Cyclic Group Projection for Enumerating Quasi-Cyclic Codes Trapping Sets

Author:

Vasiliy Usatyuk, Yury Kuznetsov, Sergey Egorov

Keyword:

Computer Science, Information Theory, Information Theory (cs.IT), Machine Learning (cs.LG)

journal:

date:

2024-01-26 00:00:00

Abstract

This paper introduces a novel approach to enumerate and assess Trapping sets in quasi-cyclic codes, those with circulant sizes that are non-prime numbers. Leveraging the quasi-cyclic properties, the method employs a tabular technique to streamline the importance sampling step for estimating the pseudo-codeword weight of Trapping sets. The presented methodology draws on the mathematical framework established in the provided theorem, which elucidates the behavior of projection and lifting transformations on pseudo-codewords

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