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International Symposium on Medical Information and Communication Technology

A Construction Method of Doped Low-Density Parity-Check Codes Based on Quadratic Residue Codes

Yong Li, Xiang Huang, Chuan Zhou, Zhen Luo, Huihui Wu

Published Apr 14, 2021• 2 citations
Publisher

Abstract

In this paper, we propose an approach to constructing a class of doped low-density parity-check (LDPC) codes, by utilizing some coded bits of an LDPC code as the information bits of a quadratic residues (QR) code and then integrating the corresponding two Tanner graphs as a whole. Herein, the trapping set information of the LDPC code is used for selecting the information bits of the QR code. Simulation results show that the proposed doped LDPC codes achieve more than 1.4 dB and 1.0 dB gains with slight rate losses, respectively, at a frame error rate of 10-5, when compared to two regular LDPC codes.

DOI
10.1109/ismict51748.2021.9434940

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In this paper, we propose an approach to constructing a class of doped low-density parity-check (LDPC) codes, by utilizing some coded bits of an LDPC code as the information bits of a quadratic residues (QR) code and then integrating the corresponding two Tanner graphs as a whole. Herein, the trapping set information of the LDPC code is used for selecting the information bits of the QR code. Simulation results show that the proposed doped LDPC codes achieve more than 1.4 dB and 1.0 dB gains with slight rate losses, respectively, at a frame error rate of 10-5, when compared to two regular LDPC codes.
In this paper, we propose a doping approach to lower the error floor of Low-Density Parity-Check (LDPC) codes. The doping component is a short block code in which the information bits are selected from the coded bits of the dominant trapping sets of the LDPC code. Accordingly, an algorithm for selecting the information bits of the short code is proposed, and a specific two-stage decoding algorithm is presented. Simulation results demonstrate that the proposed doped LDPC code achieves up to 2.0 dB gain compared with the original LDPC code at a frame error rate of 10−6. Furthermore, the proposed design can lower the error floor of original LDPC codes.
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,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.
In this paper, a method for constructing Low-Density Parity-Check (LDPC) codes of good performance in terms of Bit Error Rate (BER) using a computer search algorithm is presented. First, LDPC codes and encoding along with its Tanner graph representation is described. Then, a detailed description of the proposed construction algorithm is given. A Modified Shortest-Path (MSP) Algorithm of lower complexity is applied to obtain a code graph of the desired structure. The proposed algorithm works directly on the parity-check matrix of the LDPC code. The parity-check matrix of the code is constructed column by column subject to the bit-degree and girth constraints. Using the proposed algorithm, both regular and irregular LDPC codes have been constructed. Furthermore, not only have the girth been improved but also the rate of LDPC codes. Finally, by simulation results the constructed codes were shown to perform well over an additive white Gaussian noise (AWGN) channel.
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.
In this paper, we propose a new approach to construct quasi-cyclic low-density parity-check (QC-LDPC) codes using Hamming codewords of weight three, namely the HM-QC-LDPC codes. Thanks to the distance property of Hamming codes, length four cycles are avoided from the Tanner graph of the constructed codes, resulting in codes of girth six. This approach can be further extended to construct QC-LDPC codes of girth eight. Our numerical results show that the proposal has a better cycle profile than the progressive-edge-growth (PEG) constructed codes, and consequently prevails in performance. Moreover, the constructed QC-LDPC code prevails the LDPC code of the IEEE802.22 standard by 0.2 dB at the bit error rate (BER) of 10-8when the codeword length is within hundreds of bits, making it a promising candidate for scenarios where strict decoding latency is imposed.