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Method for configuring algorithm complex low quasi-cyclic LDPC codes

A technology of LDPC code and construction method, applied in the field of communication, can solve the problems of high complexity, high complexity, inability to control the parameters of LDPC code, etc., and achieve the effect of flexible design and low complexity

Inactive Publication Date: 2007-11-14
FUDAN UNIV
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Problems solved by technology

Based on the method of geometry over finite fields [3], the disadvantage of this method is that it can only guarantee the construction of codes with g>4
Fossorier gave the relationship between the girth g of the LDPC code constructed using the cyclic permutation matrix and the weight j, k of the row and column in [4], but did not give an effective construction method
Someone proposed a semi-random algorithm for eliminating short loops, but the complexity of this algorithm is very high [5]
Some people use the method of multiplying the matrix to eliminate the short ring, which also has a relatively high complexity [6]
In addition, these methods have a common disadvantage, that is, they are not flexible enough to control the parameters of the generated LDPC codes.

Method used

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  • Method for configuring algorithm complex low quasi-cyclic LDPC codes
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specific Embodiment approach

[0079] The specific method of construction is illustrated below with a specific construction example. Assume that the size of the matrix H we want to construct is 1008×504, that is, M=1008, N=504. The size of the permutation matrix is ​​7×7, ie q=7. Then the size of the exponential matrix is ​​144×72, that is, m=144, n=72, that is, there are 144 data nodes and 72 check nodes in the weighted Tanner graph. The degree of each data node is 6, and the degree of each check node is 12. The following distribution explains the construction process in detail.

[0080] 1. Construct the exponential matrix M(H)

[0081] A. Create an empty 144×72 matrix. That is to generate a weighted Tanner graph without adding any edges. There are 144 data nodes and 72 check nodes on the graph.

[0082] B. Use Algorithm 1 to add a specified number of edges to each data node in the weighted Tanner graph. For the pseudo code of the algorithm, see Algorithm 3 where v i is the i-th data node, c j is t...

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Abstract

The method includes to steps: (1) constructing exponent matrix of parity check matrix of QC-LDPC codes; (2) using exponent expansion to convert the exponent matrix to parity check matrix H of QC-LDPC codes. When iterative decoding, code error rate of the constructed QC-LDPC codes is lower than the rate of traditional PEG algorithm obviously (specially, in condition of high SNR), and algorithm complexity is mach lower than algorithm complexity of traditional algorithm so that the constructing speed is much fast than speed of traditional method. Moreover, when constructing QC-LDPC codes, the disclosed method can control each parameter for generating code flexibly.

Description

technical field [0001] The invention belongs to the technical field of communication, and in particular relates to a fast algorithm for designing quasi-cyclic LDPC codes. Background technique [0002] LDPC code (Low Density Check Code) [1] is a linear check code whose check matrix is ​​a sparse matrix. Because the bit error rate can approach the Shannon limit under Gaussian white noise, LDPC codes have received extensive attention in recent years. QC-LDPC codes (Quasi-Cyclic Low Density Check Codes) have become a research hotspot in recent years because they can be coded with linear complexity. [0003] The LDPC code can be uniquely determined by its check matrix H or its corresponding Tanner graph [2]. The parity check matrix of LDPC code is a sparse matrix of n×m. If each row and each column of the matrix has the same weight j, k (the number of 1 in a row or a column is called weight), the LDPC code is said to be regular, otherwise the LDPC code is irregular. The perfo...

Claims

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Application Information

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IPC IPC(8): H03M13/11
Inventor 王江张建秋
Owner FUDAN UNIV
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