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IEEE Communications Letters

Generalized ACE Constrained Progressive Edge-Growth LDPC Code Design

Dejan Vukobratović, V. Šenk

Published Jan 1, 2008• 74 citations
Publisher

Abstract

In this letter, we propose a generalization of the progressive edge-growth (PEG) algorithm with the aim of designing LDPC code graphs with substantially improved approximated cycle extrinsic message degree (ACE) properties. The proposed realization of generalized PEG algorithm outperforms original PEG algorithm and its subsequent modification proposed by Xiao and Banihashemi.

DOI
10.1109/lcomm.2008.071457

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In this letter, we propose a generalization of the progressive edge-growth (PEG) algorithm with the aim of designing LDPC code graphs with substantially improved approximated cycle extrinsic message degree (ACE) properties. The proposed realization of generalized PEG algorithm outperforms original PEG algorithm and its subsequent modification proposed by Xiao and Banihashemi.
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.
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.
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.
The progressive edge-growth (PEG) algorithm is a general method to construct short low-density parity-check (LDPC) codes and it is a greedy method to place each edge with large girths. In order to improve the performance of LDPC codes, many improved PEG (IPEG) algorithms employ multi metrics to select surviving edges in turn. In this paper, the proposed edges metric (EM) based on message-passing algorithm (MPA) is introduced to PEG algorithm and the proposed EM constrained PEG (EM-PEG) algorithm mainly considers the independence of message passing from different nodes in Tanner graph. The numerical results show that our EM-PEG algorithm brings better bit error rate (BER) performance gains to LDPC codes than the traditional PEG algorithm and the powerful multi-edge multi-metric constrained PEG algorithm (MM-PEGA) proposed recently. In addition, the multi-edge EM constrained PEG (M-EM-PEG) algorithm which adopts multi-edge EM may further improve the BER performance.