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International Conference on Emerging Intelligent Data and Web Technologies

The Systematic Form of a Class of Regular Structured LDPC Codes

Xiuni Wang, Dongqing Xie

Published Sep 1, 2013• 0 citations
Publisher

Abstract

In this paper, we propose a systematic form about a class of regular structured LDPC codes. This class of LDPC codes is quasi-cyclic code with variable node degree dv= 2 on the Tanner graph. The defining parity-check matrices are composed of circulant permutation matrices. By columns permutation, we can locate the information bits and parity check bits easily. Furthermore, the values of associated parity check bits can be calculated directly on the Tanner graph.

DOI
10.1109/eidwt.2013.116

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In this paper, we propose a systematic form about a class of regular structured LDPC codes. This class of LDPC codes is quasi-cyclic code with variable node degree dv= 2 on the Tanner graph. The defining parity-check matrices are composed of circulant permutation matrices. By columns permutation, we can locate the information bits and parity check bits easily. Furthermore, the values of associated parity check bits can be calculated directly on the Tanner graph.
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Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.
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.
An approach for studying quasi-cyclic codes based on matrix transformations via Fourier transforms and row and column permutations is presented. These transformations put a parity-check matrix in the form of an array of circulant matrices into a diagonal array of matrices of the same size over an extension field. The approach is used to characterize certain structural properties of low-density parity-check (LDPC) codes such as the girths of their Tanner graphs. Many constructions of quasi-cyclic LDPC codes can be unified under the proposed approach.
To reduce the cycles in the Tanner graph which may affect the code performance,a recursive method to construct low-density parity-check(LDPC) codes was proposed.The method used a parity-check matrix of a short LDPC code as its mother matrix upon which a long code was constructed with circulant permutation matrices.By choosing the circulant permutation matrix parameters properly,the number of cycles having a given length in the Tanner graph of the constructed long codes were equal to or less than that of the short code.Either regular or irregular LDPC codes were constructed.Simulation results show that the LDPC codes constructed by this method have very low error-floor and almost no performance degradation due to their special structure as compared with random LDPC codes.
This paper shows that a cyclic code can be put into quasi-cyclic form by decomposing a circular parity-check matrix through column and row permutations. Such a decomposition of a circular parity-check matrix of a cyclic code produces a group of shorter cyclic or quasi-cyclic codes and leads to a new method for constructing long cyclic codes from short cyclic codes. Also in this paper, new classes of cyclic and quasi-cyclic LDPC codes are derived from cyclic Euclidean geometry LDPC codes by decomposing their circular parity-check matrices. These new LDPC codes perform well and enlarge the repertoire of cyclic and quasi-cyclic LDPC codes.