Efficacy of the Metropolis Algorithm for the Minimum Weight Codeword Problem using Codeword and Generator Search Spaces

Shenoy, Ajitha K B and Biswas, Somenath and Kurur, Piyush P (2020) Efficacy of the Metropolis Algorithm for the Minimum Weight Codeword Problem using Codeword and Generator Search Spaces. IEE Transaction and Evolutionary computation. ISSN 1089-778X

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Abstract

This paper studies the efficacy of the Metropolis algorithm for the minimum weight codeword problem. The input is a linear code C given by its generator matrix and our task is to compute a non-zero codeword in the code C of least weight. In particular, we study the Metropolis algorithm on two possible search spaces for the problem, the codeword space and the generator space. The former is the space of all codewords of the input code and is the most natural one to use and hence has been used in previous work on this problem. The latter is the space of allgeneratormatricesoftheinputcodeandisstudiedforthefirst timeinthiswork.Inthispaper,weshowthatforanappropriately chosen temperature parameter the Metropolis algorithm mixes rapidly when either of the search spaces mentioned above are used. Experimentally, we demonstrate that the Metropolis algorithm performs favourably when compared to previous attempts. When using the generator space, the Metropolis algorithm is able to outperform the previous algorithms in most of the cases. We have also provided both theoretical and experimental justification to show why the generator space is a worthwhile search space to use for this problem.

Item Type: Article
Uncontrolled Keywords: —Metropolis Algorithm, Minimum Weight Codeword, Markov Chain, Mixing Time Analysis, Combinatorial optimization, Randomized Local Search Heuristics
Subjects: Engineering > MIT Manipal > Information and Communication Technology
Depositing User: MIT Library
Date Deposited: 25 Sep 2020 05:59
Last Modified: 25 Sep 2020 05:59
URI: http://eprints.manipal.edu/id/eprint/155627

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