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International Symposium on Information Theory and its Applications

Reed-Solomon based nonbinary LDPC codes

Juane Li, Keke Liu, Shu Lin, Khaled Abdel Ghaffar

Published Oct 1, 2016• 1 citation
OpenAlex

Abstract

This paper is concerned with designs and constructions of nonbinary LDPC codes based on the conventional parity-check matrices of Reed-Solomon codes.

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This paper presents a construction of a class of partial geometries based on RS codes of prime lengths and shows that LDPC codes constructed based on Reed-Solomon codes of prime lengths are finite geometry LDPC codes. Furthermore, a new method for design and construction of nonbinary quasi-cyclic LDPC codes based on the conventional parity-check matrices of Reed-Solomon codes is presented. Simulation results show that the constructed nonbinary LDPC codes perform well over the additive white Gaussian channel.
In this paper, we first propose a general framework for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes based on a two-dimensional (2-D) maximum distance separable (MDS) code. Two classes of QC-LDPC codes are defined, whose parity-check matrices are transposes of each other. We then use a 2-D generalized Reed-Solomon (GRS) code to give a concrete construction. The decoding parity-check matrices have a large number of redundant parity-check equations while their Tanner graphs have a girth of at least 6. The minimum distances of the codes are very respectable as far as LDPC codes are concerned. We further show that many existing constructions of QC-LDPC codes based on finite fields in the literature can be unified under this construction. Experimental studies show that the constructed QC-LDPC codes perform well with the sum-product algorithm (SPA).