Quasi-Cyclic LDPC Codes: An Algebraic Construction, Rank Analysis, and Codes on Latin Squares

• Published in: IEEE transactions on communications Vol. 58; no. 11; pp. 3126 - 3139
• Main Authors: Li Zhang, Qin Huang, Shu Lin, Abdel-Ghaffar, K, Blake, I F
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algebra; Algorithms; Applied sciences; Arrays; Channels; Coding, codes; Combinatorial analysis; Computer simulation; Construction; Construction industry; Decoding; Dispersion; Exact sciences and technology; Finite element methods; Information, signal and communications theory; Latin square; Mathematical analysis; Null space; Parity check codes; quasi-cyclic LDPC code; row-column constraint; row-distance constraint; Signal and communications theory; Telecommunications and information theory; Performance evaluation; Finite field; Binary channel; Cyclic code; AWGN; quasi-cyclic LDPC code; Latin square; row-distance constraint; Algorithm; Iterative decoding; Implementation; row-column constraint; Combinatorial method; Message passing; Simulation; Noisy channel; Error correcting code; Parity check codes; Parity check
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2010.091710.090721

Quasi-cyclic LDPC codes are the most promising class of structured LDPC codes due to their ease of implementation and excellent performance over noisy channels when decoded with message-passing algorithms as extensive simulation studies have shown. In this paper, an approach for constructing quasi-cyclic LDPC codes based on Latin squares over finite fields is presented. By analyzing the parity-check matrices of these codes, combinatorial expressions for their ranks and dimensions are derived. Experimental results show that, with iterative decoding algorithms, the constructed codes perform very well over the AWGN and the binary erasure channels.