coded codewords transmitted through the channel, usually expressed in the form of log-likelihood ratio (LLR) for each bit. This soft information sequence is used as the input of the interleaved CA-SCL decoder.

[0126] 2. Initialization of the interleaved CA-SCL decoder: Start the CRC-assisted SCL decoder and set the decoder list capacity. It initializes the decoding path list, path metric, and other decoding state information, and prepares to perform recursive decoding operations based on the polar code construction.

[0127] 3. Path Expansion and Input Bit Decision: Each input bit is processed sequentially according to the bit order constructed by the polar coding. If it is a frozen bit, it is forcibly assigned a value of 0 on all paths; if it is an information bit (i.e., containing information bits or inserted CRC bits), it is expanded into two candidate branches, "0" and "1", on each path, and the path metric is updated, retaining the path with the best metric. One path is selected, and the rest are eliminated.

[0128] 4. Dynamic CRC Check and Path Filtering: When the current decoding position happens to be an inserted CRC bit, a CRC check is performed on the corresponding part of the path based on the set of information bits that the CRC bit depends on (which can be directly obtained from the aforementioned equivalent echelon matrix). If a path fails the CRC check, that path is immediately discarded; if all paths fail the check, decoding is terminated early and the decoding is deemed a failure; if a path still passes the CRC check, it is retained and subsequent path expansion is performed. This mechanism allows erroneous paths to be eliminated midway through decoding, avoiding resource waste and significantly reducing the average decoding latency, thus improving decoding efficiency.

[0129] 5. Termination of Decoding and Path Selection: After all input bits have been processed, the final output path is selected from the remaining paths. Typically, the path with the lowest path metric and that passes the final CRC check is chosen as the final output path, and the extended information sequence estimate is output. This extended information sequence estimate is then deinterleaved and stripped by CRC to output the information sequence estimate. If all paths ultimately fail the complete CRC check, decoding failure information can be reported for use by upper-layer error correction or retransmission mechanisms.

[0130] This invention proposes an interleaved CRC-Polar code design scheme based on code redistribution optimization. This scheme determines the positions where CRC decoding can be terminated early by analyzing the dependency relationship between CRC bits and information bits. It then calculates the impact of all possible placement positions on the CRC-Polar code redistribution and finally selects the optimal CRC bit distribution strategy to balance decoding delay control and BLER performance improvement (i.e., reducing the block error rate).

[0131] In 5G NR (5G New Radio) systems, the PDCCH (Physical Downlink Control Channel) carries downlink control information, and its transmission reliability directly affects the correctness of user scheduling and resource allocation. Since control information is typically short, Polar codes are often used for encoding protection, with additional CRC bits for error detection. Current standards employ either a tail-based CRC scheme or a simple distributed CRC scheme. However, these schemes do not consider optimizing code weight distribution (i.e., optimal error correction performance) by adjusting the placement of CRC bits, while maintaining the advantages of early CRC error detection. This invention employs an interleaved CRC-Polar code based on optimized code weight distribution, selecting the optimal CRC bit distribution strategy to balance decoding delay control and BLER performance improvement. Therefore, the interleaved CRC-Polar code based on optimized code weight distribution proposed in this invention can be widely applied to downlink control channel transmission scenarios in 5G NR systems for signaling transmission in physical channels, reducing block error rate (BOR) and average decoding delay.

[0132] In summary, the interleaved CRC-Polar code design method based on code redistribution optimization proposed in this invention can be widely applied in fields including but not limited to 5G control channels, IoT (Internet of Things) short packet communication, vehicle-to-everything (V2X) control signaling, and spaceborne short frame communication. Any equivalent scheme based on this technical approach, which optimizes the CRC insertion position to improve BLER or delay performance, should be within the scope of protection of this invention.

[0133] Furthermore, based on the aforementioned interleaved cyclic redundancy check (CRC) polar code encoding and decoding method based on code redundancy distribution optimization, this invention also provides an interleaved CRC polar code encoding and decoding system based on code redundancy distribution optimization. A preferred embodiment of the interleaved CRC polar code encoding and decoding system based on code redundancy distribution optimization is as follows: Figure 3 As shown, it specifically includes a transmitter 01 and a receiver 02:

[0134] The transmitting end 01 is used to acquire the information sequence and CRC check matrix, and uses a step-wise algorithm to convert the CRC check matrix into an equivalent step-wise matrix. Based on the equivalent step-wise matrix, it determines the optimal insertion position scheme for the CRC bits corresponding to the optimal code redistribution. Based on the equivalent step-wise matrix and the optimal insertion position scheme, it performs interleaved CRC encoding on the information sequence to obtain an extended information sequence. It then performs polar encoding on the extended information sequence to obtain polar encoded codewords, and transmits the polar encoded codewords to the receiving end 02 through the channel.

[0135] The receiver 02 is used to perform interleaved CA-SCL decoding on the polarized codewords transmitted through the channel to obtain the optimal information sequence estimate.

[0136] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal that includes that element.

[0137] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.). This program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The computer-readable storage medium can be a memory, magnetic disk, optical disk, etc.

[0138] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A coding and decoding method for interleaved cyclic redundancy check polar codes based on code redundancy distribution optimization, characterized in that, The interleaved cyclic redundancy check polar code encoding and decoding method based on code redundancy optimization includes: The sending end acquires the information sequence and CRC check matrix, uses a laddering algorithm to convert the CRC check matrix into an equivalent ladder matrix, and determines the optimal insertion position scheme of the CRC bits corresponding to the optimal code redistribution based on the equivalent ladder matrix. The transmitting end performs interleaved CRC encoding on the information sequence according to the equivalent ladder matrix and the optimal insertion position scheme to obtain the extended information sequence; The transmitting end performs polar coding on the extended information sequence to obtain polar coded codewords, and transmits the polar coded codewords to the receiving end through the channel; The receiving end performs interleaved CA-SCL decoding on the polarized codewords transmitted through the channel to obtain the optimal information sequence estimate.

2. The interleaved cyclic redundancy check polar code encoding and decoding method based on code redistribution optimization according to claim 1, characterized in that, The step-by-step algorithm for converting the CRC check matrix into an equivalent ladder-type matrix specifically includes: The number of rows and columns of the CRC check matrix are set to correspond to the number of information bits and the number of CRC bits, respectively; Construct a row index set and a column index set for the CRC check matrix, wherein the row index set and the column index set record the row index of the processed row and the column index of the processed column in the CRC check matrix, respectively; The unprocessed column with the fewest elements of value 1 in the unprocessed column of the CRC check matrix is ​​taken as the priority column. The rows with unprocessed values ​​of 1 in the priority column are extracted, and the row index of the row is recorded in the row index set. The column index of the priority column is also recorded in the column index set. Repeatedly update the row index set and the column index set until the row indexes of all rows of the CRC check matrix have been recorded in the row index set. Then, record the column indexes of the columns that have not yet been processed in the CRC check matrix into the column index set in the original order of the columns that have not yet been processed. The CRC check matrix is ​​rearranged according to the order of the row indices in the row index set and the order of the column indices in the column index set to obtain an equivalent ladder matrix that satisfies the row-column progressive structure.

3. The interleaved cyclic redundancy check polar code encoding and decoding method based on code redistribution optimization according to claim 2, characterized in that, The method for determining the optimal insertion position of the CRC bits corresponding to the optimal code redistribution based on the equivalent ladder matrix specifically includes: Based on the dependency relationship between each CRC bit and the information bit reflected in the equivalent ladder matrix and the order of each CRC bit in the equivalent ladder matrix, the set of candidate insertion positions for each CRC bit is determined. Based on the candidate insertion position set of each CRC bit, multiple candidate insertion position schemes for all CRC bits are obtained; Calculate the code weight distribution of the interleaved cyclic redundancy check polar code corresponding to each of the candidate insertion position schemes, and take the candidate insertion scheme corresponding to the optimal code weight distribution among the multiple code weight distributions as the optimal insertion position scheme for all CRC bits.

4. The interleaved cyclic redundancy check polar code encoding and decoding method based on code redistribution optimization according to claim 3, characterized in that, The step of determining the candidate insertion position set for each CRC bit based on the dependency relationship between each CRC bit and the information bit reflected in the equivalent echelon matrix and the order of each CRC bit in the equivalent echelon matrix specifically includes: The CRC bits are processed one by one according to their order in the equivalent ladder matrix; For the currently processed CRC bit, the information bit on which the CRC bit depends is determined based on the dependency relationship between the CRC bit and the information bit reflected by the equivalent ladder matrix. The positions that satisfy the constraint conditions among all positions after the last information bit in the information bits are taken as candidate insertion positions of the CRC bits, thus obtaining the set of candidate insertion positions of the CRC bits. The constraints include the insertion position of the processed CRC bit before the candidate insertion position of the currently processed CRC bit and the insertion position of the unprocessed CRC bit after the candidate insertion position of the currently processed CRC bit.

5. The interleaved cyclic redundancy check polar code encoding and decoding method based on code redistribution optimization according to claim 4, characterized in that, The step of calculating the code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes, and taking the candidate insertion scheme corresponding to the optimal code weight distribution among the multiple code weight distributions as the optimal insertion position scheme for all CRC bits, specifically includes: The code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes is calculated using the Polar code distance spectrum analysis method. The code weight distribution includes the number of codewords with the minimum code weight and the number of codewords with a code weight lower than a set threshold. The candidate insertion scheme corresponding to the optimal code redistribution among the multiple code redistributions is taken as the optimal insertion position scheme for all CRC bits. The optimal insertion position scheme includes the optimal insertion position for each of the CRC bits.

6. The interleaved cyclic redundancy check polar code encoding and decoding method based on code redistribution optimization according to claim 1, characterized in that, The transmitting end performs interleaved CRC encoding on the information sequence according to the equivalent ladder matrix and the optimal insertion position scheme to obtain an extended information sequence, specifically including: The transmitting end inputs the information sequence into the interleaved CRC encoder, and obtains the CRC sequence based on the information sequence and the equivalent ladder matrix corresponding to the interleaved CRC encoder, wherein the information sequence includes information bits and the CRC sequence includes CRC bits; The transmitting end inserts the CRC bits from the CRC sequence into the information sequence according to the optimal insertion position scheme to obtain the extended information sequence.

7. The interleaved cyclic redundancy check polar code encoding and decoding method based on code redistribution optimization according to claim 1, characterized in that, The transmitting end performs polar coding on the extended information sequence to obtain polar coded codewords, and transmits the polar coded codewords to the receiving end through the channel, specifically including: The transmitting end fills the extended information sequence into the information bits in the input bit set of the polarization encoder; The transmitting end sets the frozen bits in the input bit set to fixed values ​​to obtain the first input bit sequence of the polarization encoder; The transmitting end performs a polarization transformation on the first input bit sequence using a polarization coding process to obtain a polarized codeword of a preset code length. The transmitting end transmits the polarization-coded codeword to the receiving end through the channel.

8. The interleaved cyclic redundancy check polar code encoding and decoding method based on code redistribution optimization according to claim 7, characterized in that, The receiving end performs interleaved CA-SCL decoding on the polar-coded codewords transmitted through the channel to obtain the optimal information sequence estimate, specifically including: The receiving end uses the polarized codeword transmitted through the channel as the second input bit sequence of the interleaved CA-SCL decoder. The receiving end decodes each input bit in the second input bit sequence in sequence. If the input bit corresponds to a frozen bit, the input bit is assigned a value of 0 on each candidate path. If the input bit corresponds to an information bit, each candidate path is expanded into two candidate branches, 0 and 1, and the metric value of the candidate path is updated. The candidate path with the best metric value is retained, and the remaining candidate paths are eliminated. When the decoding process reaches the CRC bit, the receiving end performs CRC verification based on the set of information bits that the CRC bit depends on. After all input bits have been decoded, the receiver takes the candidate path with the smallest metric value and that passes the CRC check as the final output path, and uses the output result of the final output path as the optimal extended information sequence estimate. The receiving end performs deinterleaving and CRC stripping on the optimal extended information sequence estimate to obtain the optimal information sequence estimate.

9. The interleaved cyclic redundancy check polar code encoding and decoding method based on code redistribution optimization according to claim 8, characterized in that, When the decoding process reaches the CRC bit, the receiving end performs CRC verification based on the set of information bits that the CRC bit depends on, specifically including: When the decoding process reaches the CRC bit, the receiving end performs CRC verification on the associated information bit sequence corresponding to the information bit set on the candidate path based on the information bit set to which the CRC bit depends. If the associated information bit sequence passes the CRC check, the candidate path is retained and the candidate path is extended. If the associated information bit sequence fails the CRC check, the candidate path is eliminated.

10. A coding and decoding system for interleaved cyclic redundancy check polar codes based on code redundancy distribution optimization, characterized in that, The interleaved cyclic redundancy check polar code encoding and decoding system based on code redundancy distribution optimization includes a transmitter and a receiver: The transmitting end is used to acquire the information sequence and the CRC check matrix, and uses a laddering algorithm to convert the CRC check matrix into an equivalent ladder matrix. Based on the equivalent ladder matrix, it determines the optimal insertion position scheme for the CRC bits corresponding to the optimal code redistribution. Based on the equivalent ladder matrix and the optimal insertion position scheme, it performs interleaved CRC encoding on the information sequence to obtain an extended information sequence. It then performs polar encoding on the extended information sequence to obtain polar encoded codewords, and transmits the polar encoded codewords to the receiving end through the channel. The receiving end is used to perform interleaved CA-SCL decoding on the polarized codewords transmitted through the channel to obtain the optimal information sequence estimate.

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