Minimizing the Alphabet Size in Codes with Restricted Error Sets

Mira Gonen, Michael Langberg, Alex Sprintson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In many such settings, a smaller field size is achievable than that offered by MDS and other standard codes. We establish a connection between the minimum alphabet size for this generalized setting and the combinatorial properties of a hypergraph that represents the prespecified collection of error patterns. We also show a connection between error and erasure correcting codes in this specialized setting. This allows us to establish bounds on the minimum alphabet size and show an advantage of non-linear codes over linear codes in a generalized setting. We also consider a variation of the problem which allows a small probability of decoding error and relate it to an approximate version of the hypergraph coloring problem.

Original languageEnglish
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages940-945
Number of pages6
ISBN (Electronic)9781538682098
DOIs
StatePublished - 12 Jul 2021
Event2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia
Duration: 12 Jul 202120 Jul 2021

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2021-July

Conference

Conference2021 IEEE International Symposium on Information Theory, ISIT 2021
Country/TerritoryAustralia
CityVirtual, Melbourne
Period12/07/2120/07/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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