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

Abstract

In this thesis, we propose a systematic design of binary 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 structures of 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. Moreover, we design finite-length binary irregular protograph-based QC-LDPC codes with good waterfall performance and low error floor. To achieve a low error floor, we eliminate a targeted set of dominant elementary trapping sets (ETS) L in the Tanner graph of the code. This is a more challenging task since the variety of problematic structures is much larger than that of regular codes. For a given rate and girth, the codes are designed to be free of the largest set of problematic ETSs for a given block length, or to have the shortest block length while a given set of ETSs is avoided. The design is based on a search algorithm that identifies whether any instance of any structure within L exists in the Tanner graph of the constructed code or not. The search algorithm performs this task with minimal complexity, making it feasible to construct practical codes by running the search algorithm a large number iii

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