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IEEE Communications Letters

Construction of Irregular QC-LDPC Codes via Masking with ACE Optimization

Guojun Han, Yong Liang Guan, Lingjun Kong

Published Jan 31, 2014• 34 citations
Publisher

Abstract

Quasi-cyclic low-density parity-check (QC-LDPC) codes constructed by using algebraic approaches, such as finite geometry and finite field, generally have good structural properties and very low error-floors, and facilitate hardware implementation. Irregular QC-LDPC codes constructed from such QC-LDPC codes by using the masking technique, when decoded with the sum-product algorithm (SPA), have low decoding complexity, but often show early error-floors. In this paper, the relationship of cycle, girth and approximate cycle EMD (ACE) between the masking matrix and masked matrix is investigated, and the ACE algorithm is modified and used to construct the masking matrix for irregular QC-LDPC codes. Simulations demonstrate that the codes constructed by masking with ACE optimization exhibit much improved waterfall performance and lower error floors.

DOI
10.1109/lcomm.2014.010214.132463

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Quasi-cyclic low-density parity-check (QC-LDPC) codes constructed by using algebraic approaches, such as finite geometry and finite field, generally have good structural properties and very low error-floors, and facilitate hardware implementation. Irregular QC-LDPC codes constructed from such QC-LDPC codes by using the masking technique, when decoded with the sum-product algorithm (SPA), have low decoding complexity, but often show early error-floors. In this paper, the relationship of cycle, girth and approximate cycle EMD (ACE) between the masking matrix and masked matrix is investigated, and the ACE algorithm is modified and used to construct the masking matrix for irregular QC-LDPC codes. Simulations demonstrate that the codes constructed by masking with ACE optimization exhibit much improved waterfall performance and lower error floors.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes require less hardware resources due to the quasi-cyclic structure of parity-check matrices.In this paper, two improved methods for constructing QC-LDPC codes are proposed.Firstly, in order to make sure the masked LDPC codes have flexible code rate and code length, an improved construction of masking matrix is presented.The proposed regular masking matrix of QC-LDPC codes have the girth at least 6.Then, the irregular codes are constructed by using improved finite field approach and PEG algorithm, which result in large girth and less short cycles.Simulations demonstrate that the proposed QC-LDPC codes have both lower error floor and good waterfall performance.
This paper presents a simple and very flexible method for constructing quasi-cyclic (QC) low density paritycheck (LDPC) codes based on finite fields. The code construction is based on two arbitrary subsets of elements from a given field. Some well known constructions of QC-LDPC codes based on finite fields and combinatorial designs are special cases of the proposed construction. The proposed construction in conjunction with a technique, known as masking, results in codes whose Tanner graphs have girth 8 or larger. Experimental results show that codes constructed using the proposed construction perform well and have low error-floors. Also presented in the paper is a reduced-complexity iterative decoding scheme for QC-LDPC codes based on the section-wise cyclic structure of their parity-check matrices. The proposed decoding scheme is an improvement of an earlier proposed reduced-complexity iterative decoding scheme.
A modified construction method of LDPC (Low-density Parity-check) codes based on polynomial of cycles of PEG (Progressive-Edge-Growth) is proposed according to reaction on the performance of LDPC codes by polynomial of cycles based on PEG and connectivity of cycles. It can reduce the number of the shortest cycles, increase average local girth and improve connectivity of cycles while deleting short cycles by considering girth of check matrix, number of the shortest cycles and ACE (Approximate Cycle EMD), so that it can improve performance of decoding. At the same time, a construction method of QC-LDPC (quasi-cyclic-LDPC) codes based on ACE and polynomial of cycles of PEG is also proposed to deal with the complexity of implementation on hardware of unstructured codes. Simulation results show that the performance of this code is better than unstructured Mackay code and it is easier for implementation on hardware.
An efficient method of constructing irregular quasi-cyclic (QC) low-density parity-check (LDPC) codes is proposed. In order to find the degree distribution with low convergence threshold, the extrinsic information transfer (EXIT) chart is utilized to optimize the degree distribution of LDPC codes. Then, a modified progressive edge growth (PEG) algorithm is used to get the mask matrix with the optimal degree distribution. Finally, the parity-check matrix of QC LDPC code is constructed based on the mask matrix, and the shift values are optimized to eliminate short cycles. Simulation results show that the constructed irregular QC LDPC codes with optimized degree distribution significantly outperform the regular QC LDPC codes in the additive white Gaussion noise (AWGN) channel.
In this paper, we consider the construction of irregular QC-LDPC codes by jointly optimizing the girth, the number and approximate cycle extrinsic message degree (ACE) of short cycles to further improve the error-floor performance of irregular QC-LDPC codes with given degree distributions. By selecting the best edges, each of which must make the cycles consisting of the current variable node have the best lower bound of ACE or the minimum number of cycles with ACE lower bound, for each variable node via the progressive Edge growth (PEG) approaches, irregular QC-LDPC codes with better tradeoff between girth, the shortest cycle number and ACE could be constructed. Simulation results show that the proposed codes achieve better error-floor performance compared with the codes using the same degree distributions constructed by the recent proposed methods.