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International Conference on Wireless Communications, Networking and Mobile Computing

Construction of Quasi Cyclic LDPC Codes Based on Girth Opt-PSO Algorithm

Hua Xu

Published Oct 1, 2008• 0 citations
Publisher

Abstract

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.

DOI
10.1109/wicom.2008.352

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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.
This article presents a highly flexible method for constructing high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes. The proposed algorithm constructs a Tanner graph formed by connecting groups of rows (check nodes) and columns (variable nodes) of the constructed code. To obtain a sub-matrix structure, rows and columns are divided into groups of equal sizes. Rows and columns in a group are connected in their numerical (positional) order to obtain a cyclic structure. Connected rows and columns must satisfy the desired minimum cycle length. We present conditions that guarantee desired girths. The proposed algorithm is by far more flexible in constructing a wide range (rates and lengths) of regular and irregular QC-LDPC codes compared to existing methods. The algorithm, which has linear complexity with respect to the number of rows or columns, provides an easy and fast way to construct QC-LDPC codes. Constructed codes show good bit error rate performances.
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.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.
This paper proposes a new technique for constructing the Quasi-Cyclic low density parity check (QC-LDPC) codes based on row division method. The new codes offer more flexibility in term of girth, code rates and codeword length. In this method of code construction, the rows are used to form as the distance graph. Then they are transformed to a parity-check matrix in order to acquire the desired girth. The new QC-LDPC codes show good bit-error rate performance as compared to the renowned Mackay codes for given values of Eb/Noby 0.12 dB at BER of10-7.
A parity-check matrix H with large girth has important significance to improve the performance of LDPC codes.And the key to the encoder implementation is the algebraic code structure.This paper proposed a novel code construction algorithm with low complexity based on the Column-Difference Search(CDS) Algorithm,which can design regular Quasi-Cyclic LDPC codes with large girth and arbitrary code rate.It has linear encoding complexity and is friendly to hardware implementation.The experimental results show that CDS-LDPC codes with different code rates perform better than Tanner codes and Array codes,which increase 0.79~3.28dB than another two classical QC-LDPC codes,and also outperform the counterparts of random codes.In addition,CDS-LDPC codes have more flexibility on the design of code length and rate.