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JOURNAL OF ELECTRONICS INFORMATION TECHNOLOGY

Optimization of Construction and Encoding for Finite Length Irregular LDPC Codes

N Cetc

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The main influence for the performance of finite length Low-Density Parity-Check(LDPC) codes is analyzed. According to optimum choice for degree distribution, a check matrix is constructed with improved Progressive-Edge-Growth (PEG) algorithm. A practical efficient encoding algorithm is proposed to optimize the check matrix. A finite length irregular LDPC code with low error-floor performance and approximate linear encoding complexity is obtained. This optimization method can be easily extended to general communication channels.

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The main influence for the performance of finite length Low-Density Parity-Check(LDPC) codes is analyzed. According to optimum choice for degree distribution, a check matrix is constructed with improved Progressive-Edge-Growth (PEG) algorithm. A practical efficient encoding algorithm is proposed to optimize the check matrix. A finite length irregular LDPC code with low error-floor performance and approximate linear encoding complexity is obtained. This optimization method can be easily extended to general communication channels.
A novel construction for irregular low-density parity-check (LDPC) codes based on a modification of the Progressive Edge Growth (PEG) algorithm is presented. Edge placement of the PEG 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. The codes constructed by the proposed methods are tested in the AWGN channel and significant performance improvements are achieved. The flexibility of the proposed decoder optimisation operation is then shown by its use in modifying the Improved PEG (IPEG) algorithm to achieve further performance gains.
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.
In this paper, we present a construction method based on the progressive edge-growth (PEG) algorithm to design irregular low-density parity-check (LDPC) codes without small stopping sets. We show how to choose the connections in the PEG algorithm when having multiple choices to connect a variable node with a check node. Since preventing small stopping sets also prevents a low minimum distance, our construction method also leads to LDPC codes with a higher minimum distance. Furthermore, we show by simulation that our construction method improves the performance over the binary erasure channel and over the additive white Gaussian noise channel for a low erasure probability and a high signal-to-noise ratio, respectively.
The progressive-edge-growth (PEG) algorithm of Hu et al. is modified to improve the error floor performance of the constructed low-density parity-check (LDPC) codes. To improve the error floor, the original PEG algorithm is equipped with an efficient algorithm to find the dominant elementary trapping sets (ETS's) that are added to the Tanner graph of the under-construction code by the addition of each variable node and its adjacent edges. The aim is to select the edges, among the candidates available at each step of the original PEG algorithm, that prevent the creation of dominant ETS's. The proposed method is applicable to both regular and irregular variable node degree distributions. Simulation results are presented to demonstrate the superior ETS distribution and error floor performance of the constructed codes compared to similar codes constructed by the original and other modifications of the PEG algorithm.
In this paper, we are concerned with the finite-length analysis of low-density parity-check (LDPC) codes when used over additive white Gaussian noise (AWGN) channels. We present the iterative decoding algorithm of LDPC codes, and we also discuss the encoding methods and the bipartite graph representation of LDPC codes ensemble. Finite-length LDPC code performances are investigated, and the influence of cycle is pointed out. Simulation results show that irregular LDPC codes with variable and check node degree distribution optimized for infinite-length codes are not optimal for finite-length LDPC codes, and the error patterns of both regular and irregular codes are investigated as an effort to improve the performance and design methodology of finite-length LDPC codes.
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.