Linear Complexity Computation of Code Distance and Minimum Size of Trapping Sets for LDPC Codes with Bounded Treewidth

Abstract: It is well known that, given (b\ge 0), finding an $(a,b)$-trapping set with the minimum (a) in a binary linear code is NP-hard. In this paper, we demonstrate that this problem can be solved with linear complexity with respect to the code length for codes with bounded treewidth. Furthermore, suppose a tree decomposition corresponding to the treewidth of the binary linear code is known. In that case, we also provide a specific algorithm to compute the minimum (a) and the number of the corresponding ((a, b))-trapping sets for a given (b) with linear complexity. Simulation experiments are presented to verify the correctness of the proposed algorithm.