An integer programming-based search technique for error-prone structures of LDPC codes

In this paper, an efficient, general framework is presented for finding common, devastating error-prone structures (EPS) of any finite-length low-density parity-check (LDPC) code. The smallest stopping set for the binary erasure channel (BEC), the smallest fully absorbing set, the smallest absorbing set, and the smallest elementary trapping set for the binary symmetric channel (BSC) are found and the dominant EPS are enumerated. The method involves integer programming optimization techniques, which guarantees that the results are provably optimal.