IEEE International Symposium on Information Theory (ISIT)

Necessary conditions for quasi-cyclic LDPC codes to have a given girth

Kyung-Joong Kim, Jin-Ho Chung, Kyeongcheol Yang

Published Jul 1, 2013• 0 citations

Abstract

Short cycles in the Tanner graph of a low-density parity-check (LDPC) code may cause a severe performance degradation. In this paper, we investigate the cycle properties of quasi-cyclic LDPC (QC-LDPC) codes. We first analyze a necessary and sufficient condition for a cycle of a given length to exist, by using the sequence representation of a parity-check matrix for a QC-LDPC code. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. Our necessary conditions are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds for many classes of regular QC-LDPC codes.

DOI: 10.1109/isit.2013.6620709

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