A coding method and apparatus for polygonal quasi-cyclic LDPC codes based on finite fields.

Abstract

This invention discloses an encoding method and apparatus for a polygonal quasi-cyclic LDPC code based on a finite field, comprising: determining a basis matrix according to the target code parameters, wherein the basis matrix contains at least one non-zero element with a value greater than 1, indicating that a polygonal cyclic matrix with a row and column weight greater than 1 needs to be constructed; generating an initial matrix based on a finite field and mapping its elements to cyclic shift values; performing a composite operation on the shift values ​​guided by the basis matrix to allocate multiple shift values ​​to specific positions; and finally, constructing the final polygonal quasi-cyclic LDPC code parity-check matrix according to the allocated set of shift values ​​and the expansion factor. This invention, by incorporating a polygonal structure into a quasi-cyclic framework, effectively optimizes the ring distribution of codewords while maintaining the advantages of low encoding complexity and easy hardware implementation. Compared with traditional single-sided quasi-cyclic LDPC code encoding methods, it significantly reduces the error plane and has a faster decoding convergence speed.

Description

Technical Field

[0001] This invention relates to the field of communication and electronic systems technology, and in particular to an encoding method and apparatus for a polygonal quasi-cyclic LDPC code based on a finite field. Background Technology

[0002] Low-Density Parity-Check (LDPC) codes are excellent channel coding schemes with performance approaching the Shannon limit. Due to their superior error correction performance and parallelizable iterative decoding structure, they have been widely used in 5G mobile communication data channel standards. Among them, Quasi-Cyclic LDPC (QC-LDPC) codes have become the mainstream choice in practical applications due to their unique cyclic structure. The parity-check matrix of a QC-LDPC code consists of a cyclic permutation matrix (CPM) or a zero matrix. This structure allows the encoding process to be implemented using linearly complex shift registers, greatly reducing hardware implementation overhead and power consumption. Furthermore, the QC structure only needs to store the base matrix and cyclic shift values, rather than the entire parity-check matrix, significantly saving storage resources and naturally supporting layered decoding to improve throughput.

[0003] Despite the success of QC-LDPC codes in 5G, as wireless mobile communication technology evolves to 6G, channel coding, as one of the core technologies for wireless air interface transmission, faces demands for higher performance, lower latency, and wider coverage. This presents significant challenges to the evolution of QC-LDPC codes to meet the higher performance requirements of 6G. Typical 6G application scenarios, such as ultra-high-speed communication (bit error rate below 10^-9), ultra-low latency (less than 1 millisecond), and wide-area high-reliability communication, place even more stringent demands on the performance of channel coding, especially on the convergence speed in the "waterfall region" and the "error floor" under low signal-to-noise ratio. In the current 5G standard QC-LDPC codes, each CPM in the parity-check matrix has a row and column weight of 1. These codes are referred to in coding theory as "one-sided" LDPC codes. Their construction methods mainly rely on copying and edge permutation of the fundamental graph, or on optimizing the distribution of rings through computer search. However, this single, regular connection structure is prone to forming "trap sets" in the decoder's Tanner graph, causing the decoder to stagnate in specific error modes, thus triggering a high error level and limiting its application performance in extremely low bit error rate scenarios.

[0004] To overcome the performance bottleneck of single-edge LDPC codes, the academic community has proposed the concept of "multi-edge-type" (MET) LDPC codes. Multi-edge-type LDPC codes allow the row and column weights of the cyclic submatrices in their parity-check matrix to be greater than 1, i.e., constructing a more heterogeneous graph structure through the composite operation of cyclic permutation matrices. This enhanced connectivity complexity can effectively disrupt the clustering effect of trap sets, thereby significantly reducing the error flatness and achieving gains in thresholding performance.

[0005] However, most current high-performance polygonal LDPC code designs rely on random or density-evolutionary computer search methods. Codes constructed using these methods lack clear, regular structural characteristics, making it difficult to perform efficient matrix operations on their parity-check matrices. This results in high encoder complexity and hinders the hardware implementation of parallel decoding. This significantly impedes the application of polygonal LDPC codes in practical communication systems, especially in mobile terminals with stringent hardware efficiency requirements.

[0006] Therefore, how to provide an encoding method and apparatus for polygonal quasi-cyclic LDPC codes that combines the advantages of low-error flat layers of polygonal codes and low-complexity hardware implementation of quasi-cyclic codes is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In response to the aforementioned research status, this invention provides an encoding method and apparatus for polygonal quasi-cyclic LDPC codes based on finite fields. By effectively integrating the polygonal structure into the quasi-cyclic algebraic framework based on finite fields, an LDPC code channel coding scheme with structural characteristics, easy implementation, and good iterative decoding performance in noisy channels is formed.

[0008] The present invention provides an encoding method for polygonal quasi-cyclic LDPC codes based on finite fields, comprising the following steps:

[0009] S1: Construct a base matrix B based on the target code parameters, wherein the base matrix B contains at least one non-zero element with an element value greater than 1, which is used to indicate that the cyclic submatrix corresponding to the position is a polygonal cyclic square matrix with a row and column weight greater than 1.

[0010] S2: Based on the selected finite field GF(q), construct a one-sided initial matrix, wherein the elements of the initial matrix are taken from the finite field GF(q), and q is a prime number or a prime power;

[0011] S3: Guided by the base matrix B, perform a composition operation on the elements of the initial matrix to construct a polygonal cyclic matrix formed by adding multiple cyclic permutation matrices; wherein the composition operation includes:

[0012] For each position in the base matrix B where the element value is 1, the single cyclic shift value mapped to the corresponding position in the initial matrix is ​​assigned as the shift value for constructing the cyclic submatrix at that position.

[0013] For positions in the base matrix B where the element value is greater than 1, the cyclic shift value mapped to one or more other positions in the initial matrix is ​​compounded to the cyclic shift value mapped to that position, such that multiple cyclic shift values ​​are assigned to that position; and the compounding operation follows the criterion of keeping the row and column weights of the base matrix B unchanged;

[0014] S4: Based on the set of cyclic shift values ​​finally assigned to each position of the base matrix B and the preset expansion factor, construct the final check matrix H of the polygonal quasi-cyclic LDPC code; wherein, for a shift value, it is replaced with the corresponding cyclic permutation matrix; for multiple shift values, it is replaced with a cyclic square matrix obtained by adding the corresponding multiple cyclic permutation matrices.

[0015] S5: Perform polygonal quasi-cyclic LDPC encoding on the sequence of information to be encoded according to the parity check matrix H, and / or perform polygonal quasi-cyclic LDPC decoding on the sequence of data to be decoded according to the parity check matrix H.

[0016] Preferably, in S1: the base matrix B is formed by horizontally splicing, vertically splicing, or two-dimensional splicing of multiple identical basic modules.

[0017] Preferably, the step of constructing the initial matrix of the one-sided type in S2 includes:

[0018] S21: Choose a primitive element α of the finite field GF(q), and use the power of α to form the primitive element α. -∞ =0,α 0 =1,α 1 ,α 2 ,...,α q-2 Generate all q elements of GF(q), and α q-1 =α 0 =1;

[0019] S22: Construct a field of size (q-1) based on the finite field GF(q). 2 ×(q-1) 2 array matrix H GF(q) :

[0020] H GF(q) =[I(α) i +α j )];

[0021] Where 0≤i≤q-2, 0≤j≤q-2, I(α) i +α j) is based on element (α) i +α j The hashed permutation matrix is ​​a cyclic ring permutation matrix of size (q-1)×(q-1);

[0022] S23: Based on the number of rows m and columns n of the base matrix B, from the array matrix H GF(q) Select an array matrix H of size (mq-m)×(nq-n). FF :

[0023]

[0024] The rule for selecting the array matrix is: Using array matrix H... FF The selection objective is to maximize the length of the shortest cycle and minimize the number of shortest cycles in the corresponding Tanner graph.

[0025] S24: According to the array matrix H FF Determine the corresponding Exponent matrix as the initial matrix:

[0026]

[0027] Preferably, the array matrix H FF It satisfies the following structural characteristics:

[0028] Array matrix H FF All elements in any row / column are distinct elements in the finite field GF(q);

[0029] Array matrix H FF Each row / column contains at most one zero element;

[0030] Array matrix H FF The elements in any two rows / columns are distinct in all corresponding positions.

[0031] Preferably, any 2×2 submatrix of the initial matrix is ​​non-full rank.

[0032] Preferably, in S3, the criteria followed by the composite operation include: among all composite schemes that satisfy the row and column weight invariance constraint of the base matrix B, selecting the scheme that maximizes the shortest cycle length in the Tanner graph corresponding to the finally constructed verification matrix H.

[0033] Preferably, the parity check matrix H of the polygonal quasi-cyclic LDPC code constructed by the method has a length of at least 6; the length refers to the length of the shortest cycle in the Tanner graph corresponding to the parity check matrix H.

[0034] Preferably, in step S5, the constructed polygonal quasi-cyclic LDPC code is applied to the channel coding of the information sequence to be encoded in the 6G communication system, and / or the constructed polygonal quasi-cyclic LDPC code is applied to the channel decoding of the data sequence to be decoded in the 6G communication system.

[0035] The present invention also provides a communication device, including a memory and a processor, wherein the memory stores a computer program, characterized in that the processor, when executing the program, implements the encoding method of the polygonal quasi-cyclic LDPC code based on finite field.

[0036] The present invention also provides a computer-readable storage medium storing computer instructions thereon, characterized in that, when the instructions are executed by a processor, they implement the encoding method of the polygonal quasi-cyclic LDPC code based on finite fields.

[0037] Compared with existing technologies, which suffer from incomplete sensor coverage and blind spots, insufficient adaptability to dynamic scenes, and low efficiency in multi-objective optimization, this invention has the following advantages:

[0038] The polygonal quasi-cyclic LDPC code constructed in this invention significantly outperforms the traditional single-sided quasi-cyclic LDPC code in iterative decoding performance. Specifically:

[0039] Under additive white Gaussian noise (AWGN) channels, it exhibits superior performance in the waterfall region and achieves a gain of approximately 0.5 dB in the low bit error rate (BER) region; simultaneously, its error flatness is significantly reduced. Furthermore, the code demonstrates faster decoding convergence, requiring fewer iterations to approach optimal performance, thus reducing decoding latency. These performance improvements stem from its optimization of the ring distribution in the Tanner graph through composite operations, effectively reducing the number of short rings and disrupting the error trap set. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely embodiments of the present invention, and those skilled in the art can obtain other drawings based on the provided drawings without creative effort.

[0041] Figure 1 This is a flowchart of the encoding method for polygonal quasi-cyclic LDPC codes based on finite fields provided in the embodiments of the present invention;

[0042] Figure 2 This is a performance comparison diagram of the ring distribution of the polygonal quasi-cyclic LDPC code C2 constructed according to the embodiments of the present invention and the unilateral quasi-cyclic LDPC code C1 constructed based on finite fields;

[0043] Figure 3 This is a convergence performance diagram of the polygonal quasi-cyclic LDPC code constructed according to an embodiment of the present invention. Detailed Implementation

[0044] 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, and 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.

[0045] The first aspect of this invention discloses an encoding method for polygonal quasi-cyclic LDPC codes based on finite fields, such as... Figure 1 The diagram shows a flowchart of the encoding method for polygonal quasi-cyclic LDPC codes based on finite fields. The specific execution process includes the following steps:

[0046] S1: Construct a base matrix B based on the target code parameters. The base matrix B contains at least one non-zero element with a value greater than 1, which indicates that the corresponding cyclic submatrix is ​​a polygonal cyclic square matrix with a row and column weight greater than 1.

[0047] In one embodiment, in S1: the base matrix B is formed by horizontally splicing, vertically splicing, or two-dimensional splicing of multiple identical basic modules.

[0048] S2: Based on the selected finite field GF(q), construct a one-sided initial matrix, where the elements of the initial matrix are taken from the finite field GF(q), and q is a prime number or a prime power.

[0049] In one embodiment, the step of constructing the one-sided initial matrix in S2 includes:

[0050] S21: Choose a primitive element α of the finite field GF(q), and use the power of α to form the primitive element α. -∞ =0,α 0 =1,α 1 ,α 2 ,...,α q-2 Generate all q elements of GF(q), and α q-1 =α 0 =1;

[0051] S22: Construct a field of size (q-1) based on the finite field GF(q). 2 ×(q-1) 2 array matrix H GF(q) :

[0052] H GF(q) =[I(α) i+α j )];

[0053] Where 0≤i≤q-2, 0≤j≤q-2, I(α) i +α j ) is based on element (α) i +α j The hashed permutation matrix is ​​a cyclic ring permutation matrix of size (q-1)×(q-1);

[0054] S23: Based on the number of rows m and columns n of the base matrix B, from the array matrix H GF(q) Select an array matrix H of size (mq-m)×(nq-n). FF :

[0055]

[0056] Select array matrix H FF The rule is: using array matrix H FF The selection objective is to maximize the length of the shortest cycle and minimize the number of shortest cycles in the corresponding Tanner graph.

[0057] S24: According to the array matrix H FF Determine the corresponding Exponent matrix as the initial matrix:

[0058]

[0059] In this embodiment, the array matrix H FF It satisfies the following structural characteristics:

[0060] Array matrix H FF All elements in any row / column are distinct elements in the finite field GF(q);

[0061] Array matrix H FF Each row / column contains at most one zero element;

[0062] Array matrix H FF The elements in any two rows / columns are distinct in all corresponding positions.

[0063] In one embodiment, any 2×2 submatrix of the initial matrix is ​​non-full rank.

[0064] S3: Guided by the basis matrix B, perform composition operations on the elements of the initial matrix to construct a polygonal cyclic matrix formed by the addition of multiple cyclic permutation matrices; the composition operations include:

[0065] For each position in the base matrix B where the element value is 1, the single cyclic shift value that corresponds to that position in the initial matrix is ​​assigned as the shift value for constructing the cyclic submatrix at that position.

[0066] For positions in the base matrix B where the element value is greater than 1, the cyclic shift value mapped to one or more other positions in the initial matrix is ​​compounded to the cyclic shift value mapped to that position, so that multiple cyclic shift values ​​are assigned to that position; and the compounding operation follows the principle of keeping the row and column weights of the base matrix B unchanged.

[0067] In one embodiment, in S3, the criteria followed by the composition operation include: among all composition schemes that satisfy the row and column weight invariance constraint of the basis matrix B, selecting the scheme that maximizes the shortest cycle in the corresponding Tanner graph of the final constructed check matrix H.

[0068] In one embodiment, the parity check matrix H of the polygonal quasi-cyclic LDPC code constructed by the method has a length of at least 6; the length refers to the length of the shortest cycle in the Tanner graph corresponding to the parity check matrix H.

[0069] S4: Based on the set of cyclic shift values ​​finally assigned to each position of the base matrix B and the preset expansion factor, construct the final check matrix H of the polygonal quasi-cyclic LDPC code; where, for a shift value, it is replaced with the corresponding cyclic permutation matrix; for multiple shift values, it is replaced with the cyclic square matrix obtained by adding the corresponding multiple cyclic permutation matrices.

[0070] S5: Perform polygonal quasi-cyclic LDPC encoding on the sequence of information to be encoded based on the parity check matrix H, and / or perform polygonal quasi-cyclic LDPC decoding on the sequence of data to be decoded based on the parity check matrix H.

[0071] In one embodiment, in S5, the constructed polygonal quasi-cyclic LDPC code is applied to the channel coding of the information sequence to be encoded in the 6G communication system, and / or the constructed polygonal quasi-cyclic LDPC code is applied to the channel decoding of the data sequence to be decoded in the 6G communication system.

[0072] The following is a detailed description of the first aspect of the present invention regarding the construction of the basis matrix:

[0073] Drawing inspiration from the design of unilateral quasi-cyclic LDPC codes, we construct the basic modules of the basis matrix of polygonal quasi-cyclic LDPC codes by using the method of cyclic permutation matrix composition, and design polygonal codes with larger code rates and code lengths based on the basic modules.

[0074] Suppose we construct a regular polygonal code with a code rate of 0.5, a row weight of 3, and a column weight of 6. The Exponent matrix of the unilateral quasi-cyclic LDPC code is:

[0075]

[0076] By removing some shift values ​​and combining them with other shift values, the row and column weights must remain unchanged during the combination. For example, we remove the shift value p. 0,0 ,p 1,1 ,p 2,2 ,p 0,3 ,p 1,4 ,p 2,5 and combine them separately into p 1,0 ,p 2,1 ,p 0,2 ,p 1,3 ,p 2,4 ,p 0,5 Thus, the original one-sided Exponent matrix is ​​transformed into a polygonal Exponent matrix, as follows:

[0077]

[0078] Here, adding two shift values ​​represents adding the cyclic permutation matrices corresponding to the two shift values. For example, p 1,0 +p 0,0 Represents a cyclic matrix I(p) 1,0 )+I(p 0,0 It can be observed that this compound operation ensures the regularity of the polygonal code, meaning that the row and column weights remain unchanged. The basis matrix corresponding to the polygonal Exponent matrix P is...

[0079]

[0080] By observing the basis matrix B, we can see that it has symmetry and contains two identical matrices.

[0081]

[0082] Therefore, we obtain the fundamental module of the basis matrix, namely the matrix.

[0083]

[0084] Note that, to avoid confusion and to standardize the basic modules, the specific position of element 2 is not given in the basis matrix above; instead, element 1 is used to represent element 2. In the actual construction of polygonal codes, optimization can be performed according to the code construction method. The specific position of element 2 needs to be determined based on the optimization process, but the row and column weights of the basic modules must remain unchanged. This is achieved by arranging n basic modules B... 3,3 That is, [B] 3,3 B 3,3 ,...,B 3,3, a polygonal quasi - cyclic LDPC code with column weight 3 and row weight 3n can be constructed. Note that the code length of this polygonal quasi - cyclic LDPC code is 3nP, and the code rate is approximately

[0085]

[0086] In addition, according to the row and column weights and other code parameters required by the code design, the construction forms of other basic matrix basic modules are also given, such as:

[0087]

[0088] According to different code requirements, set the code parameters and select the appropriate basic matrix basic module to construct the corresponding polygonal quasi - cyclic LDPC code.

[0089] Next, the construction principle of the polygonal quasi - cyclic LDPC code based on the finite field in the first aspect of the embodiment of the present invention is given:

[0090] Let GF(q) be a finite field containing q elements, where q is a prime number or a power of a prime number. Let α be a primitive element of GF(q), then the powers α -∞ = 0, α 0 = 1, α 1 , α 2 ,..., α q-2 can generate all q elements of GF(q), and α q-1 = α 0 = 1.

[0091] Next, according to the non - zero elements of the finite field GF(q), define their corresponding (q - 1)×(q - 1) cyclic permutation matrices (CPMs):

[0092] A CPM is uniquely determined by the position of the only non - zero element 1 in its first row (row 0). Its row and column numbers are both from 0 to q - 2, and there are a total of q - 1 different (q - 1)×(q - 1) CPMs. For 0 ≤ j < q - 1, the non - zero element α j of the finite field GF(q) can be represented as a (q - 1)×(q - 1) CPM, denoted as I(α j ), and the only element 1 in its first row is located in the j - th column. The representation of the matrix I(α j ) is also called the field element α jThe (q-1)-fold CPM hash is given. Since GF(q) has q-1 non-zero elements and there are q-1 different (q-1)×(q-1) binary CPMs, there is a one-to-one correspondence between the non-zero elements of the finite field GF(q) and the (q-1)×(q-1) CPMs. For the zero elements of the finite field GF(q), its matrix hash is defined as a (q-1)×(q-1) all-zero matrix, denoted as I(α-∞) or I(-1).

[0093] Construct a finite field GF(q) of size (q-1). 2 ×(q-1) 2 array matrix H GF(q) H GF(q) =[I(α) i +α j Based on the number of rows m and columns n of the base matrix B, from the array matrix H GF(q) Construct an array matrix of size (mq-m)×(nq-n). And the corresponding Exponent matrix.

[0094] The following is a detailed description of the first aspect of the present invention regarding the construction of a polygonal cyclic matrix composed of the sum of multiple cyclic permutation matrices based on a composite operation:

[0095] The core idea of ​​the construction is to ensure that the resulting polygonal code has a large circumference and the fewest shortest loops during the process of shifting value composition.

[0096] The specific implementation scheme is as follows: Based on the position of the 0 element in the base matrix, find the corresponding shift value in the Exponent matrix P, and place this value in another position in the same row. Note that the element of the base matrix corresponding to the position cannot be 0. If there are many possible positions, determine the final placement position according to the principle of "maximum girth and minimum shortest ring of the resulting polygonal quasi-cyclic LDPC code". Repeat the above process until all shift values ​​are combined.

[0097] The effectiveness of the above construction method will be verified through examples below:

[0098] The numerical simulation conditions are an additive white Gaussian noise (AWGN) channel, binary phase shift keying (BPSK) modulation, and the decoding algorithm used is the sum-product algorithm (SPA).

[0099] Assume we construct a quasi-cyclic LDPC code with a code rate of 0.5 and a code length of 378. Based on the design scheme, we choose a basic module of size 3×3:

[0100]

[0101] Construct a basis matrix of size 3×6:

[0102]

[0103] Suppose α is a primitive element of the finite field GF(64). Based on the finite field GF(64), a finite field of size 63 can be constructed. 2 ×63 2 array matrix H GF(64) :

[0104] H GF(64) =[I(α) i +α j )],

[0105] Where 0≤i≤62, 0≤j≤62;

[0106] Based on the 3 rows and 6 columns of the base matrix B, from the array matrix H GF(64) An array matrix H of size 189×378 is constructed. FF :

[0107] H FF =[I(α) k +α l )] 1≤k≤3,1≤l≤6 .

[0108] The array matrix H FF The null space gives a one-sided quasi-cyclic (378,191) LDPC code C1. The array matrix H FF The Exponent matrix is:

[0109]

[0110] Based on the 3×6 basis matrix B constructed above 3×6 And based on the computer-implemented construction method, the specific basis matrix was obtained:

[0111]

[0112] The following Exponent matrix P was constructed. Pro

[0113]

[0114] The Exponent matrix PPro Replacing the shift value in the matrix with the corresponding 63×63CPM yields an array matrix H of size 189×378. Pro The matrix H Pro The null space gives a polygonal quasi-cyclic (378,189) LDPC code C2.

[0115] like Figure 2 As shown, the bit error rate (BER) and word error rate (WER) performance of the two quasi-cyclic LDPC codes C1 and C2 are presented. From... Figure 2 It can be seen that when BER=10 -6 At that time, the constructed polygonal code C2 has a performance gain of approximately 0.5 dB compared to the unilateral code C1 constructed based on finite fields.

[0116] like Figure 3 As shown, the bit error rate (BER) performance of the constructed polygonal quasi-cyclic LDPC code C2 is presented at 1, 3, 5, 10, 20, and 50 iterations. Figure 3 It is evident that this code exhibits a relatively fast convergence speed in iterative decoding. When BER = 10... -6 At that time, the performance difference between 10 and 50 iterations was approximately 0.2 dB, while the performance difference between 20 and 50 iterations was only 0.15 dB, indicating that the iterative decoding was close to full convergence. Furthermore, Figure 3 This indicates that the constructed polygonal quasi-cyclic LDPC code has a low error flatness.

[0117] Table 1 shows the ring distributions of the constructed polygonal quasi-cyclic LDPC code C2 and the unilateral quasi-cyclic LDPC code C1 based on finite fields.

[0118]

[0119] Table 1 shows the ring distributions of the quasi-cyclic (378,191) LDPC code C1 constructed based on finite fields and the constructed polygonal quasi-cyclic (378,189) LDPC code C2. As can be seen from Table 1, both quasi-cyclic LDPC codes have a girth of 6, but the constructed polygonal quasi-cyclic LDPC code has fewer short rings than the unilateral quasi-cyclic LDPC code constructed based on finite fields.

[0120] A second aspect of the present invention discloses a communication device, including a memory and a processor, wherein the memory stores a computer program, characterized in that the processor executes the program to implement the encoding method of polygonal quasi-cyclic LDPC codes based on finite fields disclosed in the first aspect of the present invention.

[0121] The third aspect of the present invention discloses a computer-readable storage medium storing computer instructions thereon, characterized in that the instructions, when executed by a processor, implement the encoding method of polygonal quasi-cyclic LDPC codes based on finite fields disclosed in the first aspect of the present invention.

[0122] The coding method for polygonal quasi-cyclic LDPC codes based on finite fields proposed in this invention has better structural characteristics and iterative decoding performance. It can be seen that by introducing the concept of polygons, the ring distribution and related correlation structure of quasi-cyclic LDPC codes can be further improved, making it easier to construct high-performance quasi-cyclic LDPC codes. This provides a new design idea and scheme for LDPC coding for 6G communication systems.

[0123] The above provides a detailed description of the encoding method and apparatus for a polygonal quasi-cyclic LDPC code based on a finite field provided by the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

[0124] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. An encoding method for polygonal quasi-cyclic LDPC codes based on finite fields, characterized in that, Includes the following steps: S1: Construct a base matrix B according to the target code parameters, wherein the base matrix B contains at least one non-zero element with an element value greater than 1, which is used to indicate that the cyclic submatrix corresponding to the position of the non-zero element is a polygonal cyclic square matrix with a row and column weight greater than 1. S2: Based on the selected finite field GF(q), construct a one-sided initial matrix, wherein the elements of the initial matrix are taken from the finite field GF(q), and q is a prime number or a prime power; S3: Guided by the base matrix B, perform a composition operation on the elements of the initial matrix to construct a polygonal cyclic matrix formed by adding multiple cyclic permutation matrices; wherein the composition operation includes: For each position in the base matrix B where the element value is 1, the single cyclic shift value mapped to the corresponding position in the initial matrix is ​​assigned as the shift value for constructing the cyclic submatrix at that position. For positions in the base matrix B where the element value is greater than 1, the cyclic shift value mapped to one or more other positions in the initial matrix is ​​compounded to the cyclic shift value mapped to that position, such that multiple cyclic shift values ​​are assigned to that position; and the compounding operation follows the criterion of keeping the row and column weights of the base matrix B unchanged; S4: Based on the set of cyclic shift values ​​finally assigned to each position of the base matrix B and the preset expansion factor, construct the final check matrix H of the polygonal quasi-cyclic LDPC code; wherein, for a shift value, it is replaced with the corresponding cyclic permutation matrix; for multiple shift values, it is replaced with a cyclic square matrix obtained by adding the corresponding multiple cyclic permutation matrices. S5: Perform polygonal quasi-cyclic LDPC encoding on the sequence of information to be encoded according to the parity check matrix H, and / or perform polygonal quasi-cyclic LDPC decoding on the sequence of data to be decoded according to the parity check matrix H.

2. The encoding method for a polygonal quasi-cyclic LDPC code based on a finite field according to claim 1, characterized in that, In S1: the base matrix B is formed by horizontally splicing, vertically splicing, or two-dimensional splicing of multiple identical basic modules.

3. The encoding method for a polygonal quasi-cyclic LDPC code based on a finite field according to claim 1, characterized in that, The steps for constructing the initial matrix of the one-sided form in S2 include: S21: Select a finite field GF( q The fundamental element α ,Depend on α powers α -∞ =0, α 0 =1, α 1 , α 2 ,..., α q-2 Generate GF( q (all) q 1 element, and α q-1 = α 0 =1; S22: According to the finite field GF( q Construct a space of size ( q -1) 2 ×( q -1) 2 array matrix : ； in, , For elements The size of the hash is ( q -1)×( q The cyclic permutation matrix of -1); S23: Based on the row number of the basis matrix B m Number of columns n From the array matrix Select one of size ( mq - m )×( nq - n array matrix : ； Select array matrix The rule is: use array matrix The selection objective is to maximize the length of the shortest cycle and minimize the number of shortest cycles in the corresponding Tanner graph. S24: According to the array matrix H FF Determine the corresponding Exponent matrix as the initial matrix: 。 4. The encoding method for a polygonal quasi-cyclic LDPC code based on a finite field according to claim 3, characterized in that, Array matrix H FF It satisfies the following structural characteristics: Array matrix H FF All elements in any row / column are finite fields GF( q The elements that are distinct from each other in the array; Array matrix H FF Each row / column contains at most one zero element; Array matrix H FF The elements in any two rows / columns are distinct in all corresponding positions.

5. The encoding method for a polygonal quasi-cyclic LDPC code based on a finite field according to claim 3, characterized in that, Any 2×2 submatrix of the initial matrix is ​​non-full rank.

6. The encoding method for a polygonal quasi-cyclic LDPC code based on a finite field according to claim 1, characterized in that, In S3, the criteria followed by the composite operation include: among all composite schemes that satisfy the row and column weight invariance constraint of the base matrix B, selecting the scheme that maximizes the shortest cycle length in the Tanner graph corresponding to the finally constructed verification matrix H.

7. The encoding method for a polygonal quasi-cyclic LDPC code based on a finite field according to claim 1, characterized in that, The parity check matrix H of the polygonal quasi-cyclic LDPC code constructed by the method has a length of at least 6; the length refers to the length of the shortest cycle in the Tanner graph corresponding to the parity check matrix H.

8. The encoding method for a polygonal quasi-cyclic LDPC code based on a finite field according to claim 1, characterized in that, In step S5, the constructed polygonal quasi-cyclic LDPC code is applied to the channel coding of the information sequence to be encoded in the 6G communication system, and / or the constructed polygonal quasi-cyclic LDPC code is applied to the channel decoding of the data sequence to be decoded in the 6G communication system.

9. A communication device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When the instructions are executed by the processor, they implement the method as described in any one of claims 1 to 8.

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