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Construction method and encoding method for multiple LDPC code

A technology of LDPC code and construction method, which is applied in the field of communication and can solve the problems of complex coding process and high storage space.

Inactive Publication Date: 2008-12-31
SUN YAT SEN UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

However, there are many problems in the existing multivariate LDPC codes, including higher storage space and more complicated encoding process, etc.

Method used

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  • Construction method and encoding method for multiple LDPC code
  • Construction method and encoding method for multiple LDPC code
  • Construction method and encoding method for multiple LDPC code

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Embodiment 1

[0026] Let GF(q) be a finite field with q elements, and α be a primitive element. A multivariate LDPC code C with code length N and dimension K can be described by a multivariate check matrix H. The dimension of the parity check matrix is ​​(M×N). a vector c =(c 1 , c 2 ,...,c N-1 ) is a codeword in C if and only if c h T = 0 , where H T Represents the transpose of the matrix H, 0 Represents an all-zero vector of length M.

[0027] The construction of the multivariate LDPC code is mainly divided into two steps: the construction of the block matrix and the replacement of non-zero elements, which include the following steps:

[0028] a. The parity check matrix H of the multivariate LDPC code is a block matrix on the finite field GF(q), which is composed of (m×n) sub-matrices; Matrix H i，j is determined by the scaling factor β i，j ∈GF(q) is multiplied by a (l×l) identity matrix, and then cyclically shifted left by column s i，j times, where 0≤i≤m-1, 0≤j≤n-1, 0≤s i，j...

Embodiment 2

[0079] In this embodiment, the method of constructing a multivariate LDPC code is described by constructing a binary basis matrix and replacing non-zero elements.

[0080] 1) Construction of binary basis matrix

[0081] For any positive integer l, form a set Z of all positive integers less than l and relatively prime to it l * , these positive integers form a multiplicative group under the modulo l multiplication operation. Tanner pointed out in the article "LDPCBlock and Convolutional Codes Based on Circulant Matrices" published in 2001: If Z l * There are two elements a, b in , and the order of a is m, and the order of b is n, then the following binary matrix H can be constructed (b)

[0082] H ( b ) = h 0 , 0 ...

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Abstract

The invention belongs to the communication technology field, particularly relates to a structuring method of a multi-LDPC code. The method comprises steps as follows: the check matrix H of the multi-LDPC code is a partitioned matrix which consists of (m multiplying n) sub-matrixes of H<i, j>, and each sub-matrix H<i, j> is obtained from that a scale factor beta<i, j> epsilon GF(q) is multiplied by a unit matrix of (1 multiplying 1) and then left moved by s<i, j> times according to a line cycle; wherein, GF(q) is a finite field having q elements; the check matrix H of the multi-LDPC code can be divided into two parts, namely, H is equal to (H1H2); wherein, the H2 is a dual partitioned diagonal matrix with a size of m multiplying m and the H1 consists of sub-matrixes left in the H; the H1 corresponds to information symbols and the H2 corresponds to check symbols. In addition, the invention also provides a fast coding method applicable to the invented multi-LDPC code.

Description

technical field [0001] The invention belongs to the technical field of communication, and in particular relates to a construction method and an encoding method of a multivariate LDPC code. technical background [0002] Low-density parity-check code (LDPC code) is a linear block code approaching the Shannon limit, which can be described by a check matrix. As early as 1962, Gallager proposed the LDPC code and proved that the code can be closer to the Shannon limit than other error-correcting codes. However, due to its high complexity, it did not attract people's attention at the time. With the introduction of Turbo codes, Mackay and Neal rediscovered LDPC codes in 1995. Since then, LDPC codes have attracted widespread attention. [0003] According to the generation process of check matrix, LDPC codes can be divided into two categories: random type and structured type. When the code length is long, a sparse matrix is ​​randomly generated as the parity check matrix of the LD...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03M13/11
Inventor 马啸王秀妮白宝明
Owner SUN YAT SEN UNIV
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