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IEEE Vehicular Technology Conference

Regular and Irregular Quasi-Cyclic LDPC Codes

Xueqin Jiang, Moon Ho Lee, Jia Hou

Published May 1, 2011• 0 citations
Publisher

Abstract

This paper presents methods to the construction of regular and irregular low-density parity-check (LDPC) codes based on Euclidean geometries. Codes constructed by these methods are quasi-cyclic. The degree distributions of proposed LDPC codes can be optimized by the curve fitting approach in the extrinsic information transfer (EXIT) charts. Simulation results show that these codes perform very well with the iterative decoding.

DOI
10.1109/vetecs.2011.5956127

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This paper presents methods to the construction of regular and irregular low-density parity-check (LDPC) codes based on Euclidean geometries. Codes constructed by these methods are quasi-cyclic. The degree distributions of proposed LDPC codes can be optimized by the curve fitting approach in the extrinsic information transfer (EXIT) charts. Simulation results show that these 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.
An efficient method of constructing irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes is proposed. In order to find the degree distribution with low convergence threshold, the extrinsic information transfer (EXIT) chart is utilized to optimize the degree distribution of LDPC codes. Then, a modified progressive edge growth (PEG) algorithm is used to get the mask matrix with the optimal degree distribution. Finally, the parity-check matrix of QC LDPC code is constructed based on the mask matrix, and the shift values are optimized to eliminate short cycles. Simulation results show that the constructed irregular QC LDPC codes with optimized degree distribution significantly outperform the regular QC LDPC codes in the additive white Gaussion noise (AWGN) channel.
Two algebraic methods for systematic construction of structured regular and irregular low-density parity-check (LDPC) codes with girth of at least six and good minimum distances are presented. These two methods are based on geometry decomposition and a masking technique. Numerical results show that the codes constructed by these methods perform close to the Shannon limit and as well as random-like LDPC codes. Furthermore, they have low error floors and their iterative decoding converges very fast. The masking technique greatly simplifies the random-like construction of irregular LDPC codes designed on the basis of the degree distributions of their code graphs