A Construction of High Rate Quasi-Cyclic Regular LDPC Codes from Cyclic Difference Families with Girth 8

Shojiro SAKATA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A    No.5    pp.1055-1061
Publication Date: 2007/05/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.5.1055
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
LDPC code,  quasi-cyclic code,  cyclic difference family,  girth,  minimum distance,  

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In this paper we propose a method of constructing quasi-cyclic regular LDPC codes from a cyclic difference family, which is a kind of combinatorial design. The resulting codes have no 4-cycle, i.e. cycles of length four and are defined by a small set of generators of codes with high rate and large code length. In particular, for LDPC codes with column weight three, we clarify the conditions on which they have no 6-cycle and their minimum distances are improved. Finally, we show the performance of the proposed codes with high rates and moderate lengths.