Polar code encoding / decoding method, device and system

Abstract

The present disclosure proposes a polarization code encoding / decoding method, device and system, which relate to the field of mobile communications. During encoding, n-level polarization encoding is performed in the order from the nth level polarization encoding to the first level polarization encoding, where n is a positive integer greater than 1, to achieve multi-level polarization code encoding. During decoding, n-level polarization decoding is performed on the received codeword sequence in the order from the first level polarization encoding to the nth level polarization encoding, and the codeword sequence corresponding to the (j+1)th level polarization encoding in the output of the jth level polarization decoding is used as the input of the (j+1)th level polarization decoding to achieve multi-level polarization code decoding. The multi-level polarization encoding / decoding method is used to improve the degree of polarization.

Description

Technical Field

[0001] The present disclosure relates to the field of mobile communications, and in particular to a polar code encoding / decoding method, device and system. Background Art

[0002] Erdal Arikan's research pointed out that the cutoff rate of the channel can be improved by performing channel combination and channel decomposition operations on discrete memoryless channels. When the total channel capacity remains unchanged, the capacity of some channels is increased while the capacity of other channels is reduced, and the concept of channel polarization is proposed. The longer the code length, the closer it is to the Shannon limit, and when the code length tends to infinity, it can reach the Shannon limit.

[0003] Polarization coding formula: Among them, x 1 N Represents the use of the generator matrix G N Treat the encoding codeword set u 1 N The polar code with length N is obtained through polarization coding, u λ represents the set of information symbols to be encoded, u λ c represents the set of frozen codewords to be encoded, λ represents the set of information channels, which is used to identify the position of the information channel; G N (λ) is the generator matrix G N The first submatrix composed of the rows selected from λ corresponds to the information channel coding used to transmit the information symbol set to be encoded; c represents the frozen channel set used to transmit the frozen codeword set to be encoded, and is used to identify the position of the frozen channel; GN(λ c ) represents the generator matrix G N The second sub-matrix remaining except the first sub-matrix corresponds to the frozen channel code used to transmit the frozen symbol set to be encoded.

[0004] Figure 1a It is a schematic diagram of the distribution of polarization channel positions and channel symmetric capacity (set as I(W)). Figure 1b This is a diagram showing the relationship between the logarithm of the code length and the proportion of channels with symmetric capacity within 0.05-0.95. Figure 1a and 1bAs shown, when the code length is 256 short codes, about 28% of the channel capacity is between 0.05-0.95, which means that if the channel capacity is greater than 0.95 as the threshold of the information channel, only (100%-28%) / 2=36% of the available information channels, and the coding rate is about 1 / 3; when the code length is 512, about 20% of the channel capacity is between 0.05-0.95, which means that if the channel capacity is greater than 0.95 as the threshold of the information channel for transmitting information, only (100%-20%) / 2=40% of the available information channels, and the coding rate is 2 / 5. In order to increase the available channels, the traditional method can only reduce the channel capacity threshold, but this will bring more information transmission errors. Summary of the invention

[0005] In order to solve the above problems, the embodiments of the present disclosure adopt a multi-level polarization encoding / decoding method to improve the degree of polarization, thereby correspondingly improving the number of available channels and the coding rate when the code length and the available channel capacity threshold remain unchanged, or correspondingly improving the available channel capacity threshold and the bit error rate performance when the code length and the coding rate remain unchanged.

[0006] Some embodiments of the present disclosure provide a polar code encoding method, including:

[0007] The n-level polarization coding is performed in order from the n-th level polarization coding to the 1st level polarization coding, where n is a positive integer greater than 1.

[0008] In some embodiments, performing n-level polarization coding includes: using the output of a previous level of polarization coding as the input of a next level of polarization coding.

[0009] In some embodiments, performing n-level polarization coding includes: using the output of a previous level of polarization coding as the input of information symbols of a next level of polarization coding.

[0010] In some embodiments, performing n-level polarization encoding includes:

[0011] For the nth level polarization coding, according to the coding formula Encoding;

[0012] For the i-th level polarization coding, i is a positive integer from (n-1) to 1. According to the coding formula Encoding;

[0013] in:

[0014] represents the XOR operation,

[0015] The length is The output symbol set of the nth level polar coding,

[0016] The length is The n-th level polar coding symbol sequence to be encoded, u λn is the set of information symbols to be encoded for the nth level polarization coding, is the set of frozen code elements to be encoded for the nth level polarization coding,

[0017] λ n Indicates that it is used to transmit u λn The information channel set is used to identify the location of the information channel of the nth level polarization coding. The code length from the nth level polarization code is The generator matrix The first submatrix composed of the rows selected from λn The information channel set λ n The encoding corresponds to

[0018] Indicates that it is used to transmit The frozen channel set is used to identify the position of the frozen channel of the nth level polarization coding. express The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit The set of frozen channels The encoding corresponds to

[0019] The length is The output symbol set of the i-th level polar coding,

[0020] The length is The i-th level polar coding symbol sequence to be encoded, is the first set of information symbols to be encoded for the i-th level polar coding, is the set of frozen codewords to be encoded for the i-th level polar coding, is the second set of information symbols to be encoded for the i-th level polarization coding, and is also the output symbol set for the (i+1)-th level polarization coding.

[0021] Indicates that it is used to transmit A first information channel set is used to identify the position of each first information channel of the i-th level polarization coding, The code length from the i-th level polarization code is The generator matrix The third sub-matrix composed of the rows selected from The first information channel set The encoding corresponds to

[0022] Indicates that it is used to transmit A set of second information channels of the i-th level polarization coding is used to identify the position of each second information channel of the i-th level polarization coding, is generated from the matrix The fourth sub-matrix composed of the rows selected from the third sub-matrix is ​​used to transmit The second information channel set The encoding corresponds to

[0023] Indicates that it is used to transmit The frozen channel set is used to identify the position of the frozen channel of the i-th level polarization coding. express The fifth sub-matrix remaining in addition to the third sub-matrix and the fourth sub-matrix is ​​used to transmit The set of frozen channels The encoding corresponds.

[0024] In some embodiments, two-level polarization coding is performed in order from the second-level polarization coding to the first-level polarization coding, including:

[0025] For the second level polarization coding, according to the coding formula Encoding;

[0026] For the first level polarization coding, according to the coding formula Encoding;

[0027] in:

[0028] represents the XOR operation,

[0029] x 1，2 N / 2 is the output symbol set of the second-level polar coding with length N / 2,

[0030] u 1，2 N / 2 is the codeword sequence to be encoded of the second-level polar coding with a length of N / 2, u 1，2 N / 2 =(u λ2 ,u λ2 c ),u λ2 is the set of information symbols to be encoded for the second-level polarization coding, u λ2 c is the set of frozen codewords to be encoded for the second-level polar coding,

[0031] λ 2 Indicates that it is used to transmit u λ2 The information channel set is used to identify the location of the second-level polarization coded information channel, G N / 2，2 (λ 2 ) is the generator matrix G with a coding length of N / 2 from the second-level polar coding N / 2，2 The first submatrix composed of the rows selected from λ2 The information channel set λ2 The encoding corresponds to

[0032] λ 2 c Indicates that it is used to transmit u λ1 c The frozen channel set is used to identify the location of the frozen channel of the second-level polarization coding, G N / 2，2 (λ 2 c ) represents G N / 2，2 The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit u λ1 c The frozen channel set λ 2 c The encoding corresponds to

[0033] x 1，1 N is the output symbol set of the first-level polar coding with length N,

[0034] u 1，1 N is the first-level polar coding symbol sequence to be encoded with a length of N, u 1，1 N =(u λ1 1 ,u λ1 2 ,u λ1 c ),u λ1 1 is the first set of information symbols to be encoded in the first level polar coding, u λ1 c is the set of frozen codewords to be encoded for the first level polar coding, u λ1 2 is the second information symbol set to be encoded of the first level polarization coding, and is also the output symbol set of the second level polarization coding.

[0035] λ 1 1 Indicates that it is used to transmit u λ1 1The first information channel set G is used to identify the position of each first information channel of the first level polarization coding, N，1 (λ 1 1 ) is the generator matrix G with a coding length of N from the first-level polar coding N，1 The third submatrix composed of the rows selected from λ1 1 The first information channel set λ 1 1 The encoding corresponds to

[0036] λ 1 2 Indicates that it is used to transmit u λ1 2 The second information channel set G is used to identify the position of each second information channel of the first level polarization coding, N，1 (λ 1 2 ) is generated from the matrix G N，1 The fourth submatrix composed of the rows selected from the third submatrix is ​​used to transmit u λ1 2 The second information channel set λ 1 2 The encoding corresponds to

[0037] λ 1 c Indicates that it is used to transmit u λ1 c The frozen channel set is used to identify the location of the frozen channel of the first level polarization coding, G N，1 (λ 1 c ) represents G N，1 The fifth submatrix remaining in addition to the third submatrix and the fourth submatrix is ​​used to transmit u λ1 c The frozen channel set λ 1 c The encoding corresponds.

[0038] In some embodiments, three-level polarization coding is performed in the order of third-level polarization coding, second-level polarization coding, and first-level polarization coding, including:

[0039] For the third level polarization coding, according to the coding formula Encoding;

[0040] For the second level polarization coding, according to the coding formula Encoding;

[0041] For the first level polarization coding, according to the coding formula Encoding;

[0042] in:

[0043] represents the XOR operation,

[0044] x 1，3 N / 4 is the output symbol set of the third-level polar coding with length N / 4,

[0045] u 1，3 N / 4 is the codeword sequence to be encoded of the third-level polar coding with a length of N / 4, u 1，3 N / 4 =(u λ3 ,u λ3 c ),u λ3 is the set of information symbols to be encoded for the third-level polarization coding, u λ3 c is the set of frozen codewords to be encoded for the third-level polar coding,

[0046] λ 3 Indicates that it is used to transmit u λ3 The information channel set is used to identify the location of the third-level polarization coded information channel, G N / 4，3 (λ 3 ) is the generator matrix G with a coding length of N / 4 from the third-level polar coding N / 4，3 The first submatrix composed of the rows selected from λ3 The information channel set λ 3 The encoding corresponds to

[0047] λ 3 c Indicates that it is used to transmit u λ3 c The frozen channel set is used to identify the location of the frozen channel of the third-level polarization coding, G N / 4，3 (λ 3 c )express 4 G N / 4，3 The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit u λ3 c The frozen channel set λ 3 c The encoding corresponds to

[0048] x 1，2 N / 2 is the output symbol set of the second-level polar coding with length N / 2,

[0049] u 1，2 N / 2 is the codeword sequence to be encoded of the second-level polar coding with a length of N / 2, u 1，2 N / 2 =(u λ2 1 ,u λ2 2 ,u λ2 c ),u λ2 1 is the first set of information symbols to be encoded for the second-level polarization coding, u λ2 c is the set of frozen codewords to be encoded for the second-level polar coding, u λ2 2 is the second information symbol set to be encoded of the second level polarization coding, and is also the output symbol set of the third level polarization coding.

[0050] λ 2 1 Indicates that it is used to transmit u λ2 1 The first information channel set G is used to identify the position of each first information channel of the second-level polarization coding, N / 2，2 (λ 2 1 ) is the generator matrix G with a coding length of N / 2 from the second-level polar coding N / 2，2 The third submatrix composed of the rows selected from λ2 1 The first information channel set λ 2 1 The encoding corresponds to

[0051] λ 2 2 Indicates that it is used to transmit u λ2 2 The second information channel set G is used to identify the position of each second information channel of the second level polarization coding. N / 2，1 (λ 2 2 ) is generated from the matrix G N / 2，2 The fourth submatrix composed of the rows selected from the third submatrix is ​​used to transmit u λ2 2 The second information channel set λ 2 2 The encoding corresponds to

[0052] λ 2 c Indicates that it is used to transmit u λ2 cThe frozen channel set is used to identify the location of the frozen channel of the second-level polarization coding, G N / 2，2 (λ 2 c ) represents G N / 2，2 The fifth submatrix remaining in addition to the third submatrix and the fourth submatrix is ​​used to transmit u λ2 c The frozen channel set λ 2 c The encoding corresponds to

[0053] x 1，1 N is the output symbol set of the first-level polar coding with length N,

[0054] u 1，1 N is the first-level polar coding symbol sequence to be encoded with a length of N, u 1，1 N =(u λ1 1 ,u λ1 2 ,u λ1 c ),u λ1 1 is the first set of information symbols to be encoded in the first level polar coding, u λ1 c is the set of frozen codewords to be encoded for the first level polar coding, u λ1 2 is the second information symbol set to be encoded of the first level polarization coding, and is also the output symbol set of the second level polarization coding.

[0055] λ 1 1 Indicates that it is used to transmit u λ1 1 The first information channel set G is used to identify the position of each first information channel of the first level polarization coding, N，1 (λ 1 1 ) is the generator matrix G with a coding length of N from the first-level polar coding N，1 The sixth submatrix composed of the rows selected from λ1 1 The first information channel set λ 1 1 The encoding corresponds to

[0056] λ 1 2 Indicates that it is used to transmit u λ1 2The second information channel set G is used to identify the position of each second information channel of the first level polarization coding, N，1 (λ 1 2 ) is generated from the matrix G N，1 The seventh submatrix composed of the rows selected from the sixth submatrix is ​​used to transmit u λ1 2 The second information channel set λ 1 2 The encoding corresponds to

[0057] λ 1 c Indicates that it is used to transmit u λ1 c The frozen channel set is used to identify the location of the frozen channel of the first level polarization coding, G N，1 (λ 1 c ) represents G N，1 The remaining eighth submatrix except the sixth and seventh submatrices is used to transmit u λ1 c The frozen channel set λ 1 c The encoding corresponds.

[0058] In some embodiments, the second information symbol set to be encoded of the i-th level polar coding is The codeword sequence to be encoded at the i-th level polar coding In the front position.

[0059] Some embodiments of the present disclosure provide a polar code decoding method for the aforementioned polar code encoding method, including:

[0060] In order from the 1st level polarization coding to the nth level polarization coding, the received codeword sequence is subjected to n-level polarization decoding, and the codeword sequence corresponding to the (j+1)th level polarization coding in the output of the jth level polarization decoding is used as the input of the (j+1)th level polarization decoding, where n is a positive integer greater than 1, and j is a positive integer from 1 to (n-1).

[0061] In some embodiments, the continuous elimination SC decoding algorithm is used to perform each level of polarization decoding, and the decoding length of the j-th level polarization decoding is The decoding length of the last level n polarization decoding is

[0062] Some embodiments of the present disclosure provide a polar code encoding device, including:

[0063] Memory; and

[0064] A processor coupled to the memory, wherein the processor is configured to execute a polar code encoding method based on instructions stored in the memory.

[0065] Some embodiments of the present disclosure provide a polar code decoding device, including:

[0066] Memory; and

[0067] A processor is coupled to the memory, and the processor is configured to execute a polar code decoding method based on instructions stored in the memory.

[0068] Some embodiments of the present disclosure provide a polar code encoding device, including: n-stage polarization encoders cascaded in order from an n-th stage polarization encoder to a first-stage polarization encoder, where n is a positive integer greater than 1.

[0069] Some embodiments of the present disclosure provide a polar code decoding device for a polar code encoding device, including: n-level polarization decoders cascaded in order from a first-level polarization decoder to an n-level polarization decoder, and a symbol sequence corresponding to a (j+1)-level polarization code in an output of a j-level polarization decoder is used as an input of a (j+1)-level polarization decoder.

[0070] Some embodiments of the present disclosure provide a polar code encoding and decoding system, including: a polar code encoding device; and a polar code decoding device.

[0071] Some embodiments of the present disclosure provide a non-transitory computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, the steps of the polar code encoding / decoding method are implemented. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] The following is a brief introduction to the drawings required for use in the embodiments or related technical descriptions. The present disclosure can be more clearly understood according to the following detailed description with reference to the drawings.

[0073] Obviously, the drawings described below are only some embodiments of the present disclosure, and a person skilled in the art can obtain other drawings based on these drawings without creative work.

[0074] Figure 1a It is a schematic diagram of the distribution of polarization channel positions and channel symmetric capacity (set as I(W)).

[0075] Figure 1b It is a diagram showing the relationship between the logarithm of the code length and the proportion of channels with symmetric capacity within the range of 0.05-0.95.

[0076] Figure 2 A schematic diagram showing the principles of polar code encoding methods according to some embodiments of the present disclosure is shown.

[0077] Figure 3 A schematic diagram showing the principles of a polar code decoding method according to some embodiments of the present disclosure is shown.

[0078] Figure 4a A schematic diagram showing a polar code encoding device according to some embodiments of the present disclosure.

[0079] Figure 4b A schematic diagram showing a polar code encoding device according to some embodiments of the present disclosure.

[0080] Figure 5a A schematic diagram showing a polar code decoding device according to some embodiments of the present disclosure.

[0081] Figure 5b A schematic diagram showing a polar code decoding device according to some embodiments of the present disclosure.

[0082] Figure 6 A schematic diagram showing a polar code encoding and decoding system according to some embodiments of the present disclosure is shown. DETAILED DESCRIPTION

[0083] The technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure.

[0084] Unless otherwise specified, descriptions such as “first” and “second” in the present disclosure are used to distinguish different objects and are not used to indicate meanings such as size or time sequence.

[0085] As mentioned above, for the traditional first-level polarization coding, the polarization coding formula is: Among them, x 1 N Represents the use of the generator matrix G N Treat the set of encoding symbols u 1 N The polar code with length N is obtained through polarization coding, u λ represents the set of information symbols to be encoded, u λ c represents the set of frozen code elements to be encoded, λ represents the set of information channels, which is used to identify the position of each information channel; G N (λ) is the generator matrix G N The first submatrix composed of the rows selected from λ corresponds to the information channel coding used to transmit the information symbol set to be encoded; c represents the frozen channel set used to transmit the frozen codeword set to be encoded, and is used to identify the position of each frozen channel; GN(λ c ) represents the generator matrix G NThe second submatrix remaining except the first submatrix corresponds to the frozen channel coding used to transmit the frozen symbol set to be coded. If a channels with the largest channel capacity are used as information channels and p channels with the smallest information capacity are used as frozen channels, a+p=N, and the coding rate r=a / N.

[0086] Generate Matrix Among them B N is the inverse order transformation matrix, is the n-th order Kronecker matrix multiplication of the F matrix.

[0087]

[0088] According to the relationship between channel capacities, channels with larger capacities are used as information channels, and channels with smaller capacities are used as frozen channels. Therefore, information channels are figuratively called "good channels" and frozen channels are figuratively called "bad channels."

[0089] The multi-level polarization coding method proposed in the embodiment of the present disclosure includes: performing n-level polarization coding in an order from n-th level polarization coding to 1st level polarization coding (that is, coding sequence), where n is a positive integer greater than 1.

[0090] In some embodiments, performing n-level polarization coding includes: according to the coding sequence, using the output of the previous level polarization coding as the input of the next level polarization coding.

[0091] In some embodiments, performing n-level polarization coding includes: according to the coding sequence, using the output of the previous level polarization coding as the input of the information codeword of the next level polarization coding.

[0092] In some embodiments, performing n-level polarization encoding includes:

[0093] For the nth level polarization coding, according to the coding formula Encoding;

[0094] For the i-th level polarization coding, i is a positive integer from (n-1) to 1. According to the coding formula Encoding;

[0095] in:

[0096] represents the XOR operation,

[0097] The length is The output symbol set of the nth level polarization coding, N is the length of the polarization code to be output after multi-level polarization coding,

[0098] The length is The n-th level polar coding symbol sequence to be encoded, u λn is the set of information symbols to be encoded for the nth level polarization coding, is the set of frozen code elements to be encoded for the nth level polarization coding,

[0099] λ n Indicates that it is used to transmit u λn The information channel set is used to identify the location of the information channel of the nth level polarization coding. The code length from the nth level polarization code is The generator matrix The first submatrix composed of the rows selected from λn The information channel set λ n The encoding corresponds to

[0100] Indicates that it is used to transmit The frozen channel set is used to identify the position of the frozen channel of the nth level polarization coding. express The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit The set of frozen channels The encoding corresponds to

[0101] The length is The output symbol set of the i-th level polar coding,

[0102] The length is The i-th level polar coding symbol sequence to be encoded, is the first set of information symbols to be encoded for the i-th level polar coding, is the set of frozen codewords to be encoded for the i-th level polar coding, is the second set of information symbols to be encoded for the i-th level polarization coding, and is also the output symbol set for the (i+1)-th level polarization coding.

[0103] Indicates that it is used to transmit A set of first information channels is used to identify the positions of the first information channels of the i-th level polarization coding, The code length from the i-th level polarization code is The generator matrix The third sub-matrix composed of the rows selected from The first information channel set The encoding corresponds to

[0104] Indicates that it is used to transmit A set of second information channels of the i-th level polarization coding is used to identify the position of each second information channel of the i-th level polarization coding, is generated from the matrix The fourth sub-matrix composed of the rows selected from the third sub-matrix is ​​used to transmit The second information channel set The encoding corresponds to

[0105] Indicates that it is used to transmit The frozen channel set is used to identify the position of the frozen channel of the i-th level polarization coding. express The fifth sub-matrix remaining in addition to the third sub-matrix and the fourth sub-matrix is ​​used to transmit The set of frozen channels The encoding corresponds.

[0106] The second set of information symbols to be encoded for the i-th level polar coding (i.e., the output symbol set of the (i+1)th level polar coding) The symbol sequence to be encoded at the i-th level polar coding In order to shorten the waiting time of the next level of decoding during decoding.

[0107] With respect to the multi-level polar code encoding method, the multi-level polar code decoding method proposed in the embodiment of the present disclosure includes: performing n-level polarization decoding on a received codeword sequence in an order from the first level polarization coding to the n-th level polarization coding, and using a codeword sequence corresponding to the (j+1)-th level polarization coding in an output of the j-th level polarization decoding as an input of the (j+1)-th level polarization decoding, where n is a positive integer greater than 1, and j is a positive integer from 1 to (n-1).

[0108] The SC (successive-cancellation) decoding algorithm is used to perform polarization decoding at each level, and the decoding length of the j-th level polarization decoding is The decoding length of the last level n polarization decoding is

[0109] The following uses two-level polarization code encoding and three-level polarization code encoding as examples to illustrate the multi-level polarization encoding method. Those skilled in the art can understand that, by analogy, more levels of polarization encoding can be performed as needed, which will not be exhaustively listed here.

[0110] Figure 2 A schematic diagram showing the principles of a two-level polar code encoding method according to some embodiments of the present disclosure is shown.

[0111] like Figure 2 As shown, the two-level polarization code encoding method includes: performing two-level polarization encoding in the order from the second level polarization encoding to the first level polarization encoding, including:

[0112] For the second level polarization coding, according to the coding formula Encoding;

[0113] For the first level polarization coding, according to the coding formula Encoding;

[0114] in:

[0115] represents the XOR operation,

[0116] x 1，2 N / 2 is the output symbol set of the second-level polar coding with length N / 2,

[0117] u 1，2 N / 2 is the codeword sequence to be encoded of the second-level polar coding with a length of N / 2, u 1，2 N / 2 =(u λ2 ,u λ2 c ),u λ2 is the set of information symbols to be encoded for the second-level polarization coding, u λ2 c is the set of frozen code elements to be encoded for the second-level polar coding, usually all 0s.

[0118] λ 2 Indicates that it is used to transmit u λ2 The information channel set is used to identify the location of the second-level polarization coded information channel, G N / 2，2 (λ 2 ) is the generator matrix G with a coding length of N / 2 from the second-level polar coding N / 2，2 The first submatrix composed of the rows selected from λ2 The information channel set λ 2 The encoding corresponds to

[0119] λ 2 c Indicates that it is used to transmit u λ1 c The frozen channel set is used to identify the location of the frozen channel of the second-level polarization coding, G N / 2，2 (λ 2 c ) represents G N / 2，2The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit u λ1 c The frozen channel set λ 2 c The encoding corresponds to

[0120] x 1，1 N is the output symbol set of the first-level polar coding with length N,

[0121] u 1，1 N is the first-level polar coding symbol sequence to be encoded with a length of N, u 1，1 N =(u λ1 1 ,u λ1 2 ,u λ1 c ),u λ1 1 is the first set of information symbols to be encoded in the first level polar coding, u λ1 c is the set of frozen code elements to be encoded for the first level polar coding, usually all 0, u λ1 2 is the second information symbol set to be encoded of the first level polarization coding, and is also the output symbol set of the second level polarization coding.

[0122] λ 1 1 Indicates that it is used to transmit u λ1 1 The first information channel set G is used to identify the position of each first information channel of the first level polarization coding, N，1 (λ 1 1 ) is the generator matrix G with a coding length of N from the first-level polar coding N，1 The third submatrix composed of the rows selected from λ1 1 The first information channel set λ 1 1 The encoding corresponds to

[0123] λ 1 2 Indicates that it is used to transmit u λ1 2 The second information channel set G is used to identify the position of each second information channel of the first level polarization coding, N，1 (λ 1 2 ) is generated from the matrix G N，1The fourth submatrix composed of the rows selected from the third submatrix is ​​used to transmit u λ1 2 The second information channel set λ 1 2 The encoding corresponds to

[0124] λ 1 c Indicates that it is used to transmit u λ1 c The frozen channel set is used to identify the location of the frozen channel of the first level polarization coding, G N，1 (λ 1 c ) represents G N，1 The fifth submatrix remaining in addition to the third submatrix and the fourth submatrix is ​​used to transmit u λ1 c The frozen channel set λ 1 c The encoding corresponds.

[0125] If a 1 The channel with the largest channel capacity is u λ1 channel, and p 1 The channel with the smallest channel capacity is u λ1 c The channel, a 1 +p 1 =N / 2, in the remaining channels, a 2 The channel with the largest channel capacity is u λ2 channel, and p 2 The channel with the smallest channel capacity is u λ2 c The channel, a 2 +p 2 =N / 2, then the coding rate of the two-level polar code is r=(a 1 +a 2 ) / N.

[0126] like Figure 2 As shown, the transmitter uses a two-stage polarization code encoding method to obtain N polarization code elements x 1，1 -x N，1 The polar code (denoted as x 1，1 N ), each polar code symbol is transmitted through the physical channel W to the receiving end, and the receiving end receives N receiving code symbols Y 1 -Y N The received codeword sequence (denoted as Y 1 N ).

[0127] Figure 3A schematic diagram showing the principles of a two-level polar code decoding method according to some embodiments of the present disclosure.

[0128] like Figure 3 As shown, for the two-level polar code encoding method, the two-level polar code decoding method of this embodiment includes: performing two-level polarization decoding on the received codeword sequence in an order from the first level polarization coding to the second level polarization coding, and the SC decoding algorithm can be used to perform each level of polarization decoding.

[0129] Specifically, the received symbol sequence is used as the input of the first-level polarization decoding, and is subjected to the first-level polarization decoding by the SC decoder with a decoding length of N to obtain the output of the first-level polarization decoding (including u^ λ1 1 、u~ λ1 2 ,u^ λ1 c ); the symbol sequence corresponding to the second-level polarization coding in the output of the first-level polarization decoding (i.e., u~ λ1 2 , including u~ λ2 and u~ λ2 c ) is used as the input of the second-level polarization decoding, and is subjected to the second-level polarization decoding by the SC decoder with a decoding length of N / 2 to obtain the output of the second-level polarization decoding (including u^ λ2 ,u^ λ2 c ).

[0130] The following describes the three-level polar code encoding method.

[0131] The three-level polarization code encoding method includes: performing three-level polarization encoding in the order of third-level polarization encoding, second-level polarization encoding, and first-level polarization encoding, including:

[0132] For the third level polarization coding, according to the coding formula Encoding;

[0133] For the second level polarization coding, according to the coding formula Encoding;

[0134] For the first level polarization coding, according to the coding formula Encoding;

[0135] in:

[0136] represents the XOR operation,

[0137] x 1，3 N / 4is the output symbol set of the third-level polar coding with length N / 4,

[0138] u 1，3 N / 4 is the codeword sequence to be encoded of the third-level polar coding with a length of N / 4, u 1，3 N / 4 =(u λ3 ,u λ3 c ),u λ3 is the set of information symbols to be encoded for the third-level polarization coding, u λ3 c is the set of frozen code elements to be encoded for the third-level polarization coding, usually all 0s.

[0139] λ 3 Indicates that it is used to transmit u λ3 The information channel set is used to identify the location of the third-level polarization coded information channel, G N / 4，3 (λ 3 ) is the generator matrix G with a coding length of N / 4 from the third-level polar coding N / 4，3 The first submatrix composed of the rows selected from λ3 The information channel set λ 3 The encoding corresponds to

[0140] λ 3 c Indicates that it is used to transmit u λ3 c The frozen channel set is used to identify the location of the frozen channel of the third-level polarization coding, G N / 4，3 (λ 3 c )express 4 G N / 4，3 The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit u λ3 c The frozen channel set λ 3 c The encoding corresponds to

[0141] x 1，2 N / 2 is the output symbol set of the second-level polar coding with length N / 2,

[0142] u 1，2 N / 2 is the codeword sequence to be encoded of the second-level polar coding with a length of N / 2, u 1，2 N / 2 =(u λ2 1 ,u λ2 2 ,u λ2c ),u λ2 1 is the first set of information symbols to be encoded for the second-level polarization coding, u λ2 c is the set of frozen code elements to be encoded for the second-level polar coding, usually all 0, u λ2 2 is the second information symbol set to be encoded of the second level polarization coding, and is also the output symbol set of the third level polarization coding.

[0143] λ 2 1 Indicates that it is used to transmit u λ2 1 The first information channel set G is used to identify the position of each first information channel of the second-level polarization coding, N / 2，2 (λ 2 1 ) is the generator matrix G with a coding length of N / 2 from the second-level polar coding N / 2，2 The third submatrix composed of the rows selected from λ2 1 The first information channel set λ 2 1 The encoding corresponds to

[0144] λ 2 2 Indicates that it is used to transmit u λ2 2 The second information channel set G is used to identify the position of each second information channel of the second level polarization coding. N / 2，1 (λ 2 2 ) is generated from the matrix G N / 2，2 The fourth submatrix composed of the rows selected from the third submatrix is ​​used to transmit u λ2 2 The second information channel set λ 2 2 The encoding corresponds to

[0145] λ 2 c Indicates that it is used to transmit u λ2 c The frozen channel set is used to identify the location of the frozen channel of the second-level polarization coding, G N / 2，2 (λ 2 c ) represents G N / 2，2 The fifth submatrix remaining in addition to the third submatrix and the fourth submatrix is ​​used to transmit u λ2 c The frozen channel set λ 2c The encoding corresponds to

[0146] x 1，1 N is the output symbol set of the first-level polar coding with length N,

[0147] u 1，1 N is the first-level polar coding symbol sequence to be encoded with a length of N, u 1，1 N =(u λ1 1 ,u λ1 2 ,u λ1 c ),u λ1 1 is the first set of information symbols to be encoded in the first level polar coding, u λ1 c is the set of frozen code elements to be encoded for the first level polar coding, usually all 0, u λ1 2 is the second information symbol set to be encoded of the first level polarization coding, and is also the output symbol set of the second level polarization coding.

[0148] λ 1 1 Indicates that it is used to transmit u λ1 1 The first information channel set G is used to identify the position of each first information channel of the first level polarization coding, N，1 (λ 1 1 ) is the generator matrix G with a coding length of N from the first-level polar coding N，1 The sixth submatrix composed of the rows selected from λ1 1 The first information channel set λ 1 1 The encoding corresponds to

[0149] λ 1 2 Indicates that it is used to transmit u λ1 2 The second information channel set G is used to identify the position of each second information channel of the first level polarization coding, N，1 (λ 1 2 ) is generated from the matrix G N，1 The seventh submatrix composed of the rows selected from the sixth submatrix is ​​used to transmit u λ1 2 The second information channel set λ 12 The encoding corresponds to

[0150] λ 1 c Indicates that it is used to transmit u λ1 c The frozen channel set is used to identify the location of the frozen channel of the first level polarization coding, G N，1 (λ 1 c ) represents G N，1 The remaining eighth submatrix except the sixth and seventh submatrices is used to transmit u λ1 c The frozen channel set λ 1 c The encoding corresponds.

[0151] If a 1 The channel with the largest channel capacity is u λ1 1 channel, and p 1 The channel with the smallest information capacity is u λ1 c The channel, a 1 +p 1 =N / 2, in the remaining channels, a 2 The channel with the largest channel capacity is u λ2 1 channel, and p 2 The channel with the smallest information capacity is u λ2 c The channel, a 2 +p 2 =N / 4, in the remaining channels, a 3 The channel with the largest channel capacity is u λ3 channel, and p 3 The channel with the smallest information capacity is u λ3 c The channel, a 3 +p 3 =N / 4, the coding rate of the three-level coding is r=(a 1 +a 2 +a 3 ) / N.

[0152] With respect to the three-level polarization code encoding method, the three-level polarization code decoding method of this embodiment includes: performing three-level polarization decoding on a received codeword sequence in the order of first-level polarization coding, second-level polarization coding, and third-level polarization coding, and an SC decoding algorithm may be used to perform polarization decoding of each level.

[0153] Specifically, the received symbol sequence is used as the input of the first-level polarization decoding, and is subjected to the first-level polarization decoding by the SC decoder with a decoding length of N to obtain the output of the first-level polarization decoding (including u^ λ1 1 、u~ λ1 2 ,u^ λ1 c ); the symbol sequence corresponding to the second-level polarization coding in the output of the first-level polarization decoding (i.e., u~ λ1 2 ) is used as the input of the second-level polarization decoding, and the second-level polarization decoding is performed by the SC decoder with a decoding length of N / 2 to obtain the output of the second-level polarization decoding (including u~ λ2 1 ,u^ λ2 2 、u~ λ2 c ), the symbol sequence corresponding to the third-level polarization coding in the output of the second-level polarization decoding (i.e., u^ λ2 2 ) is used as the input of the third-level polarization decoding, and is subjected to the third-level polarization decoding by the SC decoder with a decoding length of N / 4 to obtain the output of the third-level polarization decoding (including u~ λ3 、u~ λ3 c ).

[0154] The generator matrix of the multi-level polarization coding in each of the above embodiments, such as G N，1 , G N / 2，2 , G N / 4，3 ,... Its matrix form can refer to G N The polarization coding generator matrix enables as many channels with relatively large capacities as possible to have their capacities increased after polarization coding, and as many channels with relatively small capacities as possible to have their capacities reduced after polarization coding. For example, the generator matrix that meets the requirements may be obtained by enumeration and experimentation.

[0155] Figure 4a A schematic diagram showing a polar code encoding device according to some embodiments of the present disclosure.

[0156] like Figure 4a As shown, the polar code encoding device 400 includes: a memory 410; and a processor 420 coupled to the memory, wherein the processor is configured to execute the polar code encoding method of each embodiment based on instructions stored in the memory.

[0157] Figure 4b A schematic diagram showing a polar code encoding device according to some embodiments of the present disclosure.

[0158] like Figure 4b As shown, the polar code encoding apparatus 400 includes: n-stage polarization encoders cascaded in order from the n-th stage polarization encoder to the first-stage polarization encoder.

[0159] In some embodiments, the output of the previous polarization encoder serves as the input of the next polarization encoder.

[0160] In some embodiments, the output of the previous polarization encoder is used as the input of the information symbol of the next polarization encoder. That is, the output symbol set of the previous polarization encoder is used as the second information symbol set to be encoded of the next polarization encoder, and together with the first information symbol set to be encoded and the frozen symbol set to be encoded of the next polarization encoder, they are used as the input symbol set of the next polarization encoder.

[0161] In some embodiments, the n-th level polarization encoder performs the n-th level polarization encoding of the aforementioned embodiment, and the i-th level polarization encoder performs the i-th level polarization encoding of the aforementioned embodiment, where n is a positive integer greater than 1, and i is a positive integer from (n-1) to 1.

[0162] The code length of the n-th level polar encoder is The code length of the i-th level polar encoder is

[0163] Figure 5a A schematic diagram showing a polar code decoding device according to some embodiments of the present disclosure.

[0164] like Figure 5a As shown, the polar code decoding device 500 includes: a memory 510; and a processor 520 coupled to the memory, wherein the processor is configured to execute the polar code decoding method of each embodiment based on the instructions stored in the memory.

[0165] Figure 5b A schematic diagram showing a polar code decoding device according to some embodiments of the present disclosure.

[0166] like Figure 5b As shown, the polar code decoding device 500 includes: n-stage polarization decoders cascaded in order from the first-stage polarization decoder to the n-stage polarization decoder, and the codeword sequence corresponding to the (j+1)-stage polarization code in the output of the j-stage polarization decoder is used as the input of the (j+1)-stage polarization decoder.

[0167] In some embodiments, the decoding length of the j-th polar decoder is The decoding length of the last level n polarization decoding is n is a positive integer greater than 1, and j is a positive integer from 1 to (n-1).

[0168] Figure 6 A schematic diagram showing a polar code encoding and decoding system according to some embodiments of the present disclosure is shown.

[0169] like Figure 6 As shown, the polar code encoding and decoding system 600 includes: a polar code encoding device 400; and a polar code decoding device 500.

[0170] Some embodiments of the present disclosure provide a non-transitory computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, the steps of the polar code encoding / decoding method are implemented.

[0171] The memory 410, 510 may include, for example, a system memory, a fixed non-volatile storage medium, etc. The system memory may store, for example, an operating system, an application program, a boot loader, and other programs.

[0172] Those skilled in the art will appreciate that the embodiments of the present disclosure may be provided as methods, systems, or computer program products. Therefore, the present disclosure may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present disclosure may take the form of a computer program product implemented on one or more non-transient computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer program code.

[0173] The present disclosure is described with reference to the flowchart and / or block diagram of the method, device (system), and computer program product according to the embodiment of the present disclosure. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the process and / or box in the flowchart and / or block diagram can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device for implementing the functions specified in one process or multiple processes in the flowchart and / or one box or multiple boxes in the block diagram.

[0174] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction device that implements the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0175] These computer program instructions may also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one or more processes in the flowchart and / or one or more boxes in the block diagram.

[0176] The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present disclosure should be included in the protection scope of the present disclosure.

Claims

1. A polar code encoding method, characterized in that: include: The n-level polarization coding is performed in the order from the n-th level polarization coding to the 1-th level polarization coding, where n is a positive integer greater than 1, including: For the nth level polarization coding, according to the coding formula Encoding; For the i-th level polarization coding, i is a positive integer from (n-1) to 1. According to the coding formula Encoding; in: ⊕ represents the XOR operation, The length is The output symbol set of the nth level polar coding, The length is The nth level polarization coded symbol sequence to be coded, u λn is the set of information symbols to be encoded for the nth level polarization coding, is the set of frozen code elements to be encoded for the nth level polarization coding, λ n Indicates that it is used to transmit u λn The information channel set is used to identify the location of the information channel of the nth level polarization coding. The code length from the nth level polarization code is The generator matrix The first submatrix composed of the rows selected from λn The information channel set λ n The encoding corresponds to Indicates that it is used to transmit The frozen channel set is used to identify the position of the frozen channel of the nth level polarization coding. express The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit The set of frozen channels The encoding corresponds to The length is The output symbol set of the i-th level polar coding, The length is The i-th level polar coding symbol sequence to be encoded, is the first set of information symbols to be encoded for the i-th level polar coding, is the set of frozen codewords to be encoded for the i-th level polar coding, is the second set of information symbols to be encoded for the i-th level polarization coding, and is also the output symbol set for the (i+1)-th level polarization coding. Indicates that it is used to transmit A set of first information channels is used to identify the positions of the first information channels of the i-th level polarization coding, The code length from the i-th level polarization code is The generator matrix The third sub-matrix composed of the rows selected from The first information channel set The encoding corresponds to Indicates that it is used to transmit A set of second information channels of the i-th level polarization coding is used to identify the position of each second information channel of the i-th level polarization coding, is generated from the matrix The fourth sub-matrix composed of the rows selected from the third sub-matrix is ​​used to transmit The second information channel set The encoding corresponds to Indicates that it is used to transmit The frozen channel set is used to identify the position of the frozen channel of the i-th level polarization coding. express The fifth sub-matrix remaining in addition to the third sub-matrix and the fourth sub-matrix is ​​used to transmit The set of frozen channels The encoding corresponds.

2. The method according to claim 1, characterized in that Two-level polarization coding is performed in the order from the second-level polarization coding to the first-level polarization coding, including: For the second level polarization coding, according to the coding formula x 1,2 N / 2 =u 1,2 N / 2 G N / 2,2 =u λ2 G N / 2,2 (λ2)⊕u λ2 c G N / 2,2 (λ2 c ) for encoding; For the first level polarization coding, according to the coding formula x 1,1 N =u 1,1 N G N,1 =u λ1 1 G N,1 (λ1 1 )⊕u λ1 2 G N,1 (λ1 2 )⊕u λ 1 c G N,1 ( λ1 c ) for encoding; in: ⊕ represents the XOR operation, x 1,2 N / 2 is the output symbol set of the second-level polar coding with length N / 2, u 1,2 N / 2 is the codeword sequence to be encoded of the second-level polar coding with a length of N / 2, u 1,2 N / 2 =(u λ2 ,u λ2 c ),u λ2 is the set of information symbols to be encoded for the second-level polarization coding, u λ2 c is the set of frozen codewords to be encoded for the second-level polar coding, λ2 Indicates that it is used to transmit u λ2 The information channel set is used to identify the location of the second-level polarization coded information channel, G N / 2,2 (λ2) is the generator matrix G with a code length of N / 2 from the second-level polar coding N / 2,2 The first submatrix composed of the rows selected from λ2 The information channel set λ2 The encoding corresponds to λ2 c Indicates that it is used to transmit u λ1 c The frozen channel set is used to identify the location of the frozen channel of the second-level polarization coding, G N / 2,2 (λ2 c ) represents G N / 2,2 The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit u λ1 c The frozen channel set λ2 c The encoding corresponds to x 1,1 N is the output symbol set of the first-level polar coding with length N, u 1,1 N is the first-level polar coding symbol sequence to be encoded with a length of N, u 1,1 N =(u λ1 1 ,u λ1 2 ,u λ1 c ),u λ1 1 is the first set of information symbols to be encoded in the first level polar coding, u λ1 c is the set of frozen codewords to be encoded for the first level polar coding, u λ1 2 is the second information symbol set to be encoded of the first level polarization coding, and is also the output symbol set of the second level polarization coding. λ1 1 Indicates that it is used to transmit u λ1 1 The first information channel set G is used to identify the position of each first information channel of the first level polarization coding, N,1 (λ1 1 ) is the generator matrix G with a coding length of N from the first-level polar coding N,1 The third submatrix composed of the rows selected from λ1 1 The first information channel set λ1 1 The encoding corresponds to λ1 2 Indicates that it is used to transmit u λ1 2 The second information channel set G is used to identify the position of each second information channel of the first level polarization coding, N,1 (λ1 2 ) is generated from the matrix G N,1 The fourth submatrix composed of the rows selected from the third submatrix is ​​used to transmit u λ1 2 The second information channel set λ1 2 The encoding corresponds to λ1 c Indicates that it is used to transmit u λ1 c The frozen channel set is used to identify the location of the frozen channel of the first level polarization coding, G N,1 ( λ1 c ) represents G N,1 The fifth submatrix remaining in addition to the third submatrix and the fourth submatrix is ​​used to transmit u λ1 c The set of frozen channels λ1 c The encoding corresponds.

3. The method according to claim 1, characterized in that The three-level polarization coding is performed in the order of the third-level polarization coding, the second-level polarization coding, and the first-level polarization coding, including: For the third level polarization coding, according to the coding formula x 1,3 N / 4 =u 1,3 N / 4 G N / 4,3 =u λ3 G N / 4,3 (λ3)⊕u λ3 c G N / 4,3 (λ3 c ) for encoding; For the second level polarization coding, according to the coding formula x 1,2 N / 2 =u 1,2 N / 2 G N / 2,2 =u λ2 1 G N / 2,2 (λ2 1 )⊕u λ2 2 G N / 2,1 (λ2 2 )⊕u λ2 c G N / 2,2 (λ2 c ) for encoding; For the first level polarization coding, according to the coding formula x 1,1 N =u 1,1 N G N,1 =u λ1 1 G N,1 (λ1 1 )⊕u λ1 2 G N,1 (λ1 2 )⊕u λ 1 c G N,1 ( λ1 c ) for encoding; in: ⊕ represents the XOR operation, x 1,3 N / 4 is the output symbol set of the third-level polar coding with length N / 4, u 1,3 N / 4 is the codeword sequence to be encoded of the third-level polar coding with a length of N / 4, u 1,3 N / 4 =(u λ3 ,u λ3 c ),u λ3 is the set of information symbols to be encoded for the third-level polarization coding, u λ3 c is the set of frozen codewords to be encoded for the third-level polar coding, λ3 is used to transmit u λ3 The information channel set is used to identify the location of the third-level polarization coded information channel, G N / 4,3 (λ3) is the generator matrix G with a code length of N / 4 from the third-level polar coding N / 4,3 The first submatrix composed of the rows selected from λ3 The information channel set λ3 The encoding corresponds to λ3 c Indicates that it is used to transmit u λ3 c The frozen channel set is used to identify the location of the frozen channel of the third-level polarization coding, G N / 4,3 (λ3 c )express 4 G N / 4,3 The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit u λ3 c The frozen channel set λ3 c The encoding corresponds to x 1,2 N / 2 is the output symbol set of the second-level polar coding with length N / 2, u 1,2 N / 2 is the codeword sequence to be encoded of the second-level polar coding with a length of N / 2, u 1,2 N / 2 =(u λ2 1 ， u λ2 2 ,u λ2 c ),u λ2 1 is the first set of information symbols to be encoded for the second-level polarization coding, u λ2 c is the set of frozen codewords to be encoded for the second-level polar coding, u λ2 2 is the second information symbol set to be encoded of the second level polarization coding, and is also the output symbol set of the third level polarization coding. λ2 1 Indicates that it is used to transmit u λ2 1 The first information channel set G is used to identify the position of each first information channel of the second-level polarization coding, N / 2,2 (λ2 1 ) is the generator matrix G with a coding length of N / 2 from the second-level polar coding N / 2,2 The third submatrix composed of the rows selected from λ2 1 The first information channel set λ2 1 The encoding corresponds to λ2 2 Indicates that it is used to transmit u λ2 2 The second information channel set G is used to identify the position of each second information channel of the second level polarization coding. N / 2,1 (λ2 2 ) is generated from the matrix G N / 2,2 The fourth submatrix composed of the rows selected from the third submatrix is ​​used to transmit u λ2 2 The second information channel set λ2 2 The encoding corresponds to λ2 c Indicates that it is used to transmit u λ2 c The frozen channel set is used to identify the location of the frozen channel of the second-level polarization coding, G N / 2,2 (λ2 c ) represents G N / 2,2 The fifth submatrix remaining in addition to the third submatrix and the fourth submatrix is ​​used to transmit u λ2 c The frozen channel set λ2 c The encoding corresponds to x 1,1 N is the output symbol set of the first-level polar coding with length N, u 1,1 N is the first-level polar coding symbol sequence to be encoded with a length of N, u 1,1 N =(u λ1 1 ,u λ1 2 ,u λ1 c ),u λ1 1 is the first set of information symbols to be encoded in the first level polarization coding, u λ1 c is the set of frozen codewords to be encoded for the first level polar coding, u λ1 2 is the second information symbol set to be encoded of the first level polarization coding, and is also the output symbol set of the second level polarization coding. λ1 1 Indicates that it is used to transmit u λ1 1 The first information channel set G is used to identify the position of each first information channel of the first level polarization coding, N,1 (λ1 1 ) is the generator matrix G with a coding length of N from the first-level polar coding N,1 The sixth submatrix composed of the rows selected from λ1 1 The first information channel set λ1 1 The encoding corresponds to λ1 2 Indicates that it is used to transmit u λ1 2 The second information channel set G is used to identify the position of each second information channel of the first level polarization coding, N,1 (λ1 2 ) is generated from the matrix G N,1 The seventh submatrix composed of the rows selected from the sixth submatrix is ​​used to transmit u λ1 2 The second information channel set λ1 2 The encoding corresponds to λ1 c Indicates that it is used to transmit u λ1 c The frozen channel set is used to identify the location of the frozen channel of the first level polarization coding, G N,1 (λ1 c ) represents G N,1 The remaining eighth submatrix except the sixth and seventh submatrices is used to transmit u λ1 c The frozen channel set λ1 c The encoding corresponds.

4. The method according to claim 1, characterized in that The second set of information symbols to be encoded for the i-th level polar coding The codeword sequence to be encoded at the i-th level polar coding In the front position.

5. A polar code decoding method for the polar code encoding method of claim 1, characterized in that: include: In order from the 1st level polarization coding to the nth level polarization coding, the received codeword sequence is subjected to n-level polarization decoding, and the codeword sequence corresponding to the (j+1)th level polarization coding in the output of the jth level polarization decoding is used as the input of the (j+1)th level polarization decoding, where n is a positive integer greater than 1, and j is a positive integer from 1 to (n-1).

6. The method according to claim 5, characterized in that The continuous elimination SC decoding algorithm is used to perform polarization decoding at each level. The decoding length of the j-th level polarization decoding is The decoding length of the last level n polarization decoding is 7. A polar code encoding device, characterized in that: include: Memory; as well as A processor coupled to the memory, the processor being configured to execute the method of any one of claims 1-4 based on instructions stored in the memory.

8. A polar code decoding device, characterized in that: include: Memory; as well as A processor coupled to the memory, the processor being configured to execute the method of any one of claims 5-6 based on instructions stored in the memory.

9. A polar code encoding device, characterized in that: include: An n-stage polarization encoder is cascaded in the order from the n-th stage polarization encoder to the first stage polarization encoder, where n is a positive integer greater than 1. Among them, for the nth level polarization coding, according to the coding formula Encoding; For the i-th level polarization coding, i is a positive integer from (n-1) to 1. According to the coding formula Encoding; in: ⊕ represents the XOR operation, The length is The output symbol set of the nth level polar coding, The length is The nth level polarization coded symbol sequence to be coded, u λn is the set of information symbols to be encoded for the nth level polarization coding, is the set of frozen code elements to be encoded for the nth level polarization coding, λ n Indicates that it is used to transmit u λn The information channel set is used to identify the location of the information channel of the nth level polarization coding. The code length from the nth level polarization code is The generator matrix The first submatrix composed of the rows selected from λn The information channel set λ n The encoding corresponds to Indicates that it is used to transmit The frozen channel set is used to identify the position of the frozen channel of the nth level polarization coding. express The second sub-matrix remaining in addition to the first sub-matrix is ​​used to transmit The set of frozen channels The encoding corresponds to The length is The output symbol set of the i-th level polar coding, The length is The i-th level polar coding symbol sequence to be encoded, is the first set of information symbols to be encoded for the i-th level polar coding, is the set of frozen codewords to be encoded for the i-th level polar coding, is the second set of information symbols to be encoded for the i-th level polarization coding, and is also the output symbol set for the (i+1)-th level polarization coding. Indicates that it is used to transmit A set of first information channels is used to identify the positions of the first information channels of the i-th level polarization coding, The code length from the i-th level polarization code is The generator matrix The third sub-matrix composed of the rows selected from The first information channel set The encoding corresponds to Indicates that it is used to transmit A set of second information channels of the i-th level polarization coding is used to identify the position of each second information channel of the i-th level polarization coding, is generated from the matrix The fourth sub-matrix composed of the rows selected from the third sub-matrix is ​​used to transmit The second information channel set The encoding corresponds to Indicates that it is used to transmit The frozen channel set is used to identify the position of the frozen channel of the i-th level polarization coding. express The fifth sub-matrix remaining in addition to the third sub-matrix and the fourth sub-matrix is ​​used to transmit The set of frozen channels The encoding corresponds.

10. A polar code decoding device for the polar code encoding device of claim 9, characterized in that: include: The n-stage polarization decoders are cascaded in order from the 1st-stage polarization decoder to the nth-stage polarization decoder, and the symbol sequence corresponding to the (j+1)th-stage polarization code in the output of the j-th-stage polarization decoder is used as the input of the (j+1)th-stage polarization decoder.

11. A polar code encoding and decoding system, characterized in that: include: The polar code encoding device according to any one of claims 7 and 9; as well as The polar code decoding device according to any one of claims 8 and 10.

12. A non-transitory computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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