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Asia-Pacific Conference on Communications (APCC)

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

Inseon Kim, Hong‐Yeop Song

Published Nov 1, 2018• 3 citations
Publisher

Abstract

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.

DOI
10.1109/apcc.2018.8633521

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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.
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.
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds depend on graph structure parameters (like variable degrees, check node degrees, girth) of the Tanner graph and of the underlying proto-graph. Moreover, for several classes of proto-graphs we present explicit QC LDPC code constructions that achieve (or come close) to the respective minimum Hamming distance upper bounds.
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.
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.
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.
There have been lots of efforts on the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with large girth. However, most of them focus on protographs with single edges and little research has been done for the construction of QC LDPC codes lifted from protographs with multiple (i.e., parallel) edges. Compared to single-edge protographs, multiple-edge protographs have benefits such that QC LDPC codes lifted from them can potentially have larger minimum Hamming distance. In this paper, all subgraph patterns of multiple-edge protographs, which prevent QC LDPC codes from having large girth by inducing inevitable cycles, are fully investigated based on a graph-theoretic approach. By using combinatorial designs, a systematic construction method of multiple-edge protographs is proposed for regular QC LDPC codes with girth at least 12 and another method is proposed for regular QC LDPC codes with girth at least 14. Moreover, a construction algorithm of QC LDPC codes based on certain liftings of multiple-edge protographs is proposed and it is shown that the resulting QC LDPC codes have larger upper bounds on the minimum Hamming distance than those lifted from single-edge protographs. Simulation results are provided to compare the performance of the proposed QC LDPC codes with progressive edge-growth (PEG) LDPC codes and with PEG QC LDPC codes.