Open Access

High Girth Column-Weight-Two LDPC Codes Based on Distance Graphs

EURASIP Journal on Wireless Communications and Networking20072007:048158

DOI: 10.1155/2007/48158

Received: 12 November 2005

Accepted: 25 October 2006

Published: 28 January 2007

Abstract

LDPC codes of column weight of two are constructed from minimal distance graphs or cages. Distance graphs are used to represent LDPC code matrices such that graph vertices that represent rows and edges are columns. The conversion of a distance graph into matrix form produces an adjacency matrix with column weight of two and girth double that of the graph. The number of 1's in each row (row weight) is equal to the degree of the corresponding vertex. By constructing graphs with different vertex degrees, we can vary the rate of corresponding LDPC code matrices. Cage graphs are used as examples of distance graphs to design codes with different girths and rates. Performance of obtained codes depends on girth and structure of the corresponding distance graphs.

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Authors’ Affiliations

(1)
School of Electrical and Electronic Engineering, The University of Adelaide, North Terrace

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Copyright

© G. Malema and M. Liebelt. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.