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International Symposium on Turbo Codes and Iterative Information Processing

A density-based progressive edge-growth matrix creation technique for LDPC codes

Pierre Clarel Catherine, K. M. S. Soyjaudah

Published Sep 1, 2010• 0 citations
Publisher

Abstract

In this work, we propose a method specially suited for creating high rate LDPC codes. The technique employed adds the connections of the bipartite graph on an edge-by-edge basis. Unlike other progressive edge-growth methods however, we favor the use of a density metric over the conventional distance metric for the node selection process. As benchmark, the algorithm yield codes of higher rates than those obtained from bit-filling algorithms. Because of its efficient approach in filling edges on the bipartite graph however, the algorithm may also be used to produce codes (of various rates) that are very competitive in terms of error-correcting performance.

DOI
10.1109/istc.2010.5613841

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IEEE Transactions on Communications•Jan 31, 2014•19 citations
In this work, we propose a method specially suited for creating high rate LDPC codes. The technique employed adds the connections of the bipartite graph on an edge-by-edge basis. Unlike other progressive edge-growth methods however, we favor the use of a density metric over the conventional distance metric for the node selection process. As benchmark, the algorithm yield codes of higher rates than those obtained from bit-filling algorithms. Because of its efficient approach in filling edges on the bipartite graph however, the algorithm may also be used to produce codes (of various rates) that are very competitive in terms of error-correcting performance.
Progressive Edge Growth (PEG) constructions are usually based on optimizing the distance metric by using various methods. In this work however, the distance metric is replaced by a different one, namely the betweenness centrality metric, which was shown to enhance routing performance in wireless mesh networks. A new type of PEG construction for Low-Density Parity-Check (LDPC) codes is introduced based on the betweenness centrality metric borrowed from social networks terminology given that the bipartite graph describing the LDPC is analogous to a network of nodes. The algorithm is very efficient in filling edges on the bipartite graph by adding its connections in an edge-by-edge manner. The smallest graph size the new code could construct surpasses those obtained from a modified PEG algorithm - the RandPEG algorithm. To the best of the authors' knowledge, this paper produces the best regular LDPC column-weight two graphs. In addition, the technique proves to be competitive in terms of error-correcting performance. When compared to MacKay, PEG and other recent modified-PEG codes, the algorithm gives better performance over high SNR due to its particular edge and local graph properties.
There are many algorithms to construct good low-density parity-check (LDPC) code, the most typical algorithms are bit-filling algorithm, randomly construction algorithm, and PEG (progressive edge growth) algorithm. As shown in [1], the error floor of LDPC Code is decreased by using PEG algorithm, but the error correction performance in waterfall region is compromised since a stopping set with small size will form the codeword with small Hamming weight over AWGN [2]. In this paper, we propose a novel algorithm to construct LDPC Codes. In our algorithm, we construct LDPC Code to avoid small girth and small stopping set by detecting the complete associated matrix of check node (defined in this paper) that converted from bipartite graph of LDPC Code based on the graph theory. Simulation shows that the LDPC code constructed by our algorithm has lower error floor than randomly constructed LDPC Code. The performance improvement of our algorithm is 0.1dB at BER of 10-3compared with PEG algorithm.
Given specified parameters, the number of check nodes, the expected girth and the variable node degrees, the Progressive Weight-Growth (PWG) algorithm is proposed to generate high rate low-density parity-check (LDPC) codes. Based on the theoretic foundation that is to investigate the girth impact by adding/removing variable nodes and edges of the Tanner graph, the PWG progressively increases column weights of the parity check matrix without violating the constraints defined by the given parameters. The analysis of the computational complexity and the simulation of code performance show that the LDPC codes by the PWG provide better or comparable performance in comparison with LDPC codes by some well-known methods (e.g., Mackay's random constructions, the PEG algorithm, and the bit-filling algorithm).
There exist many different algorithms to construct good low-density parity-check (LDPC) codes. To maximize the girth of the bipartite graph, which represents the LDPC code, the progressive edge-growth (PEG) algorithm was introduced. This construction methods leads for irregular LDPC codes to a lower error floor, but also to a performance loss in the waterfall region compared with randomly constructed LDPC codes. In this paper, we describe a modification of the PEG algorithm that improves the performance in the waterfall region. Furthermore, this modified PEG algorithm yields codes with lower error floors and a slightly better performance in the waterfall region than randomly constructed LDPC codes
Progressive edge-growth (PEG) algorithm construction builds a Tanner graph, or equivalently a parity-check matrix, for an LDPC code by establishing edges between the symbol nodes and the check nodes in an edge-by-edge manner and maximizing the girth in a greedy fashion. This approach is simple but the complexity of the PEG algorithm scale is O(nm), where n is the number of symbol nodes and m is the number of check nodes. We deal with this problem by construct a base matrix Hbof size mb× nbwith the PEG algorithm and simultaneously expand this base matrix into a parity-check matrix H of size mx n via the the Chinese remainder theorem (CRT), where m ≫ mband n ≥ nb. The size of the base matrix is expanded without decreasing the girth. For convenience, the PEG and CRT combined algorithm is referred to as the PEG-CRT algorithm in this paper. Since a smaller matrix is constructed with the PEG algorithm and the complexity of the CRT computation is negligible compared to the PEG algorithm, the complexity of the whole code construction process is reduced. Furthermore, the proposed algorithm has a potential advantage of saving storage space by storing a smaller matrix Hband expanding it to H "on-the-fly" in hardware. The expanded matrix H preserves the important properties of base matrix such as large girth, flexible code rate and low density. The complexity analysis shows that the complexity of the PEG-CRT algorithm does not grow with the code length n. Simulation results show that compared with the PEG LDPC codes of length nb, the expanded PEG-CRT LDPC codes have better bit error rate (BER) performance with the iterative decoding. It is also shown that compared with PEG LDPC codes of length n, which constructed with higher complexities, the PEG-CRT codes have similar BER performance.