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EURASIP Journal on Wireless Communications and Networking

A construction of the high-rate regular quasi-cyclic LDPC codes

Meng Qi, Jia Xiang Zhao, Wei Min Xu, Liang Li

Published Jan 17, 2019• 3 citations
Publisher

Abstract

In this paper, a scheme to construct the high-rate regular quasi-cyclic low-density parity-check (QC-LDPC) codes is developed based on the finite geometry low-density parity-check (LDPC) codes. To achieve this, we first decompose the EG-LDPC code into a set of the block submatrices with each of them being cyclic. Utilizing the decomposed structure, we then construct an auxiliary matrix to facilitate us for identifying and eliminating 6-cycles of the block submatrices. In the simulation, seven regular QC-LDPC codes with code rates being 4/5, 7/8, 10/11, 11/12, and 12/13 of moderate code lengths are constructed with this scheme. The performances of these codes demonstrate the effectiveness of the proposed scheme.

DOI
10.1186/s13638-018-1325-9

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In this paper, a scheme to construct the high-rate regular quasi-cyclic low-density parity-check (QC-LDPC) codes is developed based on the finite geometry low-density parity-check (LDPC) codes. To achieve this, we first decompose the EG-LDPC code into a set of the block submatrices with each of them being cyclic. Utilizing the decomposed structure, we then construct an auxiliary matrix to facilitate us for identifying and eliminating 6-cycles of the block submatrices. In the simulation, seven regular QC-LDPC codes with code rates being 4/5, 7/8, 10/11, 11/12, and 12/13 of moderate code lengths are constructed with this scheme. The performances of these codes demonstrate the effectiveness of the proposed scheme.
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Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes require less hardware resources due to the quasi-cyclic structure of parity-check matrices.In this paper, two improved methods for constructing QC-LDPC codes are proposed.Firstly, in order to make sure the masked LDPC codes have flexible code rate and code length, an improved construction of masking matrix is presented.The proposed regular masking matrix of QC-LDPC codes have the girth at least 6.Then, the irregular codes are constructed by using improved finite field approach and PEG algorithm, which result in large girth and less short cycles.Simulations demonstrate that the proposed QC-LDPC codes have both lower error floor and good waterfall performance.
For a high-rate case, it is difficult to randomly construct good low-density parity-check (LDPC) codes of short and moderate lengths because their Tanner graphs are prone to have short cycles. Also, the existing high-rate quasi-cyclic (QC) LDPC codes can be constructed only for very restricted code parameters. In this paper, based on special classes of cyclic difference families, we propose a new construction method of high-rate regular QC LDPC codes having parity-check matrices consisting of a single row of circulants with column-weight 3 or 4. The proposed QC LDPC codes can be constructed for various code rates and lengths including the minimum achievable length for given column-weight and design rate under girth 6. It is observed that the parity-check matrices of the proposed QC LDPC codes have full rank for column-weight 3 and just one redundant row for column-weight 4. It is shown that the error correcting performance of the proposed QC LDPC codes of short and moderate lengths is almost the same as that of the existing ones through numerical analysis.
Motivated by the success of constructing quasi-cyclic low-density parity-check (QC-LDPC) codes based on Reed-Solomon codes, a construction method for QC-LDPC codes is presented in this paper, using the check matrices of quadratic residues codes. Three QC-LDPC codes are obtained by utilizing two quadratic residues codes of lengths less than 100, and the resultant QC-LDPC codes are regular, high-rate and free of length-4 cycles. Simulation results show that the proposed QC-LDPC codes achieves similar performance as the random LDPC codes, but they have less short cycles. In addition, the proposed (279, 158) QC-LDPC code outperforms its counterpart constructed from Reed-Solomon codes at high signal-to-noise ratios.
This paper presents a reduced-complexity iterative decoding scheme for quasi-cyclic (QC) low-density parity-check (LDPC) codes which is devised based on the section-wise cyclic structure of their parity-check matrices. The decoding scheme significantly reduces the hardware implementation complexity of a QC-LDPC code decoder in terms of the number of message processing units and the number of wires required to connect the message processing units. A long high-rate high-performance QC-LDPC code is used to demonstrate the effectiveness of the proposed decoding scheme. Using this long code as the mother code, descendant QC-LDPC codes of various lengths and rates can be constructed by puncturing and masking the columns and rows of the parity-check matrix of the mother code. These descendant codes can be decoded by deactivating specific sets of message processing units of the mother decoder.
In this paper, we proposed a novel method for constructing quasi-cyclic low-density parity-check (QC LDPC) codes based on cyclic subgroup over GF(q) . LDPC codes constructed by this method are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN) with sum product algorithm (SPA). The main advantage is that QC LDPC codes with a variety of block lengths and rates can be easily constructed with no cycles of length four or less. Simulation results show that the proposed QC LDPC codes perform slight better than the random regular LDPC codes for short to moderate block lengths. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.