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Construction of Structured LDPC Codes for AWGN and Binary Erasure Channels

Y.Y. Tai, Longwen Lan, Lingqi Zeng, L. Chen, Shu Lin, Khaled Abdel-Ghaffar

Published Dec 10, 2005• 2 citations
Publisher

Abstract

An algebraic method for constructing structured regular and irregular LDPC codes with girth at least six is presented. The parity check matrices of the proposed codes are arrays of permutation matrices obtained by decomposing Euclidean geometries. Masking is applied to the resultant parity check matrices to yield codes with various degree distributions. The proposed codes perform well over AWGN channels and binary erasure channels when decoded iteratively.

DOI
10.1109/wirles.2005.1549400

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An algebraic method for constructing structured regular and irregular LDPC codes with girth at least six is presented. The parity check matrices of the proposed codes are arrays of permutation matrices obtained by decomposing Euclidean geometries. Masking is applied to the resultant parity check matrices to yield codes with various degree distributions. The proposed codes perform well over AWGN channels and binary erasure channels when decoded iteratively.
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This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.