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Beijing Youdian Xueyuan xuebao

Nonbinary Quasi-Cyclic LDPC Codes with Efficient Richardson-Urbanke Encoding Algorithm

Xinmei Wang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

In order to implement efficient encoding,a class of nonbinary quasi-cyclic low-density parity-check(QC-LDPC) codes is proposed,which can be encoded with Richardson-Urbanke algorithm.The right part of the parity-check matrix has weight-2 columns,which allows the construction of both regular and irregular codes.Constraints on the parity-check matrix ensure a linear encoding complexity. Simulation results show that the proposed codes,when combined with higher order modulation,perform favorably with the codes constructed by the progressive-edge-growth(PEG) constructed code and close to the Shannon limits.

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In order to implement efficient encoding,a class of nonbinary quasi-cyclic low-density parity-check(QC-LDPC) codes is proposed,which can be encoded with Richardson-Urbanke algorithm.The right part of the parity-check matrix has weight-2 columns,which allows the construction of both regular and irregular codes.Constraints on the parity-check matrix ensure a linear encoding complexity. Simulation results show that the proposed codes,when combined with higher order modulation,perform favorably with the codes constructed by the progressive-edge-growth(PEG) constructed code and close to the Shannon limits.
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.
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 order to construct nonbinary low-density parity-check(LDPC) codes with good waterfall and error floor properties,a method to improve the minimum Hamming distance of a class of nonbinary quasi-cyclic(QC) LDPC codes is presented.Two upper bounds on the minimum Hamming distance are derived for the nonbinary QC LDPC codes whose parity-check matrices consist of weight-2 columns.A special base matrix design allowing linear encoding in a parallel manner is also proposed.In addition,the design principals are given,according to which,the parallel and efficiently encodable codes reaching the upper bound on the minimum Hamming distance can be developed.Simulation shows that the proposed codes have both good waterfall and error floor properties.
In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.
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.
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.