A multi-dimensional coupled zip code coding method based on generalized integrated interleaved code

Abstract

This invention discloses a multidimensional coupled chain code encoding method based on generalized integrated interleaving codes. It selects d-dimensional chain codes from s-dimensional chain codes for generalized integrated interleaving encoding, resulting in the l-th... i The code length of the wiry chain code is [value], and the information bit length is [value]. The remaining (s-d) wiry chain code is encoded, and the l′ [value] is [value]. i' Wirachain codes use linear block codes with a code length of and an information bit length of as the basic code, and the sequence c... (t) Initialize to an all-zero sequence; set the information sequence u Divide into sL groups. For the l-th dimensional zip code, divide into groups of length k. t,l -m t,l sequence u (t,l) With a length of m t,l sequence w (t,l) The data is fed into a multiplexer to obtain a length of k. t,l sequence a (t,l) The sequence is fed into a basic code encoder for encoding to obtain a codeword sequence. Simultaneously, the sequence is fed into a generalized integrated interleaved code encoder for encoding to obtain another codeword sequence. c (t,0) , c (t,1) ,…, c (t,s‑1) The encoded output sequence c at time t is obtained by feeding it into the multiplexer. (t) This invention has the advantages of simple coding, ease of implementation, and good performance.

Description

Technical Field

[0001] This invention relates to the fields of digital communication and digital storage technology, and specifically to a multidimensional coupled chain code encoding method based on generalized integrated interleaved codes. Background Technology

[0002] With the widespread deployment of fifth-generation (5G) wireless communication technology, academia and industry have begun discussing and researching sixth-generation (6G) wireless communication technology. It is foreseeable that a key characteristic of future cyberspace will be the interconnection of everything supporting ubiquitous intelligence. Consequently, both data transmission and data storage demands will increase significantly. High-reliability, low-latency, and high-capacity wireless communication links are the physical layer foundation for realizing ubiquitous intelligence. To construct such links, it is necessary to further enhance the transmission capacity of backbone fiber optic communication links. Channel coding technology is a key technology for achieving ultra-fast and ultra-reliable fiber optic communication. Due to significant differences in system characteristics, channel coding in wireless communication is not suitable for fiber optic communication systems. First, fiber optic communication lacks a feedback link, requiring its channel coding to have an extremely low bit error rate to reduce the number of system restarts. Second, the throughput of fiber optic communication is much higher than that of wireless communication, necessitating extremely low complexity in its channel coding.

[0003] Spatial coupled product codes combine the advantages of low implementation complexity of algebraic codes with strong error correction capabilities of spatially coupled codes. Therefore, spatially coupled product codes are highly competitive in high-speed optical fiber communication. In 2010, Canadian researchers BPSmith et al. disclosed a spatially coupled product code suitable for 100Gbps high-speed optical communication, called the Staircase code, in their paper "Staircase Codes: FEC for 100Gb / s OTN" (Journal of Lightwave Technology, vol. 30, no. 1, pp. 110-117, Jan. 1, 2012). To further improve the performance of Staircase codes, Alvin Y. Sukmadji et al. disclosed a spatially coupled product code called a zipper code in their 2019 paper, "Zipper Codes: Spatially-Coupled Product-Like Codes with Iterative Algebraic Decoding" (2019 16th Canadian Workshop on Information Theory (CWIT), Hamilton, ON, Canada, 2019). This code outperforms Staircase codes at higher code rates. Furthermore, it can be decoded in parallel, making it highly suitable for high-speed optical communication systems.

[0004] At low bit error rates, the performance of spatially coupled product codes is primarily influenced by the number of errors within the minimum uncorrectable error pattern and the number of such error patterns that may appear within the decoding window. For chained codes, performance can be improved by reducing the error plane of the chained code by raising the lower bound of the number of errors within the minimum uncorrectable error pattern. In 2017, Yingquan Wu disclosed a generalized integrated interleaved code in his paper "Generalized integrated interleaved codes" (IEEE Trans. Inf. Theory, vol. 63, no. 2, pp. 1102–1119, Feb. 2017). Combining this code with multidimensionally coupled chained codes can raise the lower bound of the number of errors within the uncorrectable error pattern, thereby improving the performance of the chained codes. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned deficiencies in the prior art by providing a multidimensional coupled chain code encoding method based on generalized integrated interleaved codes. This encoding method can improve the lower limit of the number of errors within the uncorrectable error pattern of the chain code, and achieves a lower bit error rate while maintaining comparable decoding capability and latency.

[0006] The objective of this invention can be achieved by adopting the following technical solutions:

[0007] A multidimensional coupled chain code encoding method based on generalized integrated interleaving codes is proposed. Given the interleaving dimension d and the number of interleaving codes v, the generalized integrated interleaving code is defined as follows at time t: Where v is an integer greater than 0, d is an integer greater than v, a is a primitive element or a primitive polynomial of a finite field, and c (t,i) For the i-th dimension subcodeword after generalized integrated interleaving coding, C represents the offset coefficients with primitives or primitive polynomials as the standard basis. t,0 It is a linear block code with the first layer of interleaving after generalized integrated interleaving coding. It is a linear block code with a second layer of interleaving after generalized integrated interleaving coding, and satisfies For a zip code, given the coding dimension s, coding memory depth M, number of coding layers L, and mapping period q, where s is an integer greater than or equal to d, and M, L, and q are integers greater than 0; given a time t in the range 0 ≤ t < L, then at time t, a d-dimensional zip code is selected from the s-dimensional zip codes for generalized integrated interleaving coding, and the selected dimensions are denoted as l0, l1, ..., l i ,…,l d-1 After generalized integrated interleaving coding, the lth i The code length of the Vela chain is Information bit length is Where, l i Let be the dimension index of the subcode after generalized integrated interleaving encoding, 0≤i≤d-1; then encode the remaining (sd)-dimensional chain code, with the selected dimensions denoted as l′0, l′1, ..., l′ i' ,…,l′ s-d-1 , among which, for the l′ i' VeraChaincode uses a code length of 1000. Information bit length is linear block code As a basic code, l′ i' Let i' be the dimension index of the codeword after linear block coding, 0 ≤ i' < sd, l' i' ∈{0,1,…,s-1}\{l1,l2,…,l d-1}, i.e., l′ i' For the set {l1,l2,…,l d-1 In the remainder set {0,1,…,s-1}, the codewords satisfy the following relationship:

[0008] The length is The information sequence u is divided into several sub-information sequence groups, and different sub-information sequence groups are encoded at each time step, where 0 ≤ l < s-1, m t,l m represents the length of the recoded symbols in the encoded input of the l-th dimensional zip code at time t. t,l greater than zero and less than k t,l The integer; at time t, first select d segments of sub-information sequence from the group and perform generalized integrated interleaving coding to obtain codewords. Next, the remaining sub-information sequence is encoded to obtain codewords. remember The codeword sequence generated at time t; T is the code truncation length, and the value of T is a positive integer; the encoding method includes the following steps:

[0009] S1. For times t = -1, -2, ..., -M, divide the length of... sequence c (t) Initialize as an all-zero sequence, where the length is (n t,l -m t,l ) sequence c (t,l) The output of the l-th dimensional zip code at time t; the length of Information sequence u Divided into sL groups u =( u (0,0) , u (0,1) ,…,u (0,s-1) , u (1,0) , u (1 ,1) ,…, u (1,s-1) ,…, u (L-1,0) , u (L-1,1) ,…, u (L-1,s-1) ), where grouping u (t,l) The length is k t,l -m t,l ;

[0010] S2. At time t = 0, 1, ..., L-1, for the l-th dimensional pull chain code, the length of k... t,l -m t,l sequence With a length of m t,l sequence w (t,l) Input to multiplexer M l The length is k. t,l sequence Among them, the recoded sequence w (t,l) satisfy Matrix P t,l For a row number of The number of columns is The matrix; the sequence Input basic code The encoder ENC'(t,l′) i′ Encode the result to obtain a length of Validation sequence Where 0 ≤ i' < sd; then multiple sequences Simultaneously, the code is fed into the encoder ENC(t,v) of the generalized integrated interleaved code for encoding to obtain the check sequence. in, After the generalized integrated interleaved code is encoded, c (t,0) , c (t,1) ,…, c (t,s-1) The encoded output at time t is obtained by feeding it into the multiplexer M. c (t) =( c (t,0) , c (t,1) ,…, c (t,s-1)),in, c (t,l) =( u (t,l) , p (t,l) );

[0011] S3. At times t = L, L+1, ..., L+T-1, the length is... All-zero sequence ( u (t,0) , u (t ,1) , ..., u (t,s-1) )= 0 As the input for encoding, step S2 is executed to obtain a length of Encoded output c (t) =( p (t ,0) , p (t,1) , ..., p (t,s-1) ), where for 0 ≤ l < s, u (t,l) The length is (k) t,l -m t,l A sequence of all zeros.

[0012] Furthermore, the encoding steps of the encoder ENC(t,v) of the generalized integrated interleaved code in step S2 are as follows:

[0013] S21, for the sequence Using linear block codes Encode and obtain the check sequence Where i = v, v+1, ..., d-1;

[0014] S221, For the remaining sequence Encode the sequence i = v-1, v-2, ..., 0, calculate the sequence Corresponding composite polynomial Where, r v-i For verification sequence The length of a i (x) is polynomial, c i+1 (x) is a sequence The polynomial, especially π. (i) (x) is given by the following formula:

[0015]

[0016] polynomial matrix Γ (i) (x) and the polynomial matrix Θ (i) (x) are as follows:

[0017]

[0018]

[0019] Among them, g v-i (x) is the basic code. The generating polynomial of α(x) is a primitive polynomial;

[0020] S222, the composite polynomial f i (x) before The multinomial coefficients are fed into the basic code as follows: The verification sequence is obtained from the encoder.

[0021] S223, the composite polynomial f i (x) after r v-i Multinomial coefficients and check sequence The check sequence is obtained by modulo 2 summation.

[0022] Furthermore, the information sequence u is a binary sequence or a sequence defined over a multivariate finite field. The information sequences belonging to different finite fields determine the encoder used for encoding the corresponding finite field.

[0023] Furthermore, the encoder ENC'(t,l') i The encoder ENC'(t,l′) is a linear block code encoder of any type. i′ The encoding steps are as follows: For the sequence... Using linear block codes Encode the code, where i' = 0, 1, ..., sd-1, for a linear block code. Given its generating matrix is will sequence With the generating matrix Multiply to get the code word Output verification sequence

[0024] Furthermore, the encoder ENC(t,v) is a generalized integrated interleaved code encoder. The encoder ENC(t,v) can operate in a binary domain or a multi-ary domain.

[0025] Furthermore, the multiplexer M lThe multiplexer M concatenates and combines short input sequences into a new long output sequence. The multiplexer can be of any type. Multiplexer M l The output is the information sequence to be encoded, and the output of the multiplexer M is the codeword sequence to be transmitted.

[0026] Furthermore, when u is a binary sequence, the matrix P t,l It is a binary matrix of any type; when u is a sequence defined on a multivariate finite field, the matrix P is... t,l It is a multivariate matrix of any type defined over a multivariate finite field. Matrix P t,l The coupling method of the zipper code is determined, and different coupling methods affect decoding performance, encoding latency, and other factors.

[0027] The present invention has the following advantages and effects compared with the prior art:

[0028] 1. The present invention proposes a multidimensional coupled chain code encoding method based on generalized integrated interleaved code, which has the advantages of simple encoding and flexible construction.

[0029] 2. The multidimensional coupled chain code encoding method based on generalized integrated interleaving code proposed in this invention can achieve a lower bit error rate compared with existing multidimensional coupled chain codes.

[0030] 3. The present invention proposes a multidimensional coupled chain code encoding method based on generalized integrated interleaving code. It combines the encoding structure of multidimensional coupled chain code with generalized integrated interleaving code. Compared with existing multidimensional coupled chain codes, the construction of the present invention is more diverse and flexible.

[0031] 4. The present invention proposes a multidimensional coupled chain code encoding method based on generalized integrated interleaving code, which shares the redundancy of codewords with high error correction capability with other codewords with low error correction capability, thereby enabling other codewords with low error correction capability to have higher error correction capability. Compared with existing multidimensional coupled chain codes, the decoding performance of the present invention can be closer to the Shannon limit. Attached Figure Description

[0032] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0033] Figure 1 This is an encoding block diagram of a multidimensional coupled zipper code encoding method based on generalized integrated interleaved codes disclosed in this invention;

[0034] Figure 2 This is a schematic diagram of the encoding in Embodiment 1 of the present invention;

[0035] Figure 3 This is a coding performance diagram of Embodiment 1 of the present invention;

[0036] Figure 4 This is a schematic diagram of the encoding of Embodiment 2 of the present invention;

[0037] Figure 5 This is a coding performance diagram of Embodiment 2 of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Example 1

[0040] In this embodiment 1, the encoding dimension s = 2, the mapping period q = 255, the interleaving dimension d = 2, the number of interleaving codes v = 1, the encoding memory depth M = 255, and the encoding truncation length T = 255. For any dimension and any time, the binary BCH code C0[510,483] is selected as the linear block code of the 0th dimension, and the subcode C1[510,474] of C0 is selected as the linear block code of the 1st dimension. k0 = 483 and k1 = 474; for any time t and any dimension l, set m t,l =m=255, where l=0,1; set the number of coupling layers L=10000. The binary information sequence of length (k0+k1-2m)L=447×10000... u Divided into 20,000 groups u =( u (0,0) , u (0,1) , u (1,0) , u (1,1) ,…, u (9999,0) , u (9999,1) ),in, u (t,0) The length of each is k0-m=228. u (t,1) The length of each is k1-m = 219. The encoding method of this invention includes the following steps:

[0041] Step S1: Divide the binary information sequence u into 20,000 equal-length groups. u =( u (0,0) , u (0,1) , u (1,0) , u (1 ,1) ,…, u (9999,0) , u (9999,1) For times t = -1, -2, ..., -255, the sequence of length 255 × 2 is... c (t) Initialize to a sequence of all zeros.

[0042] Step S2: At time t = 0, 1, ..., 9999, process the sequence of length 228. With a sequence of length 255 w (t,0) The sequence is fed into multiplexer M0 to obtain a sequence of length 483. in, and The sequence of length 219 With a sequence of length 255 w (t,1) The sequence is fed into multiplexer M1 to obtain a sequence of length 474. in, and At the same time a (t,0) and a (t,1) The code is fed into an encoder of a generalized integrated interleaved code for encoding, resulting in parity sequences of lengths 27 and 36, respectively. and The encoded output at time t is c (t) =( c (t,0) , c (t,1) ) = ( u (t,0) , p (t,0) , u (t,1) , p (t,1) ).

[0043] Matrix P t,0 The values ​​of matrix P are: t,0Each column (j = 0, 1, ..., 255) is non-zero only at position 2jm + (t mod q); matrix P t,1 The values ​​of matrix P are: t,1 Each column (j = 0, 1, ..., 255) is non-zero only at position (2j+1)m+(tmodq); the encoding steps of the generalized integrated interleaved code are as follows: first, the sequence... a (t,0) The check sequence is obtained by encoding using BCH code C0[510,483]. and code c (t,0) =( a (t,0) , p (t,0) Secondly, in a sequence of length 474... a (t,1) End-padding with zeros to a length of 510 yields the sequence. Next, perform a modulo-2 addition operation on both to obtain the sequence. Finally, the sequence f (t) The first 474 bits of the sequence The sequence is fed into the BCH code C1[510,474] encoder to obtain the check sequence. get

[0044] Step S3: At times t = 10000, 10002, ..., 10255, convert the all-zero sequence of length 447... u (t) = 0 As input, step two is executed to obtain check sequences of lengths 27 and 36, respectively. and Encoded output at time t c (t) =( p (t,0) , p (t,1) ).

[0045] Figure 2 A schematic diagram of the multidimensional coupled chained code based on generalized integrated interleaving code in this embodiment is given. The dashed lines with arrows indicate mapping the encoded output of the current small block to the small block pointed to by the arrow, and the labels in the small blocks indicate the specific mapping relationship. Codeword c =( c (0) , c (1) ,…, c (10255) The signal is sent into a binary symmetric channel, and the receiving end receives the corresponding codeword. cThe received sequence r = ( r (0) , r (1) ,…, r (10255) A sliding window iterative hard-decision decoding algorithm with a window size of 1530 is used for decoding to obtain an estimate of the sent message sequence u.

[0046] Figure 3 The performance of the multidimensional coupled chain code encoding based on generalized integrated interleaved codes in this embodiment is presented. For performance comparison, Figure 3 The paper also presents the performance of the original chained code in a binary symmetric channel, where the decoding employs a sliding window iterative decoding algorithm with a window size of 1000. Therefore, the two codes mentioned above have the same decoding capability and comparable decoding delay. Figure 3 As can be seen, compared with existing zipper codes, the multidimensional coupled zipper code encoding based on generalized integrated interleaving code given in this embodiment has better performance.

[0047] Example 2

[0048] In this embodiment, the encoding dimension s = 3, the mapping period q = 1, the interleaving dimension d = 2, the number of interleaving codes v = 1, the encoding memory depth M = 250, and the encoding truncation length T = 250. For any dimension and any time, the binary BCH code C0[500, 473] is selected as the linear block code for the 0th and 2nd dimensions, and the subcode C1[500, 464] of C0 is selected as the linear block code for the 1st dimension. k0 = 473 and k1 = 464; for any time t and any dimension l, set m t,l =m=250, where l=0,1,2; set the number of coupling layers L=10000.

[0049] The binary information sequence of length (2k0+k1-3m)L=660×10000 u Divided into 30,000 groups u =( u (0 ,0) , u (0,1) , u (0,2) , u (1,0) , u (1,1) , u (1,2) ,…, u (9999,0) , u (9999,1) ,u (9999,2) ),in, u (t,0) and u (t,2) The length of each is k0-m=223. u (t,1) The length of each is k1-m = 214. The encoding method of this invention includes the following steps:

[0050] Step S1: Divide the binary information sequence u into 30,000 equal-length groups. u =( u (0,0) , u (0,1) , u (0,2) , u (1 ,0) , u (1,1) , u (1,2) ,…, u (9999,0) , u (9999,1) , u (9999,2) For times t = -1, -2, ..., -250, the sequence of length 250 × 3 is... c (t) Initialize to a sequence of all zeros.

[0051] Step S2: At time t = 0, 1, ..., 9999, process the sequence of length 223. With a sequence of length 250 w (t,0) The sequence is fed into multiplexer M0 to obtain a sequence of length 473. in, and w (t,0) =(c (t-1) ,c (t-2) ,…,c (t-M) )P t,0 ; a sequence of length 214 With a sequence of length 250 w (t,1) The sequence is fed into multiplexer M1 to obtain a sequence of length 464. in, and w (t,1) =(c (t-1) ,c (t-2) ,…,c (t-M) )P t,1; a sequence of length 223 With a sequence of length 250 w (t,2) The sequence is fed into multiplexer M2 to obtain a sequence of length 473.

[0052]

[0053] in, and w (t,2) =(c (t-1) ,c (t-2) ,…,c (t-M) )P t,2 At the same time a (t,0) and a (t,1) The code is fed into an encoder of a generalized integrated interleaved code for encoding, resulting in parity sequences of lengths 27 and 36, respectively. and Will a (t,2) The sequence is fed into the BCHC0[500,473] encoder for encoding, resulting in a check sequence of length 27. The encoded output at time t is c (t) =( c (t,0) , c (t,1) , c (t,2) ) = ( u (t,0) , p (t,0) , u (t,1) , p (t,1) , u (t,2) , p (t,2) ).

[0054] For j = 0, 1, 2, ..., 249, P t,0 The j-th column is non-zero only at position 3jm+2m+j; P t,1 The j-th column is non-zero only at position 3jm+j; P t,2 The j-th column is non-zero only at position 3jm+m+j. The encoding steps of the generalized integrated interleaved code are as follows: First, the sequence... a (t,0) The check sequence is obtained by encoding using BCH code C0[500,473]. and code c (t ,0) =( a(t,0) , p (t,0) Secondly, in a sequence of length 464... a (t,1) End-padding with zeros to a length of 500 yields the sequence. Next, perform a modulo-2 addition operation on both to obtain the sequence. Finally, the sequence f (t) The first 464 bits of the sequence The sequence is fed into the BCH code C1[500,464] encoder to obtain the check sequence. get c (t,1) =( u (t,1) , p (t,1) ).

[0055] Step S3: At times t = 10000, 10002, ..., 10249, convert the all-zero sequence u of length 660... (t) Taking 0 as input, execute step S2 to obtain a check sequence of length 24. and and a check sequence of length 32 Encoded output at time t c (t) =( p (t,0) , p (t,1) , p (t,2) ).

[0056] Figure 4 A schematic diagram of the multidimensional coupled chained code based on generalized integrated interleaving code in this embodiment is given. The dashed lines with arrows indicate mapping the encoded output of the current small block to the small block pointed to by the arrow, and the labels in the small blocks indicate the specific mapping relationship. Codeword c =( c (0) , c (1) ,…, c (10249) The signal is sent into a binary symmetric channel, and the receiving end receives the corresponding codeword. c The received sequence r = ( r (0) , r (1) ,…, r (10249) A sliding window iterative hard-decision decoding algorithm with a window size of 1500 is used to decode and obtain the sent message sequence. uEstimate

[0057] Figure 5 The performance of the multidimensional coupled chain code encoding based on generalized integrated interleaved codes in this embodiment is presented. For performance comparison, Figure 5 The paper also presents the performance of the original multidimensional coupled zipper code in a binary symmetric channel, where the decoding employs a sliding window iterative decoding algorithm with a window size of 1500. Therefore, the two codes mentioned above have the same decoding capability and comparable decoding delay. From Figure 5 As can be seen, compared with existing zipper codes, the multidimensional coupled zipper code encoding based on generalized integrated interleaving code given in this embodiment has better performance.

[0058] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A multidimensional coupled chain code encoding method based on generalized integrated interleaving codes, given the interleaving dimension d and the number of interleaving codes v, at time t, the definition of the generalized integrated interleaving code is as follows: in, v is an integer greater than 0, d is an integer greater than v, a is a primitive element or a primitive polynomial of a finite field, and c (t，i) Let a be the i-th dimension subcodeword after generalized integrated interleaving coding. il C represents the offset coefficients with primitives or primitive polynomials as the standard basis. t，0 For the first layer of interleaving linear block codes after generalized integrated interleaving coding, C t，v-l It is a linear block code with a second layer of interleaving after generalized integrated interleaving coding, and satisfies For a zip code, given the coding dimension s, coding memory depth M, number of coding layers L, and mapping period q, where s is an integer greater than or equal to d, and M, L, and q are integers greater than 0; given a time t in the range 0 ≤ t < L, then at time t, d-dimensional zip codes are selected from the s-dimensional zip codes for generalized integrated interleaving coding, and the selected dimensions are denoted as l0, l1, ..., l i , ..., l d-1 After generalized integrated interleaving coding, the lth i The code length of the Vela chain is Information bit length is Among them, l i Let be the dimension index of the subcode after generalized integrated interleaving encoding, 0≤i≤d-1; then encode the remaining (sd)-dimensional chain codes, with the selected dimensions denoted as l′0, l′1, ..., l′ i′ , ..., l′ s-d-1 , among which, for the l′ i′ VeraChaincode uses a code length of Information bit length is linear block code As a basic code, l′ i′ Let be the dimension index of the codeword after linear block coding, 0 ≤ i′ < sd, l′ i′ ∈{0, 1,…,s-1}\{l1, l2,…,l d-1 }, i.e., l′ i′ For the set {l1, l2, ..., l d-1 In the remainder set of the set {0, 1, ..., s-1}, the codewords satisfy the following relationship: The length is Information sequence u The information is divided into several sub-information sequences, and each time step encodes a different sub-information sequence group, where 0 ≤ l < s⁻¹, m t，l m represents the length of the recoded symbols in the encoded input of the l-th dimensional zip code at time t. t，l greater than zero and less than k t，l The integer; at time t, first select d segments of sub-information sequence from the group and perform generalized integrated interleaving coding to obtain codewords. Next, the remaining sub-information sequence is encoded to obtain codewords. remember The codeword sequence generated at time t; T is the code truncation length, and the value of T is a positive integer; characterized in that the encoding method includes the following steps: S1. For times t = -1, -2, ..., -M, divide the length of... sequence c (t) Initialize as an all-zero sequence, where the length is (n t，l -m t，l ) sequence c (t，l) The output of the l-th dimensional zip code at time t; the length of Information sequence u Divided into sL groups u =( u (0，0) , u (0，1) , ..., u (0，s-1) , u (1，0) , u (1 ，1) , ..., u (1，s-1) , ..., u (L-1，0) , u (L-1，1) , ..., u (L-1，s-1) ), where grouping u (t，l) The length is k t，l -m t，l ; S2. At time t = 0, 1, ..., L-1, for the l-th dimensional pull chain code, the length of k... t，l -m t，l sequence With a length of m t，l sequence w (t，l) Input to multiplexer M l The length is k. t，l sequence Among them, the recoded sequence w (t，l) satisfy Matrix P t，l For a row number of The number of columns is The matrix; the sequence Input basic code The encoder ENC′(t, l′) i′ Encode the result to obtain a length of Validation sequence Where 0 ≤ i′ < sd; then multiple sequences are... Simultaneously, the code is fed into the encoder ENC(t, v) of the generalized integrated interleaved code for encoding to obtain the check sequence. in, After the encoding of the generalized integrated interleaved code is completed (0≤i<d-1), the code will... c (t，0) , c (t，1) , ..., c (t，s-1) The encoded output at time t is obtained by feeding it into the multiplexer M. c (t) =( c (t，0) , c (t，1) , ..., c (t，s-1) ),in, c (t，l) =( u (t，l) , p (t，l) ); S3. At times t = L, L+1, ..., L+T-1, the length is... All-zero sequence ( u (t，0) , u (t，1) , ..., u (t，s-1) )= 0 As the input for encoding, step S2 is executed to obtain a length of Encoded output c (t) =( p (t，0) , p (t ，1) , ..., p (t，s-1) ), where for 0 ≤ l < s, u (t，l) The length is (k) t，l -m t，l A sequence of all zeros.

2. The multidimensional coupled chain code encoding method based on generalized integrated interleaved codes according to claim 1, characterized in that, The encoding steps of the encoder ENC(t, v) of the generalized integrated interleaved code in step S2 are as follows: S21, for the sequence Using linear block codes Encode and obtain the check sequence Where i = v, v+1, ..., d-1; S221, For the remaining sequence Encode the sequence i = v-1, v-2, ..., 0, calculate the sequence Corresponding composite polynomial Where, r v-i For verification sequence The length of a i (x) is polynomial, c i+1 (x) is a sequence The polynomial, especially π. (i) (x) is given by the following formula: polynomial matrix Γ (i) (x) and the polynomial matrix Θ (i) (x) are as follows: Among them, g v-i (x) is the basic code. The generating polynomial of α(x) is a primitive polynomial; S222, the composite polynomial f i (x) before The multinomial coefficients are fed into the basic code as follows: The verification sequence is obtained from the encoder. S223, the composite polynomial f i (x) after r v-i Multinomial coefficients and check sequence The check sequence is obtained by modulo 2 summation.

3. The multidimensional coupled chain code encoding method based on generalized integrated interleaved codes according to claim 1, characterized in that, In step S2, the encoder ENC′(t, l′) of the linear block code... i′ The encoding steps are as follows: For the sequence... Using linear block codes Encode the code, where i′ = 0, 1, ..., sd-1, for a linear block code. Given its generating matrix is will sequence With the generating matrix Multiply to get the code word Output verification sequence 4. The multidimensional coupled chain code encoding method based on generalized integrated interleaved codes according to claim 1, characterized in that, The information sequence u It is a binary sequence or a sequence defined on a multivariate finite field.

5. The multidimensional coupled chain code encoding method based on generalized integrated interleaved codes according to claim 1, characterized in that, Encoder ENC′(t, l′) i ) is a linear block code encoder of any type.

6. The multidimensional coupled chain code encoding method based on generalized integrated interleaved codes according to claim 1, characterized in that, The encoder ENC(t, v) is a generalized integrated interleaved code encoder.

7. The multidimensional coupled chain code encoding method based on generalized integrated interleaved codes according to claim 1, characterized in that, The multiplexer M and the multiplexer M l The input short sequence is concatenated and combined into a new long output sequence. The multiplexer can be of any type. Multiplexer M l The output is the information sequence to be encoded, and the output of the multiplexer M is the codeword sequence to be transmitted.

8. The multidimensional coupled chain code encoding method based on generalized integrated interleaved codes according to claim 3, characterized in that, when u When it is a binary sequence, the matrix P t，l It is a binary matrix of any type; when u When the matrix P is a sequence defined over a multivariate finite field, t，l It is a multivariate matrix of any type defined over a multivariate finite field.

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