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Journal of Circuits and Systems

Study on the Construction Method of Quasi-Cyclic LDPC Codes Based on Progressive Edge-Growth (PEG) Algorithm

Cheng Hao-hui

Published Jan 1, 2009• 5 citations
OpenAlex

Abstract

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.

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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.
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.
We present a new class of quasi-cyclic low density parity check (QC-LDPC) codes, whose quasi-cyclic nature makes them attractive for implementation. Both regular and irregular QC-LDPC codes are designed by modifying the progressive edge growth (PEG) graph with a quasi-cyclic constraint. Simulations show that these QC-LDPC codes offer hardware-friendly parity check matrices and have as good error correction performance as random LDPC codes and other good QC-LDPC codes. In addition, the proposed QC-LDPC codes offer a much more flexible set of parameters compared to the traditional designs.
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.
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.
In this paper, we propose an optimized belief propagation (OBP) based progressive edge-growth (PEG) method for constructing quasi-cyclic low density parity check (QC-LDPC) codes. In this proposed method, Tanner graphs are built by progressively appending the check nodes rather than the variable nodes. Moreover, this OBP-PEG method considers three new constraint conditions to select the QC-LDPC code sets constructed by the PEG method. Compared with the PEG-based QC-LDPC decoders, the proposed OBP-PEG decoders decrease the number of the input ports of check-node processer by up to 25%, accelerates the convergence speed by up to 11.7% in layered decoding process, and improves the success probability by up to ten times in constructing fast-convergence QC-LDPC codes.