research-article

Performance of metropolis algorithm for the minimum weight code word problem

Authors:

Ajitha Shenoy K B,

Somenath Biswas,

Piyush P. KururAuthors Info & Claims

GECCO '14: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

Pages 485 - 492

https://doi.org/10.1145/2576768.2598274

Published: 12 July 2014 Publication History

Abstract

We study the performance of the Metropolis algorithm for the problem of finding a code word of weight less than or equal to M, given a generator matrix of an [n,k]-binary linear code. The algorithm uses the set S_k of all kxk invertible matrices as its search space where two elements are considered adjacent if one can be obtained from the other via an elementary row operation (i.e by adding one row to another or by swapping two rows.) We prove that the Markov chains associated with the Metropolis algorithm mix rapidly for suitable choices of the temperature parameter T. We ran the Metropolis algorithm for a number of codes and found that the algorithm performed very well in comparison to previously known experimental results.

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Cited By

Shenoy APai S(2021)Search Graph Magnification in Rapid Mixing of Markov Chains Associated with the Local Search-Based MetaheuristicsMathematics10.3390/math1001004710:1(47)Online publication date: 24-Dec-2021
https://doi.org/10.3390/math10010047
Ajitha Shenoy KBiswas SKurur P(2020)Efficacy of the Metropolis Algorithm for the Minimum-Weight Codeword Problem Using Codeword and Generator Search SpacesIEEE Transactions on Evolutionary Computation10.1109/TEVC.2020.298011124:4(664-678)Online publication date: Aug-2020
https://doi.org/10.1109/TEVC.2020.2980111
Bouzkraoui HAzouaoui AHadi Y(2018)New ant colony optimization for searching the minimum distance for linear codes2018 International Conference on Advanced Communication Technologies and Networking (CommNet)10.1109/COMMNET.2018.8360246(1-6)Online publication date: Apr-2018
https://doi.org/10.1109/COMMNET.2018.8360246

Index Terms

Performance of metropolis algorithm for the minimum weight code word problem
1. Mathematics of computing
  1. Information theory
  2. Probability and statistics
    1. Probabilistic algorithms
    2. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods
        Simulated annealing
      2. Sequential Monte Carlo methods

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cover image ACM Conferences

GECCO '14: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

July 2014

1478 pages

ISBN:9781450326629

DOI:10.1145/2576768

Editor-in-chief:
Christian Igel
Ruhr University of Bochum, University of Copenhagen
,
General Chair:
Dirk V. Arnold
Dalhousie University

Copyright © 2014 ACM.

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SIGEVO: ACM Special Interest Group on Genetic and Evolutionary Computation

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Published: 12 July 2014

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SIGEVO

GECCO '14: Genetic and Evolutionary Computation Conference

July 12 - 16, 2014

BC, Vancouver, Canada

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GECCO '14 Paper Acceptance Rate 180 of 544 submissions, 33%;

Overall Acceptance Rate 1,669 of 4,410 submissions, 38%

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Cited By

Shenoy APai S(2021)Search Graph Magnification in Rapid Mixing of Markov Chains Associated with the Local Search-Based MetaheuristicsMathematics10.3390/math1001004710:1(47)Online publication date: 24-Dec-2021
https://doi.org/10.3390/math10010047
Ajitha Shenoy KBiswas SKurur P(2020)Efficacy of the Metropolis Algorithm for the Minimum-Weight Codeword Problem Using Codeword and Generator Search SpacesIEEE Transactions on Evolutionary Computation10.1109/TEVC.2020.298011124:4(664-678)Online publication date: Aug-2020
https://doi.org/10.1109/TEVC.2020.2980111
Bouzkraoui HAzouaoui AHadi Y(2018)New ant colony optimization for searching the minimum distance for linear codes2018 International Conference on Advanced Communication Technologies and Networking (CommNet)10.1109/COMMNET.2018.8360246(1-6)Online publication date: Apr-2018
https://doi.org/10.1109/COMMNET.2018.8360246

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