Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersions

Authors:
Bo Zhou;Jingyu Kang;Shumei Song;Shu Lin;Khaled Abdel-Ghaffar;Meina Xu
Affiliations:
Qualcomm Inc., San Diego, CA and Department of Electrical and Computer Engineering, University of California at Davis, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, Davis, CA;Marvell Semiconductor, Inc., Santa Clara, CA and Department of Electrical and Computer Engineering, University of California at Davis, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, Davis, CA;Northrop Grumman Space Technology, Redondo Beach, CA
Venue:
IEEE Transactions on Communications
Year:
2009

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Abstract

This paper presents two algebraic methods for constructing high performance and efficiently encodable non-binary quasi-cyclic LDPC codes based on arrays of special circulant permutation matrices and multi-fold array dispersions. Codes constructed based on these methods perform well over the AWGN and other types of channels with iterative decoding based on belief-propagation. Experimental results show that over the AWGN channel, these non-binary quasi-cyclic LDPC codes significantly outperform Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision Berlekamp-Massey algorithm or algebraic soft-decision Kötter-Vardy algorithm. Also presented in this paper is a class of asymptotically optimal LDPC codes for correcting bursts of erasures. Codes constructed also perform well over flat fading channels. Non-binary quasi-cyclic LDPC codes have a great potential to replace Reed-Solomon codes in some applications in communication environments and storage systems for combating mixed types of noises and interferences.