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IEEE Asia Pacific Conference on Circuits and Systems (APCCAS)

Improvements of quasi-cyclic low-density parity-check codes based on hybrid structures of BIBD's schemes

Chao-Chin Yang, Jen-Fa Huang, Ta-Chun Nieh, Chun-Ming Huang

Published Dec 1, 2012• 1 citation
Publisher

Abstract

In this paper, we propose a simple mathematical structure to improve the BER (bit error rate) performance of quasi-cyclic low-density parity-check (QC-LDPC) codes. Since the proposed structure can be defined in-between those of random codes and structured codes, these proposed QC-LDPC codes not only perform as well as random-LDPC codes, but also preserve the advantage of structured LDPC codes which is easier to implement over coding hardware. Moreover, the proposed structure, constructed from balanced incomplete block design (BIBD), can reduce the density of parity-check matrix and hence reduce the number of short cycles, which generally lead to better performance. At the end, we show that the error floor performance of QC-LDPC codes can be improved by proposed hybrid structures and perform well over binary-input additive white Gaussian noise (BI-AWGN) channel.

DOI
10.1109/apccas.2012.6418989

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In this paper, we propose a simple mathematical structure to improve the BER (bit error rate) performance of quasi-cyclic low-density parity-check (QC-LDPC) codes. Since the proposed structure can be defined in-between those of random codes and structured codes, these proposed QC-LDPC codes not only perform as well as random-LDPC codes, but also preserve the advantage of structured LDPC codes which is easier to implement over coding hardware. Moreover, the proposed structure, constructed from balanced incomplete block design (BIBD), can reduce the density of parity-check matrix and hence reduce the number of short cycles, which generally lead to better performance. At the end, we show that the error floor performance of QC-LDPC codes can be improved by proposed hybrid structures and perform well over binary-input additive white Gaussian noise (BI-AWGN) channel.
Two classes of well-structured binary low-density parity check codes (LDPC) are described. The first class is based on a branch of combinatorial mathematics, known as the balanced incomplete block design (BIBD). Construction of three types of codes derived from BIBD designs is illustrated in addition to a family of LDPC codes constructed by decomposition of incidence matrices of the proposed BIBD designs. The decomposition technique reduces the density of the parity check matrix and hence reduces the number of short cycles, which generally lead to better performing LDPC codes. The second class of well-structured LDPC codes, Vandermonde or array LDPC codes, are defined by a small number of parameters and cover a large set of code lengths and rates with different column weights. The presented LDPC codes are quasi-cyclic with no cycles of length four; hence simple encoding while maintaining good performance is achieved. Furthermore, the codes are compared with known random LDPC codes, in order to assess their relative achievable performance/complexity trade-offs. It is shown that well-structured LDPC codes perform very similar to the known random LDPC codes.
A method to construct a flexible length or rate of quasi-cyclic Low Density Parity Check(LDPC) codes based on Balanced Incomplete Block Design(BIBD) and cycle permutation matrix is proposed.Based on actual demand,the corresponding template matrix is constructed by BIBD method.The template matrix is extended by the appropriate cycle permutation matrix.The quasi-cyclic LDPC codes constructed by the proposed method have a good structure and flexibility.This method improves the efficiency of construction good codes which meet the needs of a practical application.Simulations show that quasi-cyclic LDPC codes constructed by the proposed method perform well over AWGN channels with iterative decoding and have a lower error floor.
Due to quasi-cyclic structure of parity-check matrices, Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes reduce hardware requirements, and thus they have a higher practical value than random LDPC codes. This paper proposes an improved construction method of QC-LDPC based on PEG Algorithm, and the girth of the QC-LDPC codes has an increase of 2. Firstly, a base matrix is generated by the PEG algorithm, and then the base matrix is expanded using the unit circle permutation matrix, at the same time, the short loop of the base matrix is eliminated. This approach has the advantages of the PEG algorithm and the QC-LDPC codes, and simulation results show that bit error rate (BER) performance of the QC-LDPC codes presented in this paper is the same as or exceeds the one of randomly constructed LDPC codes.
In this paper, a novel methodology for designing structured generalized low-density parity-check (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call low-density parity-check (LDPC) code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.
A novel construction method of Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) code is proposed in this paper, which is based on protograph and Balanced Block Design (BIBD) in combinational mathematics.The method is to fill the base matrix of protograph with the base set elements of BIBD in accordance with certain mathematical rules.And the base matrix of protograph proposed in the paper has special double diagonal structure, which overcomes the low weight code words in general structure and achieves rapid encoding at the same time.The QC-LDPC code in this paper possesses lower encoding complexity and less memory occupation; therefore it is easy for hardware implementation.In addition, it effectively avoids girth 4. Simulation results show that when the Bit Error Rate (BER) is 10 -7 , QC-LDPC codes based on Protograph and BIBD (PBIBD-LDPC) proposed in this paper has 0.5dB Net Coding Gain (NCG) compared with the protograph QC-LDPC codes that based on Vander monde matrix and PEG algorithm structure, and has 0.15dB NCG compared with the excellent code QC-LDPC that based on the lifting structure.