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Journal of Xidian University

Improved cycle elimination algorithm for construction of QC-LDPC codes

Xudong Guo

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

A novel construction algorithm for quasi-cyclic low-density parity-check codes is proposed,with which we can obtain the improved girth of the corresponding Tanner graph by generalizing Yang et al.'s constraint for any cycle detected in the base matrix to detect and break the cycles in the parity check matrix.Compared with the existing cycle elimination(CE) algorithm,a better error performance can be achieved and cycle-8 free.Simulation results show that the proposed algorithm for constructing the irregular LDPC code of rate 1/2 achieves the performance of codeword error rate of 2×10-6at Eb/N0=1.5dB with 80 iterations by the belief-propagation decoding algorithm.

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IEEE International Conference on Progress in Informatics and Computing•Dec 1, 2015•2 citations
A novel construction algorithm for quasi-cyclic low-density parity-check codes is proposed,with which we can obtain the improved girth of the corresponding Tanner graph by generalizing Yang et al.'s constraint for any cycle detected in the base matrix to detect and break the cycles in the parity check matrix.Compared with the existing cycle elimination(CE) algorithm,a better error performance can be achieved and cycle-8 free.Simulation results show that the proposed algorithm for constructing the irregular LDPC code of rate 1/2 achieves the performance of codeword error rate of 2×10-6at Eb/N0=1.5dB with 80 iterations by the belief-propagation decoding algorithm.
Quasi-cyclic LDPC code is a kind of half-structured low density parity check code.Its block-based property leads to highly structured integrated circuits implementation,without significant performance loss.An algorithm searching shift values for the nonzero entries in base matrix of a Quasi-cyclic LDPC code is proposed along with its improved version.By expanding the Tanner graph of the corresponding expansion matrix,cycles with given length can be detected.Unlike some former algorithms,arithmetic operations are avoided,which leads to a considerable complexity reduction.Given the same base matrix with code rate 0.5 as is used in the IEEE 802.16e standard,LDPC codes constructed by the proposed algorithms have better cycle distributions and achieve slightly improved error-correction performance than the IEEE 802.16e LDPC code as well.
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.
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.
The Progressive edge-growth (PEG) algorithm was proven to be a simple and effective approach in designing Low-density parity-check (LDPC) codes. However, the Tanner graph constructed with the PEG algorithm is non-structured, which leads to random distributions of the positions of 1's in the corresponding parity-check matrix. In this paper, an improved algorithm based on the PEG algorithm for constructing quasi-cyclic (QC) LDPC codes is proposed. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. What is more important, the proposed QC-LDPC codes construction method is hardware-friendly because of its quasi-cyclic structure. Our simulation results demonstrate that the codes constructed with the proposed algorithm has better performance than the PEG algorithm over the additive white Gaussian noise (AWGN) channel and Rayleigh flat fading channel.
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.
Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes have practical significance in the field of engineering, thus their construction algorithm is a hot issue in the field of LDPC codes. Based on existing construction methods, particularly the method based on Progressive Edge-Growth (PEG) algorithm, a new construction method of shift matrix is proposed. It can effectively avoid the copy of cycle structures, especially short cycles in base matrix after extension. Besides, it also relieves the time cost caused by random search, and greatly improves the length of cycles when compared with algorithms based on methods such as quadratic congruence and arithmetic sequence. Those algorithms can only eliminate short cycles with length 4, while our method can provide QC-LDPC codes without length 6 at least. Cycle analysis and simulation results show that the newly constructed QC-LDPC codes have good cycle structure and error correction performance.