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Advances in intelligent systems research/Advances in Intelligent Systems Research

Construction of Irregular LDPC Codes by Row Partition

Xiongfei Tao, Yan Zhang, Pan Liu, Hu Zuoqi

Published Jan 1, 2013• 0 citations
Publisher

Abstract

In this paper, we propose an approach to construct a class of irregular low-density parity-check (LDPC) codes based on row partition.We divide the rows of LDPC check matrix into subsets and derive an approach to arrange '1' in each column to prevent low weight code words.When decoded by iterative algorithm, the proposed codes show performance with low error floor and are subject to few undetected errors.The LDPC codes constructed based on the proposed scheme have efficiently encoding structures.

DOI
10.2991/icmt-13.2013.51

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In this paper, we propose an approach to construct a class of irregular low-density parity-check (LDPC) codes based on row partition.We divide the rows of LDPC check matrix into subsets and derive an approach to arrange '1' in each column to prevent low weight code words.When decoded by iterative algorithm, the proposed codes show performance with low error floor and are subject to few undetected errors.The LDPC codes constructed based on the proposed scheme have efficiently encoding structures.
The main influence for the performance of finite length Low-Density Parity-Check(LDPC) codes is analyzed. According to optimum choice for degree distribution, a check matrix is constructed with improved Progressive-Edge-Growth (PEG) algorithm. A practical efficient encoding algorithm is proposed to optimize the check matrix. A finite length irregular LDPC code with low error-floor performance and approximate linear encoding complexity is obtained. This optimization method can be easily extended to general communication channels.
In this paper, we propose an algorithm to design an irregular low-density parity-check (LDPC) code, with a given degree distribution pair, from a combinatorially constructed regular LDPC code. Richardson et al., (2001) showed that long LDPC codes from irregular bipartite graphs with carefully chosen degree distribution pair performed very close to the Shannon capacity limit. It is known that the cyclic or quasicyclic property of regular LDPC codes, constructed from combinatorial designs Colbourn, J et al., (1996), helps to simplify their encoding procedure and also facilitates a memory-efficient storage of the codes. The proposed algorithm involves splitting columns and rows of a regular LDPC code systematically in order to achieve an irregular code with a given distribution pair. Also, this algorithm is a useful alternative to random generation of irregular codes because it enables to exploit the structural properties of the regular code in efficiently storing the resultant irregular code.
This paper gives a new random construction for LDPC codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has low complexity and great flexible choice in LDPC code parameters including code length, code rate, least girth of the graph, and the weight of column and row in the parity-check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Simulations show that the method performs well with iterative decoding.