On the error-prone substructures for the binary-input ternary-output channel and its corresponding exhaustive search algorithm

The error floor performance of a low-density parity-check (LDPC) code is highly related to the presence of error-prone substructures (EPSs). In general, existing characterizations of the EPSs are inspired by the LDPC decoding behavior under simple binary erasure channel (BEC) and binary symmetric channel (BSC) models. In this work, we first introduce a new class of EPSs: the 1-shot EPSs and static EPSs for the binary-input ternary-output channel (BITOC). By focusing on BITOCs, which are a step closer to additive white Gaussian channels (AWGNC), the proposed EPS would better characterize the decoding behavior of the AWGNC than the existing BEC-or BSC-based definitions. We then develop an efficient search algorithm that can exhaustively enumerate all small BITOC EPSs. The new exhaustive algorithm enables us to order the harmfulness of the EPSs and distinguish within a given EPS which bits are more prone to what types of errors. The proposed algorithm can also be regarded as a unified search method for the existing EPSs such as cycles, codewords, stopping sets, and fully absorbing sets. The proposed methodology is potentially generalizable to the binary-input m-ary output channel.