A method for constructing LDPC codes

Abstract

The present invention provides a method for constructing LDPC codes, comprising the following steps: Step 1: Design base graphs with different code rates according to a given initial base graph; Step 2: Perform hierarchical lifting on the base graphs with different code rates respectively to obtain a parity-check matrix, which further includes: Step 210: Determine the number of lifting layers and the lifting factor for each layer based on the code length and the number of variable nodes of the base graph; Step 220: Perform lifting on the base graph layer by layer according to the number of lifting layers and the lifting factor. Based on the embodiments of the present invention, rate-compatible LDPC codes can be constructed simply and efficiently. The constructed rate-compatible LDPC codes have a constant code length, a wide range of code rate changes, and a large flexibility of change. The parity-check matrix of the constructed codes has a quasi-cyclic structure and a nested structure, which can not only achieve parallel encoding and decoding, but also reduce the system storage capacity, and is suitable for the specific implementation of an encoder / decoder.

Description

Technical Field

[0001] The present invention belongs to the physical layer channel coding technology in the field of wireless communication, relates to a construction method of low-density parity-check codes, and particularly relates to a construction method of rate-compatible LDPC (Multi-rate low density parity check) codes. Background Art

[0002] For current wireless communication scenarios, such as satellite communication links, terrestrial cellular communications, underwater communications, etc., channel coding needs to be adopted at the transceiver end to ensure the reliability of transmission. The protograph low-density parity-check (PTG-LDPC) code is a channel coding scheme with strong error control capabilities and low encoder / decoder complexity, and has been used in a variety of actual communication systems.

[0003] The LDPC code C is an (n, k) linear block code, with a code length of n, an information sequence length of k, and a code rate of k / n, and can be uniquely defined by its parity-check matrix H. The dimension of H is m×n, where m is the number of parity-check equations. The parity-check matrix of the LDPC code can also be represented by a Tanner graph. Figure 1 shows an example. Figure 1(b) is an LDPC parity-check matrix, and Figure 1(a) is its Tanner graph. The nodes in the Tanner graph are divided into two parts. The top nodes are check nodes, corresponding to the rows of the parity-check matrix, and the bottom nodes are variable nodes, corresponding to the columns of the check matrix. There are no edges connecting nodes of the same type, and there are only edges between the two types of nodes. If the element in the i-th row and j-th column of the parity-check matrix is non-zero and has a value of d, then there is an edge connecting the i-th check node and the j-th variable node in the Tanner graph, and the degrees of these two nodes are d. The number of edges connected to a node is the degree of the node. For example, in Figure 1(b), the element in the first row and first column of the parity-check matrix is 3, so in Figure 1(a), there is an edge connecting the first check node and the first variable node, and the degrees of these two nodes are 3. The Tanner graph is a bipartite graph.

[0004] The main current method for constructing PTG-LDPC codes is the lifting construction method based on a protograph. The main process is as follows: First, a smaller bipartite graph, called a protograph, is determined. Then, the protograph is copied Q times, and then the edges are permuted among Q independent copies to obtain a single large graph. However, due to the need for a large number of computational and search operations, the construction complexity is relatively high. In addition, currently, an algebraic method is also used to construct PTG-LDPC codes. The main steps include: basis matrix decomposition and row / column permutation. This algebraic construction method has a relatively low construction complexity, but in the step of basis matrix decomposition, the protograph needs to satisfy many constraints. Therefore, the applicable range of this method is relatively small, and the construction flexibility is relatively low. Summary of the Invention

[0005] In view of the above problems, according to the first aspect of the present invention, a method for constructing an LDPC code is proposed, including the following steps:

[0006] Step 1: Design base graphs with different code rates according to a given initial base graph;

[0007] Step 2: Perform layered lifting on the base graphs with different code rates respectively to obtain a parity-check matrix, which further includes:

[0008] Step 210: Determine the number of lifting layers and the lifting factor for each layer based on the code length and the number of variable nodes of the base graph;

[0009] Step 220: Lift the base graph layer by layer according to the number of lifting layers and the lifting factor.

[0010] In an embodiment of the present invention, Step 1 further includes performing sparsification processing on the base graphs with different code rates.

[0011] In an embodiment of the present invention, Step 210 includes:

[0012] Determine the number of lifting layers L according to the code length N and the number of variable nodes n of the base graph, let , and perform prime factorization on : , where is a prime number, representing the lifting factor of the corresponding layer.

[0013] In an embodiment of the present invention, Step 220 includes:

[0014] For each layer of lifting, determine the degree distribution in the design according to the maximum degree in the base graph. If the maximum degree distribution in the base graph for each lifting is greater than the lifting factor, combine the lifting factors to obtain a larger lifting factor;

[0015] In each layer of lifting, directly replace the node pairs in the base graph according to the lifting factor and the lifting graph to lift each node of the base graph, while ensuring that the degree of the lifted node is the same as the degree of the original node.

[0016] In an embodiment of the present invention, the lifting graph is constructed by matrix superposition, including constructing an identity matrix with a dimension of the lifting factor, and performing cyclic shift superposition on the identity matrix respectively according to the degree to generate different lifting graphs.

[0017] In an embodiment of the present invention, the sparsification processing in Step 1 includes:

[0018] For check nodes with a relatively large degree, some edges are eliminated to make the degree distribution more uniform. Among them, the decoding threshold of the base graph is calculated according to the extrinsic information transfer analysis tool of the base graph, and is used as the choice for deleting or adding node edges.

[0019] In an embodiment of the present invention, step 1 includes:

[0020] Step 110: Determine the information bits and check bits in the variable nodes according to the set C of check nodes and the set V of variable nodes of the base graph. The number of check bits is equal to the number of nodes in set C, and the number of information bits is equal to the number of nodes in set V minus the number of nodes in set C;

[0021] Step 120: Delete the variable node and its edge corresponding to the last information bit of the base graph;

[0022] Step 130: Add a check node and a variable node at the end of the base graph, and there is only one edge connecting them;

[0023] Step 140: Uniformly and randomly expand the edges between the newly added check nodes and the information bits of the variable nodes of the base graph, and perform cyclic iteration. Among them, the decoding threshold of the base graph is calculated according to the extrinsic information transfer analysis tool of the base graph, and is used as the choice for deleting or adding the node edges in the newly added row to determine the base graph for the corresponding code rate.

[0024] In an embodiment of the present invention, step 1 further includes: repeatedly executing steps 110-140 until a base graph with a desired code rate is obtained.

[0025] According to the second aspect of the present invention, there is provided a computer-readable storage medium storing one or more computer programs, which are used to implement the LDPC code construction method of the present invention when executed.

[0026] According to the third aspect of the present invention, there is provided a computing system, including:

[0027] A storage device, and one or more processors;

[0028] Wherein, the storage device is used to store one or more computer programs, and the computer programs are used to implement the LDPC code construction method of the present invention when executed by the processor.

[0029] Compared with the prior art, the advantages of the present invention are that it can simply and efficiently construct rate-compatible LDPC codes. The constructed rate-compatible LDPC codes have a constant code length, a wide range of code rate changes, and a large flexibility of change. The parity-check matrix of the constructed codes has a quasi-cyclic structure and a nested structure, which can not only realize parallel encoding and decoding, but also reduce the system storage capacity, and is suitable for the specific implementation of the encoder and decoder. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings here are incorporated into the description and constitute a part of this description, showing embodiments consistent with the present invention, and are used together with the description to explain the principles of the present invention. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings. In the accompanying drawings:

[0031] FIG. 1 shows an example of the basic mode diagram of the present invention;

[0032] FIG. 2 shows an example of the basic mode diagram for determining information bits and parity bits in an embodiment of the present invention;

[0033] FIG. 3 shows a schematic diagram of deleting the variable node corresponding to the last information bit in an embodiment of the present invention;

[0034] FIG. 4 shows a schematic diagram of adding a parity node and a variable node in an embodiment of the present invention;

[0035] FIG. 5 shows a schematic diagram of uniformly expanding edges in an embodiment of the present invention;

[0036] FIG. 6 shows a schematic diagram of non-uniform degree distribution in an embodiment of the present invention;

[0037] FIG. 7 shows a schematic diagram of the sparsification process in an embodiment of the present invention;

[0038] Figure 8 Shows a schematic diagram of the lifting in an embodiment of the present invention;

[0039] Figure 9 Shows a schematic diagram of hierarchical lifting in an embodiment of the present invention;

[0040] Figure 10 Shows the first lifting diagram in an embodiment of the present invention;

[0041] Figure 11 Shows the second lifting diagram in an embodiment of the present invention;

[0042] Figure 12 Shows the first performance comparison diagram of the simulation of the present invention;

[0043] Figure 13 Shows the second performance comparison diagram of the simulation of the present invention;

[0044] Figure 14 Shows the flowchart of the present invention. Detailed implementation manners

[0045] In view of the problems raised in the background art, the inventors have studied PTG-LDPC codes and found that as the constraint code length changes, especially when a larger base graph is obtained by lifting from a smaller base graph, the performance of the lifted parity-check matrix deteriorates significantly. Secondly, as the rate decreases, lifting will cause the degree distribution trend of the original base graph to be destroyed, the local structure of the parity-check matrix, resulting in a decrease in the performance convergence ability, an increase in the floor, and a large resource consumption when the encoder and decoder are specifically implemented.

[0046] In view of the deficiencies of the existing methods, the present invention provides a new method for constructing PTG-LDPC codes based on graphs. During the construction process, the requirements of the constraint code length are fully considered. By combining the method of hierarchical lifting, the rate can be variable under fixed conditions, and the local structure is broken through sparse operation. At the same time, the external information transfer analysis tool based on the base graph is comprehensively used to fully optimize the structure of the parity-check matrix. As Figure 14 shown, according to an embodiment of the present invention, generally speaking, the method includes the following steps:

[0047] Step 1: Design base graphs with different code rates according to the given base graph;

[0048] Step 2: Sparsify the base graph;

[0049] Step 3: Perform hierarchical lifting on the base graph to obtain a parity-check matrix.

[0050] In the above method, through Step 2 and Step 3, the designed LDPC code can have good performance in the waterfall region and the floor region.

[0051] The above method will be introduced in detail step by step with examples below.

[0052] First, the parameters are set as follows:

[0053] Code length: N; Data length: K; Check data length: M = N – K; Code rate: R = K / N;

[0054] Base graph: Parity-check node length: m; Variable node length n (n mod N = 0);

[0055] Step 1: Design base graphs with different code rates according to the given base graph;

[0056] First, select a given base graph. The base graph B can be obtained according to the existing design methods in the art. The node set in the base graph B can be divided into two non - overlapping subsets C and V such that for each edge in B, the two nodes associated with it are respectively in C and V, and there is no edge connecting two nodes in C or V, as shown in Fig. 1(a) (Fig. 1(b) is the corresponding matrix). The nodes in set C are called check nodes, and the nodes in set V are called variable nodes. According to an embodiment of the present invention, based on the given base graph, the base graph for different code rates is constructed through the following steps:

[0057] Step 110: Determine the information bits and check bits in the variable nodes according to the numbers of C and V. Among them, the number of check bits is equal to the number of nodes in set C, and the number of information bits is equal to the number of nodes in set V minus the number of nodes in set C. To make the finally obtained codeword have a systematic structure, the check bits are selected from the later variable nodes. As shown in Fig. 2(a) (Fig. 2(b) is the corresponding matrix), C = 3, V = 8, V - C = 5. The variable nodes v0 - v4 represent information bits, and the variable nodes v5, v6, v7 represent check bits;

[0058] Step 120: Delete the variable node and the edge corresponding to the last information bit. As shown in Fig. 3(a) (Fig. 3(b) is the corresponding matrix), delete the variable node and the edge corresponding to the information bit v4;

[0059] Step 130: Add a check node and a variable node (check bit) at the end of the graph, and there is only one edge connecting them. As shown in Fig. 4(a) (Fig. 4(b) is the corresponding matrix), add the check node c and the variable node v and an edge between them;

[0060] Step 140: Uniformly and randomly expand the edges between the newly added check node and the information bits of the variable nodes, that is, randomly add edges between these nodes with the same probability. As shown in Fig. 5(a) (Fig. 5(b) shows the corresponding matrix), two edges are added between the newly added node c and v1, and one edge is added between the node c and v3.

[0061] In this way, a new base graph is obtained. It can be seen that compared with the base graph, the new base graph has the same variable nodes, but the information bits are reduced, thereby achieving a reduction in the code rate. Calculate the decoding threshold of the base graph using the extrinsic information transfer analysis tool of the base graph. As the selection of deleting or adding node edges in the newly added rows, at the same time, calculate the loop distribution in the base graph, and try to reduce the number of 4-loops and 6-loops as much as possible. Through multiple iterations of the above step 140, an optimal base graph is obtained. At the same time, each time steps 110-140 are repeated, in step 130, one more parity bit is added, that is, one less information bit is reduced. With the code length unchanged, the code rate is reduced. By repeatedly executing steps 110-140 multiple times, the code rate can be gradually reduced, thereby obtaining a set of base graphs with different code rates.

[0062] Step 2: Sparsify the base graph;

[0063] As the code rate decreases, the check nodes corresponding to the information bits often have a relatively large degree distribution. The uneven overall degree distribution will seriously affect the flat region performance of the codewords, as shown in Fig. 6(a) (Fig. 6(b) shows the corresponding matrix).

[0064] To address this problem, for the check nodes with a relatively large degree, sparsification processing is required to eliminate some edges to make the degree distribution more uniform, as shown in Fig. 7(a) (Fig. 7(b) shows the corresponding matrix). After the sparsification processing in Fig. 7(a), there is only one edge between each pair of nodes. However, those of ordinary skill in the art can also perform other forms of sparsification processing according to needs. There can be more than one edge between each pair of nodes, not limited to only one edge. Calculate the decoding threshold of the base graph using the extrinsic information transfer analysis tool of the base graph as the selection of deleting or adding node edges. Since the sparsification operation can reduce the degree distribution, the loop distribution can be further reduced.

[0065] Step 3: Perform layered lifting on the base graph to obtain a parity-check matrix;

[0066] According to an embodiment of the present invention, this step further includes the following steps:

[0067] Step 310: Determine the number of lifting layers L and the lifting factor for each layer ;

[0068] Determine the number of lifting layers L according to the code length N and the number of variable nodes n of the base graph. Let , and perform prime factorization on : , where are all prime numbers.

[0069] Step 320: Lift the base graph according to the number of lifting layers and the lifting factor;

[0070] For each layer of lifting, determine the degree distribution in the design according to the maximum degree in the base graph, and only need to ensure that the maximum degree distribution in the base graph for each lifting is less than or equal to the lifting factor. If not satisfied, the lifting factors of two layers can be combined to obtain a larger lifting factor. For example, when the maximum degree in the original graph is 3, the lifting factors 2 of two layers can be combined into the lifting factor 4.

[0071] In each layer of lifting, according to the lifting factor , different lifting graphs can be designed to directly replace the node pairs in the base graph, lift each node pair in the base graph, and at the same time ensure that the degree of the lifted node is the same as that of the original node. Figure 8 Show an example of lifting a node pair. Figure 8 In it, c0 and v0 are lifted. The lifted nodes of c0 are c1, c2,... ca1, and the lifted nodes of v0 are v1, v2,... va1. The degrees of c0 and v0 are 3. Therefore, the degree of each point in c1, c2,... ca1 and v1, v2,... va1 is 3. Lift the base graph layer by layer to obtain the parity-check matrix, as Figure 9 shown.

[0072] According to an embodiment of the present invention, the design of the lifting graph can adopt matrix superposition construction. According to the lifting factor q, construct the identity matrix .

[0073]

[0074] According to the size of the degree, perform cyclic shift superposition on . For example, for the lifting factor 4, different degree distribution lifting graphs can be designed, as shown in Figure 10 (a)-(d). Figure 10 (a) (the corresponding lifting graph is Figure 10 (e)) is used for degree 1. Figure 10 (b) (the corresponding lifting graph is Figure 10 (f)) is used for degree 2. Figure 10 (c) (the corresponding lifting graph is Figure 10 (g)) is used for degree 3. Figure 10 (d) (the corresponding lifting graph is Figure 10 (h)) is used for degree 4. Among them, cyclic shift superposition means moving the element 1 on the diagonal of the identity matrix down by 1 bit and then superposing it with the existing graph. Take Figure 10For example, the lifting graph of degree 2 is formed by superimposing the matrix obtained by shifting the element 1 on the diagonal of the identity matrix down by 1 position with the lifting graph matrix of degree 1. The lifting graph of degree 3 is formed by superimposing the matrix obtained by shifting the element 1 that has already been shifted down by 1 position in the identity matrix down by 1 position again with the lifting graph matrix of degree 2. Other methods can also be used to generate the lifting graph. For example, for the lifting graph of degree 4, as long as the sum of the elements in each column of the lifting graph matrix is the required degree.

[0075] The following further details the above lifting steps in matrix form in conjunction with Figure 9 the example of Figure 9 In the basic mode graph in

[0076] (1)

[0077] Assume that according to the target code length, it is necessary to lift by 16 times, then L = 4, = Since the maximum degree in B is 3, the first two lifting factors are combined into 4, then the lifting becomes 3 layers, = .

[0078] For the first layer of lifting, the lifting factor is 4

[0079] Each element of the matrix in formula (1) is replaced by a matrix. If the element value is 3, it is replaced by Figure 10 the matrix in (c); if the element value is 2, it is replaced by Figure 10 the matrix in (b); if the element value is 1, it is replaced by Figure 10 the matrix in (a); if the element value is 0, it is replaced by a matrix of all zeros.

[0080] After replacement, matrix B becomes a matrix, and the elements of this matrix are only 0 and 1. Therefore, for the second layer of lifting, a lifting factor of 2 is acceptable.

[0081] For the second layer of lifting, the lifting factor is 2

[0082] Figure 11 shows the corresponding matrix of the designed lifting graph when the lifting factor is 2, Figure 11 (a) for degree 2, Figure 11 (b) for degree 1, Figure 11 (c) for degree 0.

[0083] For the matrix after the above first lifting, the element 1 in it is replaced by Figure 11Replaced by the matrix in (b), where the element 0 is replaced by Figure 11(c). After replacement, it becomes a matrix, and the elements of this matrix are only 0 and 1.

[0084] The third - layer lifting, with a lifting factor of 2

[0085] For the matrix after the above - mentioned second - layer lifting, where the element 1 is replaced by Figure 11 the matrix in (b), and the element 0 is replaced by Figure 11(c). After replacement, it becomes a matrix.

[0086] The inventors of the present application simulated the above - mentioned method. The code - rate set is {8 / 9, 5 / 6, 7 / 9, 13 / 18, 2 / 3, 11 / 18, 4 / 9, 7 / 18, 1 / 3, 2 / 9} rate - compatible LDPC codes. To improve the performance, the first 900 bits in each code are punctured. Finally, the obtained code length is 16200 bits, where the base - graph code length is 18 bits, and the code length is increased by 900 times.

[0087] The following is an example of the parity - check matrix of the base - graph of the highest - code - rate code 8 / 9 (code length is 18 bits, information bits are 16):

[0088]

[0089] Among them, the first column is punctured and deleted, the middle part is the information bits, and the last 3 columns are the parity - check bits.

[0090] The simulation performance of the constructed code is as Figure 12 and Figure 13 shown, where ICT xx represents the LDPC code obtained by the method of the present invention, and DVB xx represents the LDPC code in the international standard DVB - S2X. The simulation conditions are: Gaussian white - noise channel, BPSK modulation, flooding sum - product decoding, and the maximum number of iterations is 50. It can be clearly seen from the simulation results that, compared with the LDPC code in the international standard DVB - S2, the code constructed by the present invention has better performance at each code rate, and no obvious error floor is observed when the block error rate (BLER) is .

[0091] It should be noted that although the above - mentioned steps are described in a specific order, it does not mean that the steps must be executed in the above - mentioned specific order. In fact, some of these steps can be executed concurrently or even in a different order, as long as the required functions can be achieved.

[0092] The present invention may be a system, a method, and / or a computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions thereon for causing a processor to implement aspects of the present invention.

[0093] The computer-readable storage medium may be a tangible device that retains and stores instructions for use by an instruction execution device. The computer-readable storage medium may include, for example, but is not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer-readable storage medium include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disc (DVD), a memory stick, a floppy disk, a mechanically encoded device such as a punch card or raised structures in grooves having instructions stored thereon, and any suitable combination of the foregoing.

[0094] The foregoing has been described around the present disclosure to enable any ordinary technician in the art to implement or use the present disclosure. For ordinary technicians in the art, various modifications to the present disclosure are obvious, and the general principles defined herein can also be applied to other variations without departing from the spirit or scope of the present disclosure. In addition, unless otherwise stated, all or part of any aspect and / or embodiment may be used with all or part of any other aspect and / or embodiment. Therefore, the present disclosure is not limited to the examples and design schemes described herein, but is consistent with the broadest scope of the principles and novel features disclosed herein.

Claims

1. A method for constructing LDPC codes, comprising the following steps: Step 1: Design base graphs with different code rates according to a given initial base graph; Step 2: Perform layered lifting on the base graphs with different code rates respectively to obtain a parity-check matrix, which further includes: Step 210: Determine the number of lifting layers and the lifting factor for each layer based on the code length and the number of variable nodes of the base graph; Step 220: Lift the base graph layer by layer according to the number of lifting layers and the lifting factor; Among them, Step 210 includes: Determine the lifting layer number L according to the code length N and the number n of variable nodes of the base graph, and let , for perform prime factorization: , where is a prime number, representing the lifting factor of the corresponding layer; Among them, Step 220 includes: For each layer of lifting, determine the degree distribution in the design according to the maximum degree in the base graph. If the maximum degree distribution in the base graph for each lift is greater than the lifting factor, merge the lifting factors to obtain a larger lifting factor; In each layer of lifting, directly replace the node pairs in the base graph according to the lifting factor and the lifting graph to lift each node of the base graph, while ensuring that the degree of the lifted node is the same as that of the original node.

2. The method according to claim 1, wherein Step 1 further includes sparsifying the base graphs with different code rates.

3. The method according to claim 1, wherein the lifting graph is constructed by matrix superposition, including constructing an identity matrix with a dimension of the lifting factor, and respectively performing cyclic shift superposition on the identity matrix according to the degree size to generate different lifting graphs.

4. The method according to claim 2, wherein the sparsifying process in Step 1 includes: For check nodes with a larger degree, eliminate some edges to make the degree distribution more uniform. Among them, calculate the decoding threshold of the base graph according to the extrinsic information transfer analysis tool of the base graph, and use it as the selection for deleting or adding node edges.

5. The method according to claim 2, wherein Step 1 includes: Step 110: Determine the information bits and check bits in the variable nodes according to the check node set C and the variable node set V of the base graph. The number of check bits is equal to the number of nodes in set C, and the number of information bits is equal to the number of nodes in set V minus the number of nodes in set C; Step 120: Delete the variable node and the edge corresponding to the last information bit of the base graph; Step 130: Add a check node and a variable node at the end of the base graph, and there is only one edge connected to them; Step 140: Uniformly and randomly expand the edges between the newly added check node and the information bits of the variable nodes of the base graph, and perform cyclic iteration. Among them, calculate the decoding threshold of the base graph according to the extrinsic information transfer analysis tool of the base graph, and use it as the selection for deleting or adding node edges in the newly added row to determine the base graph for the corresponding code rate.

6. The method according to claim 5, wherein step 1 further comprises: Loop and execute Steps 110 - 140 until a set of base graphs with the desired code rate is obtained.

7. A computer-readable storage medium, in which one or more computer programs are stored, and the computer programs are used to implement the method according to any one of claims 1 - 6 when executed.

8. A computing system, including: A storage device, and one or more processors; Wherein, the storage device is used to store one or more computer programs, and the computer programs, when executed by the processor, are used to implement the method according to any one of claims 1-6.

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