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Journal of Henan University of Science & Technology

An Improved ACE Algorithm Based on Structural Optimization LDPC

Wang Li

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

In order to improve the performance of LDPC code,an optimized LDPC code was constructed by calculating extrinsic message degree of the cycle.This algorithm can remove the short cycle,which is produced unavoidably in constructing LDPC codes,to improve a bipartite graph local connectivity.Experimental results show that the algorithm is better to improve LDPC codes' performance in the same code length,code rate and the degree distribution.

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International Conference on Signal Processing and Communication Systems•Dec 1, 2016•6 citations
In order to improve the performance of LDPC code,an optimized LDPC code was constructed by calculating extrinsic message degree of the cycle.This algorithm can remove the short cycle,which is produced unavoidably in constructing LDPC codes,to improve a bipartite graph local connectivity.Experimental results show that the algorithm is better to improve LDPC codes' performance in the same code length,code rate and the degree distribution.
Recently, structured LDPC codes have been focused on due to excellent performance and lower complexity. An improved construction of QC-LDPC based on a modified PEG algorithm is proposed in this paper. The modified Progressive Edge-Growth algorithm is a PEG algorithm with Approximated Cycle Extrinsic Message Degree (ACE) metric, which is used to describe the connectivity of cycles. The approach can maximize the girth of the cycles, improve the connectivity of cycles and have the advantages of QC algorithms. The simulation results demonstrate that the PEG algorithm based on ACE has lower Bit Error Rate (BER) and Frame Error Rate (FER) than the original PEG algorithm at the low Signal Noise Ratio (SNR) values, and has a relatively lower computational complexity.
In this paper, we consider the construction of irregular QC-LDPC codes by jointly optimizing the girth, the number and approximate cycle extrinsic message degree (ACE) of short cycles to further improve the error-floor performance of irregular QC-LDPC codes with given degree distributions. By selecting the best edges, each of which must make the cycles consisting of the current variable node have the best lower bound of ACE or the minimum number of cycles with ACE lower bound, for each variable node via the progressive Edge growth (PEG) approaches, irregular QC-LDPC codes with better tradeoff between girth, the shortest cycle number and ACE could be constructed. Simulation results show that the proposed codes achieve better error-floor performance compared with the codes using the same degree distributions constructed by the recent proposed methods.
In this paper we introduce a novel progressive edge-growth (PEG) algorithm, the cyclic PEG (CPEG) algorithm. The CPEG algorithm uses an alternative edge establishment sequence to construct low-density parity-check (LDPC) codes. Irregular LDPC codes constructed using the CPEG algorithm have improved girth and approximate cycle extrinsic message degree (ACE) compared to existing PEG algorithms. We also analyze the minimum codeword weight, minimum stopping set weight, local girth, and local ACE distributions for codes in four very large ensembles of irregular LDPC codes. The code ensembles analyzed were constructed using standard PEG, ACE modified standard PEG, CPEG, and ACE modified CPEG algorithms. Modifications to improve the ACE in PEG LDPC codes, by Xiao and Banihashemi, were implemented in the ‘ACE modified’ versions of the PEG algorithms. The ACE modified standard PEG algorithm constructed the code ensemble with the highest minimum codeword weight and minimum stopping set weight distributions, and the ACE modified CPEG algorithm constructed the code ensemble with the highest local girth and ACE distributions. Short block length irregular LDPC codes with good degree distributions which have higher minimum weights than have been published for similar LDPC codes were found in the four code ensembles.
This paper proposes two new cycle-optimized algorithms, called the multi-step progressive edge-growth (PEG) algorithm and the multi-step approximate cycle extrinsic message degree (ACE) constrained PEG algorithm, to design an LDPC code with larger girth and better cycle-connectivity. In addition, an efficient method is developed to calculate the distances between the variable nodes (VNs) and the check nodes (CNs) in the proposed algorithms. Simulation results show that compared to the conventional cycle-optimized algorithms, the proposed algorithms can achieve both better cycle-connectivity and foreseeable lower error floors.
We propose a simple and efficient algorithm for evaluating the girth and approximate cycle extrinsic message degree (ACE) of all short cycles through symbol nodes in short-to-medium length low-density parity-check (LDPC) code Tanner graphs. The algorithm uses single-edge tree-apex (SETA) subgraph expansions to find all the short cycles in a code graph in a direct manner, unlike existing algorithms which use message-passing algorithms or trellis representations of code graphs. The complexity of the algorithm, when applied to a parity-check matrix H of dimension m × n, is O(n m). Due to the fact that both girth and ACE are features of cycles, we adopt parameters similar to those used for girth descriptions for ACE descriptions. Accordingly, we define the `local ACE' at a symbol node or the `symbol node ACE', as the minimum ACE of the short cycles through the symbol node in the graph. This basic parameter enables the local ACE distribution, minimum and maximum local ACE, modal ACE, and the average ACE of an LDPC code graph to be determined using SETA subgraph expansions. The average ACE of an LDPC code graph is a concise single-valued measure of the overall connectivity of cycles in the graph. The proposed algorithm determines the local girth and ACE distributions in irregular short length LDPC codes in less time than existing algorithms. The algorithm is not intended for quasi-cyclic (QC) LDPC codes.