Minimizing the Alphabet Size in Codes with Restricted Error Sets

Mira Gonen, Ishay Haviv, Michael Langberg, Alex Sprintson

Research output: Contribution to journalArticlepeer-review

Abstract

This paper focuses on the study of the minimum possible alphabet size of codes in a generalized setting where the coding scheme is required to handle a pre-specified set of erasure or error patterns, naturally represented by a hypergraph. 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 of codes in this generalized setting and the combinatorial properties of the hypergraph that represents the pre-specified collection of erasure or error patterns. We also establish connections between error and erasure correcting codes in our generalized setting. Finally, we consider a variation of the problem that allows a small probability of decoding error and relate it to an approximate version of hypergraph coloring.

Original languageEnglish
Pages (from-to)1
Number of pages1
JournalIEEE Transactions on Information Theory
DOIs
StateAccepted/In press - 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
IEEE

Keywords

  • Codes
  • Color
  • Decoding
  • Encoding
  • Error correction codes
  • Linear codes
  • Symbols

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