Construction of High-Rate Regular Quasi-Cyclic LDPC Codes Based on Cyclic Difference Families

• Published in: IEEE transactions on communications Vol. 61; no. 8; pp. 3108 - 3113
• Main Authors: Park, Hosung, Hong, Seokbeom, No, Jong-Seon, Shin, Dong-Joon
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-08-2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Binary system; Code length; code rate; Codes; Coding, codes; Construction; cyclic difference families (CDFs); Design engineering; Error correction; Exact sciences and technology; Geometry; girth; Graphs; Information, signal and communications theory; Iterative decoding; Low density parity check codes; Mathematical models; Numerical analysis; Parity check codes; Quality control; quasi-cyclic (QC) low-density parity-check (LDPC) codes; Redundant; Signal and communications theory; Telecommunications and information theory; Cyclic code; Code length; Error estimation; Tanner graph; code rate; Numerical method; cyclic difference families (CDFs); quasi-cyclic (QC) low-density parity-check (LDPC) codes; girth; Error correcting code; Parity check codes; Error correction; Parity check
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2013.070213.120879

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.