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Advanced materials research

A Novel Construction Method of QC-LDPC Codes Based on Generalized ACE Constrained

Hong Hao Zhao, Fan Bo Meng, Qing Zhao, Jie Wang

Published Sep 18, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.4028/www.scientific.net/amr.760-762.1684

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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.
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.
A modified construction method of LDPC (Low-density Parity-check) codes based on polynomial of cycles of PEG (Progressive-Edge-Growth) is proposed according to reaction on the performance of LDPC codes by polynomial of cycles based on PEG and connectivity of cycles. It can reduce the number of the shortest cycles, increase average local girth and improve connectivity of cycles while deleting short cycles by considering girth of check matrix, number of the shortest cycles and ACE (Approximate Cycle EMD), so that it can improve performance of decoding. At the same time, a construction method of QC-LDPC (quasi-cyclic-LDPC) codes based on ACE and polynomial of cycles of PEG is also proposed to deal with the complexity of implementation on hardware of unstructured codes. Simulation results show that the performance of this code is better than unstructured Mackay code and it is easier for implementation on hardware.
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.