A PEG Construction of LDPC Codes Based on the Betweenness Centrality Metric

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.