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IEEE International Conference on Communication Technology (ICCT)

Construction of non-binary quasi-cyclic LDPC codes based on PEG algorithm

Yuzhen Huang, Yunpeng Cheng, Yuming Zhang, Han Han

Published Nov 1, 2010• 2 citations
Publisher

Abstract

Progressive-edge-growth (PEG) algorithm is known to construct binary low-density parity-check codes at finite block lengths with very good performance. In this paper, we propose a simple method to construct quasi-cyclic extended non-binary LDPC codes based on PEG algorithm. Simulation results show that the quasi-cyclic extended non-binary LDPC codes have almost the same good error correcting performance as the non-binary LDPC codes randomly generated by PEG algorithm.

DOI
10.1109/icct.2010.5689251

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Progressive-edge-growth (PEG) algorithm is known to construct binary low-density parity-check codes at finite block lengths with very good performance. In this paper, we propose a simple method to construct quasi-cyclic extended non-binary LDPC codes based on PEG algorithm. Simulation results show that the quasi-cyclic extended non-binary LDPC codes have almost the same good error correcting performance as the non-binary LDPC codes randomly generated by PEG algorithm.
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.
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.
Progressive-Edge-Growth(PEG) algorithm is an efficient method for constructing LDPC codes with short and intermediate block lengths.However,the complexity of codes produced directly by this algorithm is proportional to quadratic length of the codes,which restricts the implementation of the LDPC codes.To solve the problem,a method was proposed for constructing quasi-cycle extension LDPC codes with low encoding complexity and good error performance.Based on PEG algorithm,a base matrix with an approximate lower triangular was constructed,then all its elements were replaced by circulation permutations.The new method could eliminate the short cycles effectively without changing the degree distribution fraction of the basic matrix.The simulation results show that: compared with LDPC codes generated by PEG algorithm,the LDPC codes presented here have lower encoding complexity and better error performance,which is easy for implementation with hardware.
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.
We propose a general method for constructing regular and irregular quasi-cyclic LDPC codes based on the modified PEG (progressive edge growth) graph. The idea of permutation vector is introduced. Through permutation vectors, the QC-LDPC codes based on arbitrary circulant permutation matrices, which are not limited to identity matrix, Q-matrix or D-matrix, can be generated with flexible parameters such as block length, code rate, degree distribution. Simulation results demonstrate that QC-LDPC codes using the new PEG algorithm show an error correction performance comparable to the random LDPC codes based on the traditional PEG algorithm. In addition, the PEG QC-LDPC codes have more hardware-friendly parity check matrices than the random PEG LDPC codes and can fulfill linear-time encoding. The QC-LDPC codes based on D-matrix and Q-matrix are more suitable to be used in QC-LDPC codes than identity matrix because they outperform that of identity matrix by 0.1-0.2 dB in the new PEG algorithm.