Codes for graph erasures

Lev Yohananov, Eitan Yaakobi

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

3 Scopus citations


Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the information is stored on the edges of an undirected graph, and a code over graphs is a set of graphs. A node failure is the event where all edges in the neighborhood of the failed node have been erased. We say that a code over graphs can tolerate ρ node failures if it can correct the erased edges of any ρ failed nodes in the graph. While the construction of such codes can be easily accomplished by MDS codes, their field size has to be at least), O(n2) when n is the number of nodes in the graph. In this work we present several constructions of codes over graphs with smaller field size. In particular, we present optimal codes over graphs correcting two node failures over the binary field, when the number of nodes in the graph is a prime number. We also present a construction of codes over graphs correcting ρ node failures for all ρ over a field of size at least (n + 1)/2-1, and show how to improve this construction for optimal codes when ρ = 2,3.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781509040964
StatePublished - 9 Aug 2017
Externally publishedYes
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017

Publication series

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


Conference2017 IEEE International Symposium on Information Theory, ISIT 2017


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