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Performance Analysis and Design of (3,ρ) — Regular Quasi Cyclic LDPC Codes

Xu Xia, Moon Ho Lee, Choi Seung Je, Moon Myung Ryong

Published Dec 10, 2005• 0 citations
Publisher

Abstract

In this paper we construct a novel family of (3,rho)-regular quasi-cyclic (QC) low-density parity-check (LDPC) codes, derived from permutation theorem for Latin squares, when used over binary input additive white Gaussian noise (BIAWGN) channel. The codes have high code rate, girth absence of 4, good minimum distance, and sparse parity check matrices. They are designed to perform well when iteratively decoding with sum-product decoding algorithm and to allow low complexity encoding

DOI
10.1109/wirles.2005.1549580

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In this paper we construct a novel family of (3,rho)-regular quasi-cyclic (QC) low-density parity-check (LDPC) codes, derived from permutation theorem for Latin squares, when used over binary input additive white Gaussian noise (BIAWGN) channel. The codes have high code rate, girth absence of 4, good minimum distance, and sparse parity check matrices. They are designed to perform well when iteratively decoding with sum-product decoding algorithm and to allow low complexity encoding
This correspondence presents a construction of quasicyclic (QC) low-density parity-check (LDPC) codes based on a special type of combinatorial designs known as block disjoint difference families (BDDFs). The proposed construction of QC-LDPC codes gives parity-check matrices with column weight three and Tanner graphs having a girth lower-bounded by 6. The proposed QC-LDPC codes provide an excellent performance with iterative decoding over an additive white Gaussian-noise (AWGN) channel. Performance analysis shows that the proposed short and moderate length QC-LDPC codes perform as well as their competitors in the lower signal-to-noise ratio (SNR) region but outperform in the higher SNR region. Also, the codes constructed are quasicyclic in nature, so the encoding can be done with simple shift-register circuits with linear complexity.
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.
Quasi-cyclic codes are the most promising class of structured LDPC codes due to their ease of implementation and excellent performance over noisy channels when decoded with message-passing algorithms as extensive simulation studies have shown. An approach for constructing quasi-cyclic LDPC codes based on Latin squares over finite fields is presented. By analyzing the parity-check matrices of these codes, expressions for their ranks are derived. Experimental results show that, with iterative decoding algorithms, the constructed codes perform very well over the AWGN and the binary erasure channels.