Quasi-cyclic LDPC codes: an algebraic construction, rank analysis, and codes on Latin squares

Authors:
Li Zhang;Qin Huang;Shu Lin;Khaled Abdel-Ghaffar;Ian F. Blake
Affiliations:
Department of Electrical and Computer Engineering, University of California, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, CA;Electrical and Computer Engineering Department, University of British Columbia, Vancouver, BC, Canada
Venue:
IEEE Transactions on Communications
Year:
2010

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Abstract

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.