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International Conference on Advanced Information Networking and Applications (AINA)

Design of Quasi-Cyclic LDPC Codes Based on Euclidean Geometries

Yuanhua Liu, Xinmei Wang, Jianhua Ma

Published Jan 1, 2009• 7 citations
Publisher

Abstract

This paper presents an algebraic method for constructing quasi-cyclic (QC) low-density parity-check (LDPC) codes based on the structural properties of Euclidean geometries. The construction method results in a class of QC-LDPC codes with girth of at least 6. Codes in this class perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing QC Euclidean geometry LDPC codes.

DOI
10.1109/aina.2009.35

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This paper presents an algebraic method for constructing quasi-cyclic (QC) low-density parity-check (LDPC) codes based on the structural properties of Euclidean geometries. The construction method results in a class of QC-LDPC codes with girth of at least 6. Codes in this class perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing QC Euclidean geometry LDPC codes.
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.
This paper presents an improved Euclidean geometry (EG) method for constructing parity check matrix of quasi-cyclic low-density parity-check (QC-LDPC) codes to decrease the performance degradation of short cycles to the iterative decoding. The new method results in a class of QC-LDPC codes with much fewer short cycles than usual EG-LDPC codes with the same parameters. Simulation results show that the designed QC-LDPC codes with fewer short cycles perform better than the existing Euclidean geometry LDPC codes under iterative decoding.
This paper,based on algebra and graph,proposes a method for constructing structured low-density parity-check(LDPC) codes.In this method,the authors design a connected graph with three kinds of special path to ensure that the Tanner graph of the parity check matrix mapped from the connected graph is without short cycles.The construction method results in two classes of(3,k)-regular quasi-cyclic LDPC codes with girth 8 and 12 respectively.Furthermore,by extending this construction method,two classes of LDPC codes with column weight 2,whose girths are respectively 16 and 24,can be obtained.The simulation studies show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channels with iterative decoding.At the BER of 10-5,the new proposed(3,6)-regular(4356,2205) QC-LDPC code performs 1.48dB from the Shannon limit.Moreover,it outperforms the random regular LDPC code of comparable parameters by 0.1dB.For the new proposed structured LDPC codes with column weight 2,they can achieve about 2dB coding gains with respect to the random regular LDPC codes with similar block lengths and code rates.
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.