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Journal of Communications and Networks

Construction of multiple-rate quasi-cyclic LDPC codes via the hyperplane decomposing

Xueqin Jiang, Yier Yan, Moon Ho Lee

Published Jun 1, 2011• 2 citations
Publisher

Abstract

This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of q X q square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (μ-flats) and points in Euclidean geometries, respectively. By decomposing the μ -flats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.

DOI
10.1109/jcn.2011.6157428

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This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of q X q square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (μ-flats) and points in Euclidean geometries, respectively. By decomposing the μ -flats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.
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Based on the structure of parity-check matrix of RU algorithm,a class of Quasi-cycle Low-density Parity-check(QC-LDPC) codes with complexity is constructed by selecting sub-matrices reasonably to restrict and consisting of lower dual diagonal matrices.Simulation results show that not only the proposed codes have lower complexity,but also the error-correcting performance is better than QC-LDPC codes randomly constructed and practical Block-LDPC codes in the additive white Gaussion noise channel.It can get 0.3 dB Signal to Noise Ratio(SNR) gain at a Bit Error Rate(BRE) of 10-6.
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly low-density parity-check (LDPC) codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descendant codes are developed, including the characterization of the roots of the generator polynomial of a cyclic descendant code. The second part of the paper shows that cyclic and quasi-cyclic descendant LDPC codes can be derived from cyclic finite-geometry LDPC codes using the results developed in the first part of the paper. This enlarges the repertoire of cyclic LDPC codes. The third part of the paper analyzes the trapping set structure of regular LDPC codes whose parity-check matrices satisfy a certain constraint on their rows and columns. Several classes of finite-geometry and finite-field cyclic and quasi-cyclic LDPC codes with large minimum distances are shown to have no harmful trapping sets of size smaller than their minimum distances. Consequently, their error-floor performances are dominated by their minimum distances.
In this paper, a novel methodology for designing structured generalized low-density parity-check (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call low-density parity-check (LDPC) code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.