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arXiv · 2509.13040

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

Qingqing Peng·Ke Liu·Guiying Yan·Guanghui Wang
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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.

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Qingqing Peng, Ke Liu, Guiying Yan, Guanghui Wang. 2025-09-16. Linear Complexity Computation of Code Distance and Minimum Size of Trapping Sets for LDPC Codes with Bounded Treewidth. https://arxiv.org/abs/2509.13040

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