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International Conference on Information and Communication Technology Convergence (ICTC)

Performance of Reed-Solomon Based Quasi-Cyclic LDPC Codes Based on Protograph

Inseon Kim, Hong‐Yeop Song

Published Oct 1, 2018• 0 citations
Publisher

Abstract

In this paper, we exploit construction of Reed-Solomon (RS) based Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes using protograph combining two existing QC-LDPC codes construction and experiment the performance of the codes. Two constructions have benefits: One is the construction RS based QC-LDPC codes whose girth is at least 8 and another is protograph based QC-LDPC codes to increase the upper bounds of minimum Hamming distance. We construct the protographs with three strategies and two of them have coding gain in sense of bit error rate compare to existing Reed Solomon based QC-LDPC codes.

DOI
10.1109/ictc.2018.8539649

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In this paper, we exploit construction of Reed-Solomon (RS) based Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes using protograph combining two existing QC-LDPC codes construction and experiment the performance of the codes. Two constructions have benefits: One is the construction RS based QC-LDPC codes whose girth is at least 8 and another is protograph based QC-LDPC codes to increase the upper bounds of minimum Hamming distance. We construct the protographs with three strategies and two of them have coding gain in sense of bit error rate compare to existing Reed Solomon based QC-LDPC codes.
In this paper, we propose construction of Reed-Solomon(RS) based Quasi-Cyclic Low-Density Parity-Check(QC-LDPC) codes using protograph combining two existing QC-LDPC codes construction. One is the construction RS based QC-LDPC codes whose girth is at least 8 and another is protograph based QC-LDPC codes to increase the upper bounds of minimum Hamming distance. We construct the protographs to increase the upper bound of minimum Hamming distance for Proto-RS-QC-LDPC codes and simulate some experiment to show coding gain in sense of BER compare to existing QC-LDPC codes.
Designs and constructions of quasi-cyclic (QC) LDPC codes for the AWGN channel are presented. The codes are constructed based on the conventional parity-check matrices of Reed-Solomon (RS) codes and are referred to as RS-QC-LDPC codes. Several classes of RS-QC-LDPC codes are given. Cycle structural properties of the Tanner graphs of codes in these classes are analyzed and specific methods for constructing codes with girth at least eight and reducing their short cycles are presented. The designed codes perform well in both waterfall and low error-rate regions.
Quasi-cyclic low-density parity-check (QC-LDPC) codes based on protographs are of great interest to code designers because analysis and implementation are facilitated by the protograph structure and the use of circulant permutation matrices for protograph lifting. However, these restrictions impose undesirable fixed upper limits on important code parameters, such as minimum distance and girth. In this paper, we consider an approach to constructing QC-LDPC codes that uses a two-step lifting procedure based on a protograph, and, by following this method instead of the usual one-step procedure, we obtain improved minimum distance and girth properties. We also present two new design rules for constructing good QC-LDPC codes using this two-step lifting procedure, and in each case we obtain a significant increase in minimum distance and achieve a certain guaranteed girth compared to one-step circulant-based liftings. The expected performance improvement is verified by simulation results.
Quasi-cyclic low-density parity-check (QC-LDPC) codes based on protographs are of great interest to code designers because analysis and implementation are facilitated by the protograph structure and the use of circulant permutation matrices for protograph lifting. However, these restrictions impose undesirable fixed upper limits on important code parameters, such as minimum distance and girth. In this paper, we consider an approach to constructing QC-LDPC codes that uses a two-step lifting procedure based on a protograph, and, by following this method instead of the usual one-step procedure, we obtain improved minimum distance and girth properties. We also present two new design rules for constructing good QC-LDPC codes using this two-step lifting procedure, and in each case, we obtain a significant increase in minimum distance and achieve a certain guaranteed girth compared with one-step circulant-based liftings. The expected performance improvement is verified by simulation results.
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.
Quasi-cyclic Low-Density Parity-Check (QC-LDPC) codes based on protographs are of great interest to code designers because of their implementation advantages and algebraic properties that make them easy to analyze. However, the protograph structure imposes undesirable fixed upper limits on important code parameters. In this paper, we show that the upper bound on the minimum Hamming distance of protograph-based QC codes can be improved by the careful application of a two-step lifting procedure applied to the protograph. The promised improvement is validated by constructing codes with minimum distance exceeding the upper bound for QC codes based on a particular protograph.