Code redistribution optimization-based interleaving cyclic redundancy check polarization code coding and decoding method and system

Abstract

The invention relates to the technical field of channel coding, and discloses an interleaving cyclic redundancy check polarization code coding and decoding method and system based on code redistribution optimization, and the method comprises the steps: a transmitting end converts a CRC check matrix into an equivalent stepped matrix through employing a stepped algorithm, determining an optimal insertion position scheme of CRC bits corresponding to the optimal code redistribution according to the equivalent stepped matrix; according to the equivalent stepped matrix and the optimal insertion position scheme, performing interleaving CRC coding on the information sequence to obtain an extended information sequence; performing polarization coding on the extended information sequence to obtain a polarization coding codeword; and a receiving end performs interleaving CA-SCL decoding on the polarization coding codeword transmitted through the channel to obtain optimal information sequence estimation. According to the scheme of determining the optimal CRC insertion position based on code redistribution optimization, the error correction performance of the CRC-Polar code is improved, early detection termination of error decoding is realized, and average decoding delay is reduced.

Description

Technical Field

[0001] The present 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 weight distribution optimization. Background Art

[0002] By concatenating a cyclic redundancy check (CRC) code as an outer code to the polar code information bits, the CRC information can be used to select the correct decoding path, significantly improving the block error rate (BLER) performance of SCL (Successive Cancellation List) decoding. This CRC-Polar coding scheme, which appends a CRC sequence to the end of the information sequence, has been adopted in the 5G standard. However, this tail CRC-Polar coding scheme requires decoding the entire information sequence to determine whether a valid path exists, resulting in wasted computing resources and high decoding latency. To reduce latency by introducing an early termination mechanism in the SCL decoder, existing research has proposed several distributed CRC-Polar coding schemes. These include a segmented CRC-Polar coding scheme, which splits a longer CRC sequence into several short CRC sequences of fixed length, protecting the information sequence at equal intervals. A simple interleaved CRC-Polar coding scheme, which inserts CRC bits directly after the last information bit on which they depend, effectively eliminates error paths that do not meet CRC checksum requirements in real time during SCL decoding, thereby improving the error correction performance of CRC-Polar codes.

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

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

[0005] The main purpose of the present invention is to provide a method and system for encoding and decoding interleaved cyclic redundancy check polar codes based on optimized code weight distribution. This aims to address the problem that existing CRC-Polar coding schemes lack a 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 object, the present invention provides an interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization. The interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization includes: The transmitting end obtains an information sequence and a CRC check matrix, converts the CRC check matrix into an equivalent ladder-type matrix using a ladder algorithm, and determines an optimal insertion position scheme of CRC bits corresponding to optimal code redistribution based on the equivalent ladder-type matrix; The transmitting end performs interleaving CRC coding on the information sequence according to the equivalent ladder matrix and the optimal insertion position scheme to obtain an extended information sequence; The transmitting end performs polarization coding on the extended information sequence to obtain a polarization coded codeword, and transmits the polarization coded codeword to the receiving end through a channel; The receiving end performs interleaved CA-SCL decoding on the polarization coded codeword transmitted through the channel to obtain an optimal information sequence estimate.

[0007] Optionally, the step of converting the CRC check matrix into an equivalent step-type matrix using a step-type algorithm specifically includes: Setting the number of rows and columns of the CRC check matrix to correspond to the number of information bits and the number of CRC bits respectively; Constructing a row index set and a column index set of the CRC check matrix, wherein the row index set and the column index set respectively record row indices of processed rows and column indices of processed columns in the CRC check matrix; The unprocessed column of the CRC check matrix having the least number of elements with a value of 1 is selected as a priority column, unprocessed rows with a value of 1 in the priority column are extracted, row indexes of the rows are recorded in the row index set, and column indexes of the priority columns are recorded in the column index set; Repeatingly updating the row index set and the column index set until row indexes of all rows of the CRC check matrix have been recorded in the row index set, and then recording column indexes of unprocessed columns in the CRC check matrix into the column index set in the original order of the unprocessed columns; The CRC check matrix is ​​rearranged according to the order of row indices in the row index set and the order of column indices in the column index set to obtain an equivalent ladder-type matrix that satisfies a row-column progressive structure.

[0008] Optionally, determining the optimal insertion position scheme of CRC bits corresponding to the optimal code redistribution according to the equivalent ladder matrix specifically includes: Determining a set of candidate insertion positions for each CRC bit according to the dependency relationship between each CRC bit and the information bit reflected by the equivalent echelon matrix and the order of each CRC bit in the equivalent echelon matrix; Obtaining multiple candidate insertion position schemes for all CRC bits based on the candidate insertion position sets for each of the CRC bits; The code weight distribution of the interleaved cyclic redundancy check polar code corresponding to each of the candidate insertion position schemes is calculated respectively, and the candidate insertion scheme corresponding to the optimal code weight distribution among the multiple code weight distributions is used as the optimal insertion position scheme for all CRC bits.

[0009] Optionally, determining a set of candidate insertion positions for each CRC bit according to the dependency relationship between each CRC bit and the information bit reflected by the equivalent echelon matrix and the order of each CRC bit in the equivalent echelon matrix specifically includes: Processing the CRC bits one by one according to the order of the CRC bits in the equivalent ladder matrix; For a currently processed CRC bit, determining, based on the dependency relationship between the CRC bit and the information bit reflected by the equivalent echelon matrix, the information bit on which the CRC bit depends; Taking positions satisfying the constraint conditions among all positions after the last information bit in the information bits as candidate insertion positions for the CRC bits, to obtain a set of candidate insertion positions for the CRC bits; The constraint conditions include that the insertion position of the processed CRC bit is before the candidate insertion position of the currently processed CRC bit and the insertion position of the unprocessed CRC bit is after the candidate insertion position of the currently processed CRC bit.

[0010] Optionally, respectively calculating the code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes, and using 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: Calculating the code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes using a Polar code distance spectrum analysis method, where the code weight distribution includes the number of codewords with minimum code weight and the number of codewords with code weight below a set threshold; Using a candidate insertion scheme corresponding to an optimal code redistribution among the plurality of code redistributions as an optimal insertion position scheme for all CRC bits; The optimal insertion position scheme includes the optimal insertion position of each CRC bit.

[0011] Optionally, the transmitting end performs interleaving 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 an interleaved CRC encoder, and obtains a CRC sequence according to the information sequence and the equivalent ladder-type 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 in the CRC sequence into the information sequence according to the optimal insertion position scheme to obtain an extended information sequence.

[0012] Optionally, the transmitting end performs polarization coding on the extended information sequence to obtain a polarization coded codeword, and transmits the polarization coded codeword to the receiving end through a channel, specifically including: The transmitting end fills the extended information sequence into information bits in an input bit set of a polar encoder; The transmitting end sets frozen bits in an input bit set to a fixed value to obtain a first input bit sequence of the polar encoder; The transmitting end performs polarization conversion on the first input bit sequence using a polarization coding process to obtain a polarization coded codeword of a preset code length; The transmitting end transmits the polarization coding codeword to the receiving end through a channel.

[0013] Optionally, the receiving end performs interleaved CA-SCL decoding on the polar coding codeword transmitted through the channel to obtain an optimal information sequence estimate, specifically including: The receiving end uses the polarization coded codeword transmitted through the channel as a second input bit sequence of an interleaved CA-SCL decoder; The receiving end sequentially decodes each input bit in the second input bit sequence, and if the input bit corresponds to a frozen bit, assigns the input bit to 0 on each candidate path; if the input bit corresponds to an information bit, expands each candidate path into two candidate branches, 0 and 1, and updates the metric values ​​of the candidate paths, retaining the candidate path with the optimal metric value and the previously set value, and eliminating the remaining candidate paths; When the decoding process reaches the CRC bit, the receiving end performs a CRC check based on the set of information bits that the CRC bit depends on; After all input bits are decoded, the receiving end uses the candidate path with the smallest metric and passing 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 inverse interleaving and CRC stripping processing on the optimal extended information sequence estimate to obtain the optimal information sequence estimate.

[0014] Optionally, when the decoding process reaches a CRC bit, the receiving end performs a CRC check according to a set of information bits on which the CRC bit depends, specifically including: When the decoding process reaches the CRC bit, the receiving end performs a CRC check on the associated information bit sequence corresponding to the information bit set on the candidate path according to the information bit set on which the CRC bit depends; If the associated information bit sequence passes the CRC check, retaining the candidate path and performing path extension on the candidate path; If the associated information bit sequence fails the CRC check, the candidate path is eliminated.

[0015] To achieve the above-mentioned object, the present invention further provides an interleaved cyclic redundancy check polar code encoding and decoding system based on code weight distribution optimization. The interleaved cyclic redundancy check polar code encoding and decoding system based on code weight distribution optimization includes a transmitting end and a receiving end: The transmitting end is configured to obtain an information sequence and a CRC check matrix, convert the CRC check matrix into an equivalent staircase matrix using a staircase algorithm, and determine an optimal insertion position scheme for CRC bits corresponding to optimal code redistribution based on the equivalent staircase matrix; perform interleaved CRC coding on the information sequence based on the equivalent staircase matrix and the optimal insertion position scheme to obtain an extended information sequence; perform polarization coding on the extended information sequence to obtain a polarization-coded codeword, and transmit the polarization-coded codeword to a receiving end via a channel; The receiving end is used to perform interleaved CA-SCL decoding on the polarization coded codeword transmitted through the channel to obtain an optimal information sequence estimate.

[0016] In the present invention, a transmitting end obtains an information sequence and a CRC check matrix, converts the CRC check matrix into an equivalent staircase matrix using a staircase algorithm, and determines an optimal insertion position scheme for CRC bits corresponding to optimal code redistribution based on the equivalent staircase matrix; the transmitting end performs interleaved CRC coding on the information sequence based on the equivalent staircase matrix and the optimal insertion position scheme to obtain an extended information sequence; the transmitting end performs polarization coding on the extended information sequence to obtain a polarization-coded codeword, and transmits the polarization-coded codeword to a receiving end via a channel; the receiving end performs interleaved CA-SCL decoding on the polarization-coded codeword after transmission via the channel to obtain an optimal information sequence estimate. By maximizing the minimum code distance of the concatenated code and reducing low-weight codewords, the present invention effectively improves the error correction performance of CRC-Polar codes, achieving a lower block error rate compared to fixed segmented or simple interleaved CRC-Polar codes. 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 erroneous decoding. Compared to traditional tail CRC-Polar codes, this method can significantly reduce the exploration of invalid paths and lower the average decoding delay. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a flowchart of a preferred embodiment of the coding method of interleaved cyclic redundancy check polar codes based on code weight distribution optimization of the present invention; Figure 2 This is another flow chart of a preferred embodiment of the coding method of interleaved cyclic redundancy check polar codes based on code weight distribution optimization of the present invention; Figure 3 4 is a structural diagram of a preferred embodiment of the interleaved cyclic redundancy check polar code encoding and decoding system based on code weight distribution optimization of the present invention. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solutions and advantages of the present invention more clear and distinct, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0019] Polar codes can approach channel capacity with progressively larger block lengths, but their performance under finite code lengths, especially under Successive Cancellation (SC) decoding, falls short of established coding schemes such as Low-Density Parity-Check (LDPC) or Turbo codes. Successive Cancellation List Decoding, a subsequently proposed approach, significantly improves the finite-length error correction performance of Polar codes by retaining multiple candidate paths. Furthermore, by concatenating a CRC code as an outer code to the Polar code information bits, the CRC checksum can be used to select the correct decoding path, significantly improving the BLER performance of SCL decoding. This type of CRC-Polar coding scheme, which appends a CRC sequence to the end of the information sequence, has been adopted in the 5G standard. However, tail-CRC-Polar coding schemes require decoding of the entire information sequence to determine whether a valid path exists, resulting in wasted computational resources and high decoding latency. To reduce latency by introducing an early termination mechanism in the SCL decoder, existing research has proposed several distributed CRC-Polar coding schemes. These include a segmented CRC-Polar coding scheme, which splits a longer CRC sequence into several short CRC sequences of fixed length, protecting the information sequence at equal intervals. A simple interleaved CRC-Polar coding scheme, which inserts CRC bits directly after the last information bit on which they depend, effectively eliminates error paths that do not meet CRC checksum requirements in real time during SCL decoding, thereby improving the error correction performance of CRC-Polar codes.

[0020] However, most existing studies use a relatively fixed CRC cascade structure. Although it can achieve early detection and termination of error decoding, it does not perform targeted structural design on the CRC insertion position based on the optimal error correction performance, resulting in insufficient error correction performance of the CRC-Polar code. Therefore, while maintaining the advantage of early error detection, further exploring the optimization potential of the CRC bit insertion position on the error correction performance of the CRC-Polar code has become a problem to be solved in this field. Therefore, the technical problem to be solved by the present invention is to optimize the insertion position of the CRC bit in the CRC-Polar code information bit block, improve the codeword weight distribution of the CRC-Polar code on the basis of ensuring the early termination mechanism of error decoding, and theoretically approach a better maximum likelihood decoding performance.

[0021] To solve the above technical problems, the present invention provides an interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization. A transmitting end obtains an information sequence and a CRC check matrix, converts the CRC check matrix into an equivalent echelon matrix using a staircase algorithm, and determines an optimal insertion position scheme for CRC bits corresponding to an optimal code weight distribution based on the equivalent echelon matrix. The transmitting end performs interleaved CRC encoding on the information sequence based on the equivalent echelon matrix and the optimal insertion position scheme to obtain an extended information sequence. The transmitting end performs polarization encoding on the extended information sequence to obtain a polarization-coded codeword, and transmits the polarization-coded codeword to a receiving end via a channel. The receiving end performs interleaved CA-SCL decoding on the polarization-coded codeword after transmission via the channel to obtain an optimal information sequence estimate. By maximizing the minimum code distance of the concatenated code and reducing low-weight codewords, the present invention effectively improves the error correction performance of CRC-Polar codes, achieving a lower block error rate compared to fixed segmented or simple interleaved CRC-Polar codes. 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 erroneous decoding. Compared with traditional tail CRC-Polar codes, this method can significantly reduce the exploration of invalid paths, reduce computing resource usage, and lower average decoding delay.

[0022] The application content will be further explained below through description of embodiments in conjunction with the accompanying drawings.

[0023] A preferred embodiment of the interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization of the present invention is as follows: Figure 1 and Figure 2 As shown, specifically including: S1. The transmitting end obtains an information sequence and a CRC check matrix, converts the CRC check matrix into an equivalent ladder-type matrix using a ladder-type algorithm, and determines the optimal insertion position scheme of the CRC bits corresponding to the optimal code redistribution according to the equivalent ladder-type matrix.

[0024] In one implementation of this embodiment, converting the CRC check matrix into an equivalent ladder-type matrix using a ladder algorithm specifically includes: Setting the number of rows and columns of the CRC check matrix to correspond to the number of information bits and the number of CRC bits respectively; Constructing a row index set and a column index set of the CRC check matrix, wherein the row index set and the column index set respectively record row indices of processed rows and column indices of processed columns in the CRC check matrix; The unprocessed column of the CRC check matrix having the least number of elements with a value of 1 is selected as a priority column, unprocessed rows with a value of 1 in the priority column are extracted, row indexes of the rows are recorded in the row index set, and column indexes of the priority columns are recorded in the column index set; Repeatingly updating the row index set and the column index set until row indexes of all rows of the CRC check matrix have been recorded in the row index set, and then recording column indexes of unprocessed columns in the CRC check matrix into the column index set in the original order of the unprocessed columns; The CRC check matrix is ​​rearranged according to the order of row indices in the row index set and the order of column indices in the column index set to obtain an equivalent ladder-type matrix that satisfies a row-column progressive structure.

[0025] Specifically, assuming that the sending end uses a code length of , the number of information bits is Polar code, the information sequence is expressed as The CRC sequence length is bits (ie, the number of CRC bits is ), the original CRC generation matrix is , the CRC sequence is expressed as The interleaved CRC-Polar code proposed in the present invention is sent into the channel for transmission after interleaved CRC coding and polarization coding at the transmitting end, and is decoded by executing the CRC-assisted SCL (CA-SCL, CRC aided SCL, cyclic redundancy check assisted consecutive elimination list) algorithm at the receiving end (i.e., interleaved CA-SCL decoding). Among them, the specific process of interleaved CRC coding (referring to interleaved CRC coding in a broad sense, including preprocessing and interleaved CRC coding in a narrow sense) includes: stepping the original CRC check matrix, determining the CRC insertion position with the best code redistribution, and interleaved CRC coding (interleaved CRC coding in a narrow sense).

[0026] The specific process of laddering the original CRC check matrix (the CRC check matrix mentioned above) includes: Under normal circumstances, the CRC encoder can be represented by a fixed generator matrix. The generator matrix can be divided into two parts: the left side is a size of The unit matrix of , which represents the transmission relationship of the information bit itself; the right side is the unit matrix of size In the CRC check matrix, each column corresponds to a CRC bit, and the position of 1 in the column reflects which information bits each CRC bit is calculated from. In order to ensure that the front CRC bits only rely on the front information bits to achieve step-by-step check judgment, the present invention adopts a ladder algorithm to convert the original CRC check matrix into Convert to an equivalent echelon matrix (that is, the equivalent echelon matrix described above) , the structure is similar to the upper triangular matrix, in which the check relationship corresponding to each CRC bit is arranged progressively on the row and column indexes, which is helpful for subsequent coding dependency analysis. The processing algorithm steps are as follows: First, set the number of rows and columns of the current CRC check matrix, corresponding to the number of information bits respectively and the number of CRC check bits . Initialize two index sets (i.e., row index set and column index set) to record the processed row and column numbers (i.e., indexes) respectively. During the execution process, in each round, from the currently unprocessed columns of the CRC check matrix, select the column with the least "1" as the priority column. Then, extract all rows that have not yet participated in the processing and whose corresponding values ​​are "1" in the selected columns, regard them as valid information bits in the current dependent path, and record their numbers in the row index set. At the same time, record the number of the column in the column index set. Repeat the above process until all rows where the information bits are located have been included in the processing range (it should be noted that recording the row index or column index in the row index set or column index set means that the column or row has been processed, that is, it has been included in the processing range and becomes a processed row or column). Subsequently, the columns that have not yet participated are added to the column index set in their original order to ensure the integrity of the full matrix structure. Finally, according to the order of row and column indices in the obtained row index set and column index set, the original CRC check matrix is ​​rearranged to obtain an equivalent ladder matrix that satisfies the row and column progressive structure. Each column of the 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"s is the set of information bits that the CRC bit depends on), which facilitates the subsequent CRC insertion position analysis and is suitable for the optimized design of dynamic CRC insertion bits.

[0027] Example: Setting the number of information bits , CRC bits , the original CRC check matrix corresponding to the interleaved CRC encoder for: ; After the above ladder processing, the equivalent ladder matrix is ​​obtained for: ; The dependency relationship between CRC bits and information bits can be obtained from the equivalent echelon 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, 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.

[0028] In one implementation of this embodiment, determining the optimal insertion position scheme of the CRC bits corresponding to the optimal code redistribution according to the equivalent ladder matrix specifically includes: Determining a set of candidate insertion positions for each CRC bit according to the dependency relationship between each CRC bit and the information bit reflected by the equivalent echelon matrix and the order of each CRC bit in the equivalent echelon matrix; Obtaining multiple candidate insertion position schemes for all CRC bits based on the candidate insertion position sets for each of the CRC bits; The code weight distribution of the interleaved cyclic redundancy check polar code corresponding to each of the candidate insertion position schemes is calculated respectively, and the candidate insertion scheme corresponding to the optimal code weight distribution among the multiple code weight distributions is used as the optimal insertion position scheme for all CRC bits.

[0029] Specifically, the process of determining the CRC insertion position with the optimal code weight distribution includes: enumerating candidate positions (i.e., determining a set of candidate insertion positions for each CRC bit), and determining an optimal insertion position combination (i.e., an optimal insertion position scheme for all CRC bits) based on code weight analysis. It should be noted that the candidate insertion position set refers to the set of all candidate insertion positions for a single CRC bit, the candidate insertion position scheme refers to a scheme that includes candidate insertion positions for all CRC bits, and the optimal insertion position scheme refers to a scheme that includes optimal insertion positions for all CRC bits.

[0030] In one implementation of this embodiment, determining a set of candidate insertion positions for each CRC bit based on the dependency relationship between each CRC bit and the information bit reflected by the equivalent echelon matrix and the order of each CRC bit in the equivalent echelon matrix specifically includes: Processing the CRC bits one by one according to the order of the CRC bits in the equivalent ladder matrix; For a currently processed CRC bit, determining, based on the dependency relationship between the CRC bit and the information bit reflected by the equivalent echelon matrix, the information bit on which the CRC bit depends; Taking positions satisfying the constraint conditions among all positions after the last information bit in the information bits as candidate insertion positions for the CRC bits, to obtain a set of candidate insertion positions for the CRC bits; The constraint conditions include that the insertion position of the processed CRC bit is before the candidate insertion position of the currently processed CRC bit and the insertion position of the unprocessed CRC bit is after the candidate insertion position of the currently processed CRC bit.

[0031] Specifically, the specific process of enumerating candidate positions (i.e., determining a set of candidate insertion positions for each CRC bit) includes: after obtaining a stepped CRC check matrix through the aforementioned steps, the present invention further utilizes the causal dependency between information bits and CRC bits presented in the matrix to finely design the insertion position of each CRC bit in the polar code input sequence, thereby achieving early error detection and better decoding performance.

[0032] Specifically, the calculation of each CRC bit depends on a set of information bits. Based on the equivalent ladder matrix, the index of the last information bit that the CRC bit depends on can be determined. To ensure that the CRC bit is accessed after its dependent information bit during the decoding process, the present invention regards all positions after the last dependent bit as the initial candidate insertion position set for the current CRC bit. In addition, to maintain the consistency of the CRC check structure and the correctness of the decoder logic, the relative order between the CRC bits must strictly remain unchanged. That is, in the process of constructing the insertion position scheme, the subsequent CRC bits cannot be inserted before the previous CRC bits. For example, if the third CRC bit is determined by the first, second, and fifth information bits, then it can be inserted after the fifth information bit at the earliest, and must be located after the first and second CRC bits, and before the fourth CRC bit (if any).

[0033] Therefore, in the actual process of constructing the candidate insertion position set, the following strategies are adopted: 1. Sequential processing: Process the CRC bits one by one in the order of the CRC bits in the equivalent ladder matrix to ensure the consistency of the insertion order. 2. Determine the last dependent bit: For the CRC bit currently being processed, find the one with the largest index in the information bit set it depends on and determine the last dependent bit. 3. Generate a candidate insertion position set: Starting from the last dependent bit, enumerate all remaining insertable positions (i.e., positions not yet occupied by the previous CRC bit) to form a 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 bit 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. The strategy for constructing the candidate insertion position set not only retains the dependency correctness, but also provides a legal search space for the subsequent selection of the optimal insertion position based on performance indicators (such as minimum code weight), forming the basis of the interleaving optimization algorithm of the present invention. Through the above design, the CRC bits can be used for path verification and also help improve the overall distance characteristics of the polar code, thereby enhancing decoding performance.

[0034] For example: According to the above example, for , , that is, for an interleaved CRC encoder with a total length of 16 bits, the first CRC bit must be placed after the third information bit, that is, it is allowed to be placed in positions 4 to 9. The second CRC bit is allowed to be placed in positions from max(7, the first CRC bit position + 1) to 10. The third CRC bit is allowed to be placed in positions from max(10, the second CRC bit position + 1) to 11. The fourth CRC bit is allowed to be placed in positions from max(11, the third CRC bit position + 1) to 12. The fifth, sixth, seventh, and eighth CRC bits are only allowed to be placed in positions 13, 14, 15, and 16, respectively. This constitutes the set of all candidate insertion positions.

[0035] In one implementation of this embodiment, respectively calculating the code weight distribution of the interleaved cyclic redundancy check polar code corresponding to each of the candidate insertion position schemes, and using 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: Calculating the code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes using a Polar code distance spectrum analysis method, where the code weight distribution includes the number of codewords with minimum code weight and the number of codewords with code weight below a set threshold; Using a candidate insertion scheme corresponding to an optimal code redistribution among the plurality of code redistributions as an optimal insertion position scheme for all CRC bits; The optimal insertion position scheme includes the optimal insertion position of each CRC bit.

[0036] Specifically, the specific 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: Polarization coded codeword The total generator matrix It can be expressed as: ; in, is the generator matrix corresponding to the interleaved CRC encoder, 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 polar codes under the BI-AWGN (Binary Input-Additive White Gaussian Noise) channel is The upper bound is mainly determined by the total generating matrix The number of generated low-weight codewords, especially the minimum-weight codewords, determines: ; in, The code weight is The number of code words, Indicates the 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 input parameters, represents the integration variable.

[0037] From the above formula, we can know that the fewer the number of low-code weight codewords, the better the performance of the interleaved CRC-Polar code. The insertion position of CRC will affect The value affects the total generation matrix The number of low code weight codewords generated. Therefore, by evaluating the code weight distribution corresponding to all possible candidate CRC bit insertion position schemes, the optimal CRC insertion combination (i.e., the optimal insertion position scheme) is selected. For example, the existing Polar code distance spectrum analysis method can be used to evaluate the code weight distribution of the overall CRC-Polar code corresponding to all candidate insertion position schemes, especially the number of minimum code weight and low code 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, and any existing or subsequently developed method that can be used to approximate or effectively evaluate the minimum Hamming distance of codewords and their distribution characteristics can be used in the embodiments of the present invention to assist in the selection of the optimal insertion position.

[0038] For example: According to the above example, for , , The CRC-Polar code of the tail CRC-Polar code is placed at [9, 10, 11, 12, 13, 14, 15, 16], and the code weight distribution is , , ; The CRC placement position of the simple interleaved CRC-Polar code is [4, 7, 10, 11, 13, 14, 15, 16], and the code weight distribution is , , The CRC placement position of the interleaved CRC-Polar code based on code weight distribution optimization proposed in the present invention is [6, 7, 10, 11, 13, 14, 15, 16], and the code weight distribution is , , , the minimum code weight is increased from 8 to 12, and the upper bound of the error probability of maximum likelihood decoding is also reduced from 0.0957 of simple interleaving to 0.0807.

[0039] 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 an extended information sequence.

[0040] In one implementation of this embodiment, the transmitting end performs interleaving 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 an interleaved CRC encoder, and obtains a CRC sequence according to the information sequence and the equivalent ladder-type 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 in the CRC sequence into the information sequence according to the optimal insertion position scheme to obtain an extended information sequence.

[0041] Specifically, the specific process of interleaved CRC coding (in a narrow sense) includes: The information bits (i.e., information sequence) are applied to the ladder-type CRC check matrix (i.e., equivalent ladder-type matrix) to generate Then, according to the interleaving scheme optimized by code weight distribution (i.e., the optimal insertion position scheme), these CRC bits are inserted into The corresponding optimized position in the information bit is formed bits of extended information sequence.

[0042] For example: According to the above example, for , , The interleaved CRC-Polar code based on code weight distribution optimization assumes that 8 information bits (i.e., 8-bit information sequence) are , then the 8-bit CRC check bits (i.e., 8-bit CRC sequence) are According to the result of the optimal code redistribution (i.e., the optimal insertion position scheme), the information bits are placed in the positions [1, 2, 3, 4, 5, 8, 9, 12] in sequence, and the CRC bits (i.e., CRC check bits) are placed in the positions [6, 7, 10, 11, 13, 14, 15, 16] in sequence, to obtain a 16-bit extended information sequence. .

[0043] S3. The transmitting end performs polarization coding on the extended information sequence to obtain a polarization coding codeword, and transmits the polarization coding codeword to the receiving end through a channel.

[0044] In one implementation of this embodiment, the transmitting end performs polarization coding on the extended information sequence to obtain a polarization-coded codeword, and transmits the polarization-coded codeword to the receiving end through a channel, specifically including: The transmitting end fills the extended information sequence into information bits in an input bit set of a polar encoder; The transmitting end sets frozen bits in an input bit set to a fixed value to obtain a first input bit sequence of the polar encoder; The transmitting end performs polarization conversion on the first input bit sequence using a polarization coding process to obtain a polarization coded codeword of a preset code length; The transmitting end transmits the polarization coding codeword to the receiving end through a channel.

[0045] Specifically, the polar coding process includes: inserting the above-mentioned extended information sequence into the input bit set of the polar encoder, where the inserted positions are called "information bits" or "non-frozen bits." Unused positions are filled with fixed values ​​(usually zero) as frozen bits of the polar encoder. Using the standard polar coding process, the input bit sequence is polarized to generate the final coding sequence (i.e., polar coding codeword). The length of this coding sequence is the preset polar code length. The encoded codeword is used as the transmission codeword of the polarization code, and the entire transmission link is completed through subsequent modulation, physical layer transmission and other processes.

[0046] S4. The receiving end performs interleaved CA-SCL decoding on the polarization coded codeword transmitted through the channel to obtain an optimal information sequence estimate.

[0047] In one implementation of this embodiment, performing interleaved CA-SCL decoding on the polar coding codeword transmitted through the channel to obtain an optimal information sequence estimate specifically includes: The receiving end uses the polarization coded codeword transmitted through the channel as a second input bit sequence of an interleaved CA-SCL decoder; The receiving end sequentially decodes each input bit in the second input bit sequence, and if the input bit corresponds to a frozen bit, assigns the input bit to 0 on each candidate path; if the input bit corresponds to an information bit, expands each candidate path into two candidate branches, 0 and 1, and updates the metric values ​​of the candidate paths, retaining the candidate path with the optimal metric value and the previously set value, and eliminating the remaining candidate paths; When the decoding process reaches the CRC bit, the receiving end performs a CRC check based on the set of information bits that the CRC bit depends on; After all input bits are decoded, the receiving end uses the candidate path with the smallest metric and passing 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 inverse interleaving and CRC stripping processing on the optimal extended information sequence estimate to obtain the optimal information sequence estimate.

[0048] In one implementation of this embodiment, when the decoding process reaches the CRC bit, the receiving end performs a CRC check based on the information bit set on which the CRC bit depends, specifically including: When the decoding process reaches the CRC bit, the receiving end performs a CRC check on the associated information bit sequence corresponding to the information bit set on the candidate path according to the information bit set on which the CRC bit depends; If the associated information bit sequence passes the CRC check, retaining the candidate path and performing path extension on the candidate path; If the associated information bit sequence fails the CRC check, the candidate path is eliminated.

[0049] Specifically, the decoding process maintains compatibility with traditional CA-SCL decoding and combines interleaver design to achieve early error detection, path pruning, and performance improvement. The specific process of interleaved CA-SCL decoding includes: 1. Receive soft information sequence: The receiver obtains the polarization-coded codeword transmitted through the channel, usually expressed as a log-likelihood ratio (LLR) for each bit. This soft information sequence serves as the input to the interleaved CA-SCL decoder.

[0050] 2. Interleaved CA-SCL decoder initialization: Start the CRC-assisted SCL decoder and set the decoding table capacity , initialize the decoding path list, path metric and other decoding status information, and prepare to perform recursive decoding operations based on the polar code construction.

[0051] 3. Path extension and input bit judgment: Process each input bit in sequence according to the bit order of the polar coding structure. If it is a frozen bit, it is forced to be 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 of "0" and "1" on each path, and the path metric is updated, and the previous one with the best metric is retained. paths and eliminate the rest.

[0052] 4. Dynamic CRC Check and Path Selection: When the current decoding position happens to be an inserted CRC bit, a CRC check is performed on the corresponding portion of the information on the path based on the set of information bits on which the CRC bit depends (which can be directly obtained from the equivalent ladder matrix mentioned above). If a path fails the CRC check, the path is immediately eliminated. If all paths fail the check, decoding is terminated early and the decoding is deemed unsuccessful. If any paths still pass the CRC check, they are retained and further path extension is performed. This mechanism eliminates erroneous paths mid-decoding, avoiding resource waste, significantly reducing average decoding latency, and improving decoding efficiency.

[0053] 5. Decoding Termination 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 smallest path metric and passing the final CRC check is selected as the final output path, and the extended information sequence estimate is output. This extended information sequence estimate is deinterleaved and CRC stripped, and then output as the information sequence estimate. If all paths ultimately fail the full CRC check, decoding failure information is reported to higher-layer error correction or retransmission mechanisms.

[0054] This paper proposes a design for interleaved CRC-Polar codes based on optimized code weight distribution. This scheme analyzes the dependency between CRC bits and information bits to determine locations where CRC decoding can be terminated early. It then calculates the impact of all possible placements on the CRC-Polar code weight distribution. Ultimately, it selects a CRC bit distribution strategy with optimal weight distribution, balancing decoding delay control with improved BLER performance (i.e., reduced block error rate).

[0055] In 5G NR (5G New Radio) systems, the Physical Downlink Control Channel (PDCCH) carries downlink control information, and its transmission reliability directly impacts the accuracy of user scheduling and resource allocation. Because control information is typically short, Polar codes are often used for encoding and protection, with CRC bits appended for error detection. Current standards employ tail CRC or simple distributed CRC schemes. However, these schemes fail to consider optimizing the placement of CRC bits to achieve optimal code weight distribution, thereby optimizing error correction performance while maintaining the advantages of early error detection. The interleaved CRC-Polar code with optimized code weight distribution, adopted in this invention, selects a CRC bit distribution strategy with optimal code weight distribution, balancing decoding delay control and BLER performance improvement. Therefore, the interleaved CRC-Polar code with optimized code weight distribution proposed in this invention can be widely used in downlink control channel transmission scenarios in 5G NR systems, for physical channel signaling, to reduce the block error rate (BER) and average decoding delay.

[0056] In summary, the interleaved CRC-Polar code design method based on optimized code weight distribution proposed in this invention can be widely applied in fields including, but not limited to, 5G control channels, IoT (Internet of Things) short packet communications, vehicle-to-vehicle control signaling, and satellite-borne short frame communications. Any equivalent solution based on this technical approach that optimizes CRC insertion position to improve BLER or delay performance is within the scope of this invention.

[0057] In addition, based on the above-mentioned interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization, the present invention also provides an interleaved cyclic redundancy check polar code encoding and decoding system based on code weight distribution optimization. Among them, a preferred embodiment of the interleaved cyclic redundancy check polar code encoding and decoding system based on code weight distribution optimization is as follows: Figure 3 As shown, it specifically includes the sending end 01 and the receiving end 02: The transmitting end 01 is configured to obtain an information sequence and a CRC check matrix, convert the CRC check matrix into an equivalent staircase matrix using a staircase algorithm, and determine an optimal insertion position scheme for CRC bits corresponding to an optimal code redistribution based on the equivalent staircase matrix; perform interleaved CRC coding on the information sequence based on the equivalent staircase matrix and the optimal insertion position scheme to obtain an extended information sequence; perform polarization coding on the extended information sequence to obtain a polarization-coded codeword, and transmit the polarization-coded codeword to the receiving end 02 via a channel; The receiving end 02 is configured to perform interleaved CA-SCL decoding on the polarization coded codeword transmitted through the channel to obtain an optimal information sequence estimate.

[0058] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or terminal comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or terminal. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or terminal comprising the element.

[0059] Of course, those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing related hardware (such as a processor, controller, etc.) through a computer program. The program can be stored in a computer-readable storage medium that can be read by a computer. When executed, the program can include the processes in the above-described method embodiments. The computer-readable storage medium can be a memory, a magnetic disk, an optical disk, etc.

[0060] It should be understood that the application of the present invention is not limited to the above examples. For those skilled in the art, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

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

2. The interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization according to claim 1, characterized in that: The stepwise conversion of the CRC check matrix into an equivalent stepwise matrix comprises: Setting the number of rows and columns of the CRC check matrix to correspond to the number of information bits and the number of CRC bits respectively; Constructing a row index set and a column index set of the CRC check matrix, wherein the row index set and the column index set respectively record row indices of processed rows and column indices of processed columns in the CRC check matrix; The unprocessed column of the CRC check matrix having the least number of elements with a value of 1 is selected as a priority column, unprocessed rows with a value of 1 in the priority column are extracted, row indexes of the rows are recorded in the row index set, and column indexes of the priority columns are recorded in the column index set; Repeatingly updating the row index set and the column index set until row indexes of all rows of the CRC check matrix have been recorded in the row index set, and then recording column indexes of unprocessed columns in the CRC check matrix into the column index set in the original order of the unprocessed columns; The CRC check matrix is ​​rearranged according to the order of row indices in the row index set and the order of column indices in the column index set to obtain an equivalent ladder-type matrix that satisfies a row-column progressive structure.

3. The interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization according to claim 2, characterized in that: The optimal insertion position scheme of the CRC bits corresponding to the optimal code redistribution is determined according to the equivalent ladder matrix, specifically comprising: Determining a set of candidate insertion positions for each CRC bit according to the dependency relationship between each CRC bit and the information bit reflected by the equivalent echelon matrix and the order of each CRC bit in the equivalent echelon matrix; Obtaining multiple candidate insertion position schemes for all CRC bits based on the candidate insertion position sets for each of the CRC bits; The code weight distribution of the interleaved cyclic redundancy check polar code corresponding to each of the candidate insertion position schemes is calculated respectively, and the candidate insertion scheme corresponding to the optimal code weight distribution among the multiple code weight distributions is used 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 weight distribution optimization according to claim 3, characterized in that: Determining a set of candidate insertion positions for each CRC bit according to the dependency relationship between each CRC bit and the information bit reflected by the equivalent ladder matrix and the order of each CRC bit in the equivalent ladder matrix specifically includes: Processing the CRC bits one by one according to the order of the CRC bits in the equivalent ladder matrix; For a currently processed CRC bit, determining, based on the dependency relationship between the CRC bit and the information bit reflected by the equivalent echelon matrix, the information bit on which the CRC bit depends; Taking positions satisfying the constraint conditions among all positions after the last information bit in the information bits as candidate insertion positions for the CRC bits, to obtain a set of candidate insertion positions for the CRC bits; The constraint conditions include that the insertion position of the processed CRC bits is before the candidate insertion position of the currently processed CRC bits and the insertion position of the unprocessed CRC bits is after the candidate insertion position of the currently processed CRC bits.

5. The interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization according to claim 4, characterized in that: The step of respectively calculating the code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes, and using 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: Calculating the code weight distribution of the interleaved cyclic redundancy check polar codes corresponding to each of the candidate insertion position schemes using a Polar code distance spectrum analysis method, where the code weight distribution includes the number of codewords with minimum code weight and the number of codewords with code weight below a set threshold; Using a candidate insertion scheme corresponding to an optimal code redistribution among the plurality of code redistributions as an optimal insertion position scheme for all CRC bits; The optimal insertion position scheme includes the optimal insertion position of each CRC bit.

6. The interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization according to claim 1, characterized in that: The transmitting end performs interleaving CRC coding 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 an interleaved CRC encoder, and obtains a CRC sequence according to the information sequence and the equivalent ladder-type 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 in the CRC sequence into the information sequence according to the optimal insertion position scheme to obtain an extended information sequence.

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

8. The interleaved cyclic redundancy check polar code encoding and decoding method based on code weight distribution optimization according to claim 7, characterized in that: The receiving end performs interleaved CA-SCL decoding on the polar coding codeword transmitted through the channel to obtain an optimal information sequence estimate, specifically including: The receiving end uses the polarization coded codeword transmitted through the channel as a second input bit sequence of an interleaved CA-SCL decoder; The receiving end sequentially decodes each input bit in the second input bit sequence, and if the input bit corresponds to a frozen bit, assigns the input bit to 0 on each candidate path; if the input bit corresponds to an information bit, expands each candidate path into two candidate branches, 0 and 1, and updates the metric values ​​of the candidate paths, retaining the candidate path with the optimal metric value and the previously set value, and eliminating the remaining candidate paths; When the decoding process reaches the CRC bit, the receiving end performs a CRC check based on the set of information bits that the CRC bit depends on; After all input bits are decoded, the receiving end uses the candidate path with the smallest metric and passing 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 inverse interleaving and CRC stripping processing 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 weight distribution optimization according to claim 8, characterized in that: When the decoding process reaches the CRC bit, the receiving end performs a CRC check according to the information bit set on which the CRC bit depends, specifically including: When the decoding process reaches the CRC bit, the receiving end performs a CRC check on the associated information bit sequence corresponding to the information bit set on the candidate path according to the information bit set on which the CRC bit depends; If the associated information bit sequence passes the CRC check, retaining the candidate path and performing path extension on the candidate path; If the associated information bit sequence fails the CRC check, the candidate path is eliminated.

10. An interleaved cyclic redundancy check polar code encoding and decoding system based on code weight distribution optimization, characterized in that: The interleaved cyclic redundancy check polar code encoding and decoding system based on code weight distribution optimization includes a transmitting end and a receiving end: The transmitting end is configured to obtain an information sequence and a CRC check matrix, convert the CRC check matrix into an equivalent staircase matrix using a staircase algorithm, and determine an optimal insertion position scheme for CRC bits corresponding to optimal code redistribution based on the equivalent staircase matrix; perform interleaved CRC coding on the information sequence based on the equivalent staircase matrix and the optimal insertion position scheme to obtain an extended information sequence; perform polarization coding on the extended information sequence to obtain a polarization-coded codeword, and transmit the polarization-coded codeword to a receiving end via a channel; The receiving end is used to perform interleaved CA-SCL decoding on the polarization coded codeword transmitted through the channel to obtain an optimal information sequence estimate.

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