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

Author

Zhang, Li ; Huang, Qin ; Lin, Shu ; Abdel-Ghaffar, Khaled ; Blake, Ian F.

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of California, Davis, CA, USA

Volume

58

Issue

11

fYear

2010

fDate

11/1/2010 12:00:00 AM

Firstpage

3126

Lastpage

3139

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.

Keywords

AWGN channels; algebraic codes; matrix algebra; message passing; parity check codes; AWGN channels; Latin squares; algebraic construction; binary erasure channels; message passing; noisy channels; parity-check matrices; quasi-cyclic LDPC codes; rank analysis; Arrays; Construction industry; Decoding; Dispersion; Finite element methods; Null space; Parity check codes; Latin square; quasi-cyclic LDPC code; row-column constraint; row-distance constraint;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/TCOMM.2010.091710.090721

Filename

5590324