Linear Complexity Computation of Code Distance and Minimum Size of Trapping Sets for LDPC Codes with Bounded Treewidth
arXiv:2509.13040
Abstract
It is well known that, given \(b\ge 0\), finding an -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.
low-density parity-check codes, tree decomposition, trapping sets, NP-complete