On the combinatorial substructures of LDPC codes causing error floors in the AWGN channel

Finite-length low-density parity-check (LDPC) codes usually suffer from error floors in high signal-to-noise ratio (SNR) region. The error floor in the additive white Gaussian noise (AWGN) channel is known to be caused by trapping sets or absorbing sets. In this paper, we investigate combinatorial properties of trapping sets by using graph-theoretic approach. All non-isomorphic trapping sets are identified by a graph-theoretic tool and a method to distinguish the trapping sets which cannot appear in any protograph-based LDPC codes are proposed. Finally, a measure for estimating the harmfulness of trapping sets is proposed by using the linear system model of trapping sets.