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International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS)

Quasi Cyclic-LDPC codes based on PEG algorithm with maximized girth property

Patanasak Prompakdee, Watid Phakphisut, Pornchai Supnithi

Published Dec 1, 2011• 9 citations
Publisher

Abstract

In this paper, we propose a method to construct parity-check matrices of Quasi Cyclic (QC) LDPC codes based on the progressive edge-growth (PEG) algorithm with maximized girth property. The proposed algorithm can eliminate short cycles and improve the decoding performance. Simulation results illustrate that the codes constructed with the proposed algorithm have superior performance to the previous PEG-QC codes over the additive white Gaussian noise (AWGN) channel. At the BER of 10-7, the coding gain of 0.005 dB.

DOI
10.1109/ispacs.2011.6146165

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In this paper, we propose a method to construct parity-check matrices of Quasi Cyclic (QC) LDPC codes based on the progressive edge-growth (PEG) algorithm with maximized girth property. The proposed algorithm can eliminate short cycles and improve the decoding performance. Simulation results illustrate that the codes constructed with the proposed algorithm have superior performance to the previous PEG-QC codes over the additive white Gaussian noise (AWGN) channel. At the BER of 10-7, the coding gain of 0.005 dB.
In this paper, we propose the construction of quasi-cyclic (QC) LDPC codes based on the modified progressive edge-growth (PEG) algorithm to achieve the maximum local girth. Although the previously designed QC-LDPC codes based on the PEG algorithm has more flexible code rates than the conventional QC-LDPC code, in the design process, multiple choices of the edges may be chosen. In the proposed algorithm, we aim to maximize the girth property by choosing the suitable edges and thus improve the error correcting performance. Simulation results show that the QC-LDPC codes constructed from the proposed method give higher proportion of high local girths than other methods, particularly, at high code rates. In addition, the proposed codes offer superior bit error rate and block error rate performances to the previous PEG-QC codes over the additive white Gaussian noise (AWGN) channel.
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.
Progressive Edge-Growth(PEG) algorithm is a method for constructing Low Density Parity-Check(LDPC) codes based on Tanner graph.Studies show that LDPC codes constructed with the algorithm can achieve excellent error-correcting performance.Based on the algorithm,the Quasi-Cyclic(QC) LDPC codes are proposed in this paper and simulations show that the QC-LDPC codes have almost the same excellent performance as the random codes constructed with the PEG algorithm.In addition,these codes have the property of quasi-cyclic structure,and the encoding and decoding can be implemented with simple shift registers.Besides,the code rates of the LDPC codes constructed with the proposed algorithm are more flexible to be adjusted.
Based on cycle search algorithm and Progressive Edge Growth(PEG) algorithm,this paper proposes a method to construct quasi-cyclic Low-density Parity Check(LDPC) codes with big girth and linear-encoding complexity.A parity-check matrix with a form of approximate lower triangle structure is designed to achieve iterative encoding with linear-encoding complexity.PEG algorithm is used to construct the base matrix and the cycle search algorithm is used to optimize the cycle distribution.And a fast encoding method is proposed.Experimental results show that the LDPC codes constructed with the proposed method can avoid error floor and achieve better BER performance than Tanner-QC-LDPC codes and equivalent BER performance to the ones of random codes.
A novel construction for quasi-cyclic (QC) regular and irregular low-density parity-check (LDPC) codes based on a modification of the QC Progressive Edge Growth (PEG) algorithm is presented. Edge placement of the PEG-based algorithm is enhanced by use of the sum-product algorithm in the design of the parity-check matrix. The proposed algorithm is highly flexible in block length and rate, in particular when compared with algebraic constructions. The codes constructed by the proposed methods are tested in the AWGN channel and performance improvements are achieved. The proposed QC-LDPC codes provide an inherent trade-off between code performance and encoding/decoding complexity.
Since LDPC code based on progressive edge growth(PEG) algorithm construction still has many small cycles in the case of maximization of local girth,make use of polynomial cycle(PC) mark to improve PEG algorithm to be enhanced PC-PEG algorithm is proposed in this paper,and it is applied in QC-LDPC.This approach can reduce the number of small circles and improve the performance under the maximization of local girth.By using of QC-LDPC,the parity check matrix is still block based cyclic shift code,this special structure can realize parallel decoding in the engineering and save the storage memory.The experimental results demonstrate that the proposed method has smaller number of girth compared with PEG algorithm,and the special structure of cyclic shift ensures parallel decoding with the same decoding performance.