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Journal of Communications and Networks

Optimized geometric LDPC codes with quasi-cyclic structure

Xueqin Jiang, Moon Ho Lee, Shangce Gao, Yun Ping Wu

Published Jun 1, 2014• 1 citation
Publisher

Abstract

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.

DOI
10.1109/jcn.2014.000044

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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.
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