Repairing Reed-Solomon Codes Evaluated on Subspaces

Amit Berman, Sarit Buzaglo, Avner Dor, Yaron Shany, Itzhak Tamo

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

4 Scopus citations

Abstract

We consider the repair problem for Reed-Solomon (RS) codes, evaluated on an \mathbb{F}_{q}-linear subspace U \subseteq \mathbb{F}_{q^{m}} of dimension d, where q is a prime power, m is a positive integer, and \mathbb{F}_{q} is the Galois field of size q. For q > 2, we show the existence of a linear repair scheme for the RS code of length n=q^{d} and codimension q^{s}, s < d, evaluated on U, in which each of the n-1 surviving nodes transmits only r symbols of \mathbb{F}_{q}, provided that ms\geq d(m-r). For the case q=2, we prove a similar result, with some restrictions on the evaluation linear subspace U. Our proof is based on a probabilistic argument, however the result is not merely an existence result; the success probability is fairly large (at least 1/3) and there is a simple criterion for checking the validity of the randomly chosen linear repair scheme.

Original languageEnglish
Title of host publication2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages867-871
Number of pages5
ISBN (Electronic)9781538682098
DOIs
StatePublished - 12 Jul 2021
Externally publishedYes
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
ISSN (Print)2157-8095

Conference

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

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