A PEG-like LDPC code design avoiding short trapping sets

In this paper, we propose a predictive method to construct regular column-weight-three LDPC codes with girth g = 8 so that their Tanner graphs contain a minimum number of small trapping sets. Our construction is based on improvements of the Progressive Edge-Growth (PEG) algorithm. We first show how to detect the smallest trapping sets (5; 3) and (6; 4) in the computation tree spread from variable nodes during the edge assignment. A precise and rigorous characterization of trapping sets (5; 3) and (6; 4) are given, and we then derive a modification of the Randomized Progressive Edge-Growth (RandPEG) algorithm [1] to take into account a new cost function that allows to build regular column-weight d_v = 3, girth 8 LDPC codes free of (5,3) and with a minimization of (6,4). We present the construction and the performance results in the context of quasi-cyclic LDPC (QC-LDPC) codes.