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Asia-Pacific Conference on Communications (APCC)

Necessary conditions for avoiding cycles of length 4 or 6 in regular quasi-cyclic LDPC codes

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

Published Oct 1, 2012• 0 citations
Publisher

Abstract

In this paper we investigate the cycle properties of regular quasi-cyclic low-density parity-check (QC-LDPC) codes. Using the sequence representation, we analyze the conditions for short cycles to exist in regular QC-LDPC codes and then give necessary conditions for avoiding short cycles in terms of their parameters. Numerical results show that our bounds on the number of rows in the parity-check matrices for regular QC-LDPC codes without cycles of length 4 or 6 are tighter than any other known bounds.

DOI
10.1109/apcc.2012.6388262

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For a high-rate case, it is difficult to randomly construct good low-density parity-check (LDPC) codes of short and moderate lengths because their Tanner graphs are prone to have short cycles. Also, the existing high-rate quasi-cyclic (QC) LDPC codes can be constructed only for very restricted code parameters. In this paper, based on special classes of cyclic difference families, we propose a new construction method of high-rate regular QC LDPC codes having parity-check matrices consisting of a single row of circulants with column-weight 3 or 4. The proposed QC LDPC codes can be constructed for various code rates and lengths including the minimum achievable length for given column-weight and design rate under girth 6. It is observed that the parity-check matrices of the proposed QC LDPC codes have full rank for column-weight 3 and just one redundant row for column-weight 4. It is shown that the error correcting performance of the proposed QC LDPC codes of short and moderate lengths is almost the same as that of the existing ones through numerical analysis.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.