We propose a systematic design of protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes with low error floor. We first characterize the trapping sets of such codes and demonstrate, using edge coloring techniques, that the QC structure of the code eliminates some of the trapping set structures that can exist in a code with the same degree distribution and girth but lacking the QC structure. Based on this characterization, our design aims at eliminating a targeted collection of trapping sets. Considering the parent/child relationship between the trapping sets in the collection, we search for and eliminate those trapping sets that are in the collection but are not a child of any other trapping set in the collection. An efficient layered algorithm is designed for the search of these targeted trapping sets. Compared to the existing codes in the literature, the designed codes are superior in the sense that they are free of the same collection of trapping sets while having a smaller block length, or a larger collection of trapping sets while having the same block length. In addition, the efficiency of the search algorithm makes it possible to design codes with larger degrees which are free of trapping sets within larger ranges compared to the state-of-the-art.

edge coloring, elementary trapping sets, graph coloring, LDPC code construction, leafless elementary trapping sets, low error floor, Low-density parity-check (LDPC) codes, quasi-cyclic (QC) LDPC codes, trapping sets
IEEE Transactions on Communications
Department of Systems and Computer Engineering

Karimi, B. (Bashirreza), & Banihashemi, A. (2020). Construction of QC LDPC Codes With Low Error Floor by Efficient Systematic Search and Elimination of Trapping Sets. IEEE Transactions on Communications, 68(2), 697–712. doi:10.1109/TCOMM.2019.2953601