Double and Triple Node-Erasure-Correcting Codes over Graphs

Lev Yohananov, Yuval Efron, Eitan Yaakobi

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

1 Scopus citations

Abstract

In this paper we study array-based codes over graphs for correcting multiple node failures. These codes have applications to neural networks, associative memories, and distributed storage systems. We assume that the information is stored on the edges of a complete undirected graph and a node failure is the event where all the edges in the neighborhood of a given node have been erased. A code over graphs is called ρ-node-erasure-correcting if it allows to reconstruct the erased edges upon the failure of any ρ nodes or less. We present a binary optimal construction for double-node-erasure correction together with an efficient decoding algorithm, when the number of nodes is a prime number. Furthermore, we extend this construction for triple-node-erasure-correcting codes when the number of nodes is a prime number and two is a primitive element in Zn. These codes are at most a single bit away from optimality.

Original languageEnglish
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1582-1586
Number of pages5
ISBN (Electronic)9781538692912
DOIs
StatePublished - 1 Jul 2019
Externally publishedYes
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France
Duration: 7 Jul 201912 Jul 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/TerritoryFrance
CityParis
Period7/07/1912/07/19

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