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International Conference on Computer, Control and Communication

Construction of regular quasi-cyclic LDPC codes based on cosets

Pengcheng Chen, Yuansheng Tang, Zhanghua Cao, Tingsu Yan

Published Feb 1, 2009• 0 citations
Publisher

Abstract

We propose a construction method for constructing quasi-cyclic low-density parity-check (QC LDPC) codes based on subgroup's coset. Our construction method is available not only for the prime circulants size, but also for the nonprime circulants size in some conditions. And it is showed that these conditions are easy to satisfy. Regular QC LDPC codes with various lengths and rates can be easily constructed with girth at least 6. Simulation results show that they are have almost the same performance as random regular LDPC codes over AWGN channel.

DOI
10.1109/ic4.2009.4909226

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This paper proposes a coset-based Quasi-Cyclic Low Density Parity Check(QC LDPC) construction method and similar SFT-LDPC code construction method in order to guarantee the girth under high bitrate.It gives two necessary conditions of girth at least 6 when the size of cyclic permutation matrix is a composite number.This construction method with various lengths,rates and girth at least 6 can be flexiblely constructed.Simulation results show that the code constructed by this method is comparable to random ones in error correction performance over additive white Gaussian noise channel.
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.
This paper constructs Partially Balanced Incomplete Block Designs (PBIBD) based on finite fields,and uses them to construct regular Low-Density Parity-Check(LDPC) codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for the choosing of the code rate.Further,the paper even constructs QC-LDPC codes with girth at least 8,they can also be quasi-cyclic.Simulation results show that some of the codes can have slightly better performance than random regular LDPC codes over AWGN channel.
In this paper, we proposed a novel method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes based on circulant permutation matrices via a simple quadratic congruential equation. 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 and have almost the same performance as Sridara-Fuja-Tanner codes.
In this paper, we proposed a new method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes based on circulant permutation matrices via the one-coincidence sequences. 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 and have almost the same performance as Sridara- Fuja-Tanner codes.
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.