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Journal of Communications and Networks

Design of non-binary quasi-cyclic LDPC codes based on multiplicative groups and Euclidean geometries

Xueqin Jiang, Moon Ho Lee

Published Oct 1, 2010• 1 citation
Publisher

Abstract

This paper presents an approach to the construction of non-binary quasi-cyclic (QC) low-density parity-check (LDPC) codes based on multiplicative groups over one Galois field GF(q) and Euclidean geometries over another Galois field GF(2s). Codes of this class are shown to be regular with girth 6 ≤ g ≤ 18 and have low densities. Finally, simulation results show that the proposed codes perform very well with the iterative decoding.

DOI
10.1109/jcn.2010.6388486

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This paper presents an approach to the construction of non-binary quasi-cyclic (QC) low-density parity-check (LDPC) codes based on multiplicative groups over one Galois field GF(q) and Euclidean geometries over another Galois field GF(2s). Codes of this class are shown to be regular with girth 6 ≤ g ≤ 18 and have low densities. Finally, simulation results show that the proposed codes perform very well with the iterative decoding.
This paper presents methods to the construction of regular and irregular low-density parity-check (LDPC) codes based on Euclidean geometries over the Galois field. Codes constructed by these methods have quasi-cyclic (QC) structure and large girth. By decomposing hyperplanes in Euclidean geometry, the proposed irregular LDPC codes have flexible column/row weights. Therefore, the degree distributions of proposed irregular LDPC codes can be optimized by technologies like the curve fitting in the extrinsic information transfer (EXIT) charts. Simulation results show that the proposed codes perform very well with an iterative decoding over the AWGN channel.
This paper presents a method to the construction of irregular low-density parity-check (LDPC) codes based on Euclidean geometries over the Galois field. Codes constructed by this method are quasi-cyclic (QC) and have large girths. The proposed irregular LDPC codes having flexible column/row weights are obtained with a hyperplane decomposing method in Euclidean geometries. Therefore, the degree distributions of proposed irregular LDPC codes can be optimized by technologies like the curve fitting approach in the extrinsic information transfer (EXIT) charts. Simulation results show that these codes perform very well with an iterative decoding over the AWGN channel.
A new method for constructing quasi-cyclic (QC) low-density parity-check (LDPC) codes based on the structural properties of Euclidean geometries is presented. The proposed method changes the incidence vectors of some lines in the original Euclidean geometry method to construct much more parity check matrices and results in a large class of QC-LDPC codes with girth of at least 6. Simulations show that some codes in this class have better performance and lower error floor than the original Euclidean geometry codes.
A novel construction method with the advantages of simple construction and easy implementation encoding for quasi-cyclic low-density parity-check(QC-LDPC) codes based on Galois field(GF(q)) multiplicative group is proposed.This algorithm can flexibly adjust code length and code rate Furthermore,the complexity of the encoding and decoding is low.An irregular QC-LDPC(3843,3603) code suitable for optical communication systems is constructed by applying the proposed construction method.The simulation results show that the error-correction performance of the QC-LDPC(3843,3603) code is better than that of the classic RS(255,239) code,the LDPC code constructed by the SCG construction method,and the regular QC-LDPC(4221,3956) code.So the QC-LDPC(3843,3603) code is suitable for the high-speed long-haul optical communication systems.