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International Conference on Wireless Communications and Signal Processing (WCSP)

Construction of multiple-rate quasi-cyclic LDPC codes with girth eight

Jialing Li, Wen Chen, Xueqin Jiang, Xiao‐Dong Zhang, Hui-Ming Wang

Published Oct 1, 2016• 1 citation
Publisher

Abstract

This paper proposes a new approach to construct quasi-cyclic low-density parity-check (QC-LDPC) codes of girth 8. The proposed codes are based on a bipartite graph called Moore graph. By decomposing the bit nodes of the bipartite graph, the proposed QC-LDPC codes have variable code lengths and rates. Simulation results show that the proposed QC-LDPC codes have good performance with an iterative decoding over an AWGN channel.

DOI
10.1109/wcsp.2016.7752486

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This paper proposes a new approach to construct quasi-cyclic low-density parity-check (QC-LDPC) codes of girth 8. The proposed codes are based on a bipartite graph called Moore graph. By decomposing the bit nodes of the bipartite graph, the proposed QC-LDPC codes have variable code lengths and rates. Simulation results show that the proposed QC-LDPC codes have good performance with an iterative decoding over an AWGN channel.
In this paper, we propose a new approach to construct quasi-cyclic low-density parity-check (QC-LDPC) codes using Hamming codewords of weight three, namely the HM-QC-LDPC codes. Thanks to the distance property of Hamming codes, length four cycles are avoided from the Tanner graph of the constructed codes, resulting in codes of girth six. This approach can be further extended to construct QC-LDPC codes of girth eight. Our numerical results show that the proposal has a better cycle profile than the progressive-edge-growth (PEG) constructed codes, and consequently prevails in performance. Moreover, the constructed QC-LDPC code prevails the LDPC code of the IEEE802.22 standard by 0.2 dB at the bit error rate (BER) of 10-8when the codeword length is within hundreds of bits, making it a promising candidate for scenarios where strict decoding latency is imposed.
Quasi-cyclic low-density parity-check (QC-LDPC) codes are known to have algebraic structure, which suits hardware implementation. However, low girth makes their performances worse than random structured LDPC codes. Based on independent row-column mapping sequence, this work proposed a generalized method of constructing QC-LDPC codes with girth eight, which enlarges the class of girth eight QC-LDPC codes to a fairly general series. Simulation results show that the bit error rate of the constructed codes is close to that of progressive edge growth (PEG) based QC-LDPC codes under iterative decoding.
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.
For arbitrary code lengths of the form PL(P≥3L2/4+L?1),a new family of(4,L)-regular quasi-cyclic(QC) low-density parity-check(LDPC) codes was proposed explicitly with girth eight.Employing the new code as a compo-nent code in the construction method of Chinese remainder theorem(CRT),a novel class of compound QC-LDPC codes was presented with both girth at least eight and very flexible code lengths.Simulation results show that the new compound codes with rate 1/2 and moderate code lengths perform very well over the additive white Gaussian noise(AWGN) channel.
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.
In this letter, we propose a new technique to design quasi-cyclic low-density parity-check (QC-LDPC) codes with girth 8 and variable node degrees 3 and 4. Small trapping sets are avoided in the designed codes by imposing simple constraints on the cycles of length 8 in the code's Tanner graph. We also derive lower bounds on the block length of the codes that can satisfy such constraints. Simulation results are provided to demonstrate the superiority of the designed codes in comparison with similar codes in the literature.