A Low Complexity PEG-like Algorithm to Construct Quasi-Cyclic LDPC Codes

In this paper, we introduce a modified version of the Progressive Edge-Growth (PEG) algorithm that is used to construct the Tanner graphs of quasi-cyclic (QC) low-density parity-check (LDPC) codes having large girth. In our algorithms, we replace certain requirements in the original PEG algorithm, namely the expansion of subgraphs from symbol nodes and the identification of a most distant check node before placing a new edge, by the construction of certain minimal sets, called forbidden sets, that contain the problematic quasi-cyclic constraints that do not let us exceed a given girth. We propose some exponent-selection strategies that are shown to increase the chance of obtaining large girth, and reduce the number of short cycles in the Tanner graph.