Minimizing the alphabet size of erasure codes with restricted decoding sets

Mira Gonen, Ishay Haviv, Michael Langberg, Alex Sprintson

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

Abstract

A Maximum Distance Separable code over an alphabet F is defined via an encoding function C : Fk → Fn that allows to retrieve a message m Fk from the codeword C(m) even after erasing any n - k of its symbols. The minimum possible alphabet size of general (non-linear) MDS codes for given parameters n and k is unknown and forms one of the central open problems in coding theory. The paper initiates the study of the alphabet size of codes in a generalized setting where the coding scheme is required to handle a pre-specified subset of all possible erasure patterns, naturally represented by an n-vertex k-uniform hypergraph. We relate the minimum possible alphabet size of such codes to the strong chromatic number of the hypergraph and analyze the tightness of the obtained bounds for both the linear and non-linear settings. We further consider variations of the problem which allow a small probability of decoding error.

Original languageEnglish
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages144-149
Number of pages6
ISBN (Electronic)9781728164328
DOIs
StatePublished - Jun 2020
Externally publishedYes
Event2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States
Duration: 21 Jul 202026 Jul 2020

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2020-June
ISSN (Print)2157-8095

Conference

Conference2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/TerritoryUnited States
CityLos Angeles
Period21/07/2026/07/20

Bibliographical note

Publisher Copyright:
© 2020 IEEE.

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