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We propose a systematic design of protograph-based quasi-cyclic (QC)low-density parity-check (LDPC) codes with low error floor. We firstcharacterize the trapping sets of such codes and demonstrate that the QCstructure of the code eliminates some of the trapping set structures that canexist in a code with the same degree distribution and girth but lacking the QCstructure. Using this characterization, our design aims at eliminating atargeted collection of trapping sets. Considering the parent/child relationshipbetween the trapping sets in the collection, we search for and eliminate thosetrapping sets that are in the collection but are not a child of any othertrapping set in the collection. An efficient layered algorithm is designed forthe search of these targeted trapping sets. Compared to the existing codes inthe literature, the designed codes are superior in the sense that they are freeof the same collection of trapping sets with a smaller block length, or alarger collection of trapping sets with the same block length. In addition, theefficiency of the search algorithm makes it possible to design codes withlarger degrees which are free of trapping sets within larger ranges compared tothe state-of-the-art.

Construction of QC-LDPC Codes with Low Error Floor by Efficient Systematic Search and Elimination of Trapping Sets