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IET International Conference on Wireless, Mobile and Multimedia Networks (ICWMMN)

Construction of QC-LDPC codes based on PSO algorithm

Yang Yang, Xiao Yang

Published Jan 1, 2011• 0 citations
Publisher

Abstract

The well known Tanner codes are not encodable, in this paper, we derived an encodable QC LDPC codes and use PSO algorithm to determine the parameters of the parity check matrices of the QC LDPC codes. The proposed PSO code construction considers the girth 4 and BER performance to be the constrained conditions in the fitness function of PSO algorithm. Simulation results show that the QC codes constructed by the proposed method have better performance than that of random LDPC codes.

DOI
10.1049/cp.2011.0971

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The well known Tanner codes are not encodable, in this paper, we derived an encodable QC LDPC codes and use PSO algorithm to determine the parameters of the parity check matrices of the QC LDPC codes. The proposed PSO code construction considers the girth 4 and BER performance to be the constrained conditions in the fitness function of PSO algorithm. Simulation results show that the QC codes constructed by the proposed method have better performance than that of random LDPC codes.
The QC(quasi-cyclic) LDPC codes are an important subclass of LDPC codes. The key to improving the performance of QC LDPC codes is how to construct a parity-check matrix H with a girth distribution as good as possible. In this paper, method of girth detection of QC LDPC codes is described first. Furthermore, a novel algorithm, GirthOpt-PSO algorithm, is proposed to construct the QC LDPC codes, which achieves a good girth distribution based on the PSO algorithm. Simulation results show that the performance of the QC LDPC codes constructed by proposed algorithm is better than Tanner code and Array codes. Besides, the proposed algorithm is more flexible for designing the QC LDPC codes with desired block length and rate as well as good girth.
To solve the problem of the girth 4 which will lead to a serious decrease in the performance of quasi-cyclic low-density parity-check(QC LDPC) codes,this paper presents the necessary and sufficient conditions of Tanner codes without girth 4 in the form of several theorems.These theorems can be used as the constraint conditions for the construction of Tanner codes.To construct the Tanner codes without girth 4 needs to adjust the dimension and the shift factors of the circulant matrices of the given sparse parity-check matrices according to the proposed theorems.Examples are provided to verify the theorems,and computer simulation results show that the Tanner codes obtained by proposed constructions achieve good BER performance compared with that of randomly constructed LDPC codes.
Encoding of computer-generated random low-density parity-check(LDPC) codes can be rather complex.QC-LDPC codes have encoding advantage over random LDPC codes.Encoding of an QC-LDPC code can be implemented using shift-registers with linear complexity.The usual algorithm for the decoding of LDPC codes is the iterative sum-product algorithm(SPA),operating on a Tanner graph of the code.It is well known that cycle-free Tanner graph with SPA algorithm yeilds optimal decoding.The girth of the cycle -free Tanner graph is infinite.In this paper,we present an algebraic method for constructing binary QC-LDPC codes based on the rowcolumn constraint.The codes constructed by this method have girths at least 6.Experimental results show that the constructed LDPC codes decoded with SPA over the AWGN channel can perform as well as standard LDPC codes in terms of bit-error probability and block error probability.
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.
SUMMARY Low encoding complexity is very important for quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes used in wireless communication systems. In this paper, a new scheme is presented to construct QC‐LDPC codes with low encoding complexity. This scheme is called two‐stage particle swarm optimization (TS‐PSO) algorithm, in which both the threshold and girth distribution of QC‐LDPC codes are considered. The proposed scheme is composed of two stages. In the first stage, we construct a binary base matrix of QC‐LDPC code with the best threshold. The matrix is constructed by combining a binary PSO algorithm and the protograph extrinsic information transfer (PEXIT) method. In the second stage, we search an exponent matrix of the QC‐LDPC code with the best girth distribution. This exponent matrix is based on the base matrix obtained in the first stage. Consequently, the parity‐check matrix of the QC‐LDPC code with the best threshold and best girth distribution are constructed. Furthermore, bit error rate performances are compared for the QC‐LDPC codes constructed by proposed scheme, the QC‐LDPC code in 802.16e standard, and the QC‐LDPC code in Tam's study. Simulation results show that the QC‐LDPC codes proposed in this study are superior to both the 802.16e code and the Tam code on the additive white Gaussian noise (AWGN) and Rayleigh channels. Moreover, proposed scheme is easily implemented, and is flexible and effective for constructing QC‐LDPC codes with low encoding complexity. Copyright © 2012 John Wiley & Sons, Ltd.
The existing design of quasi-cyclic(QC) low-density parity-check(LDPC) codes has not considered the problems of short length girths and the rows' dependency.The first problem leads to the BER performance of QC LDPC codes to be much poorer than that of randomly constructed LDPC codes,while the second problem leads to the difficulty of construction of generator matrices from parity-check matrices.To solve the first problem,the constraint conditions for designing the QC LDPC codes are proposed,and the dimension and shift factors of the circulant matrices of the given sparse parity-check matrix are adjusted according to the test results of both girth 4 and girth 6.To solve the second problem,an approach of irregular QC LDPC codes is proposed.The proposed approach is to replace some sub-matrices by zero matrices and identity matrices at special positions in the given sparse parity-check matrix so as to get a nonsingular square matrix for the construction of the generator matrix.Though adopting bidiagonal submatrices in parity-check matrix can solve the rows' dependency problem,many code words with low weights will occur,which leads to the BER performance can not be better by increasing code lengths.Examples are provided for the proposed design of QC LDPC codes,and computer simulation results show that the proposed QC LDPC codes achieve good BER performance.