Graph information ratio

Lele Wang, Ofer Shayevitz

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

Abstract

We introduce the notion of information ratio Ir(H/G) between two (simple, undirected) graphs G and H, which characterizes the maximal number of source symbols per channel use that can be reliably sent over a channel with confusion graph H, where reliability is measured w.r.t. a source confusion graph G. Many different results are provided, including in particular lower and upper bounds on Ir(H/G) in terms of various graph properties, inequalities and identities for behavior under strong product and disjoint union, relations to graph cores, and notions of graph criticality. Informally speaking, Ir(H/G) can be interpreted as a measure of similarity between G and H. We make this notion precise by introducing the concept of information equivalence between graphs, a more quantitative version of homomorphic equivalence. We then describe a natural partial ordering over the space of information equivalence classes, and endow it with a suitable metric structure that is contractive under the strong product. Various examples and intuitions are discussed.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages913-917
Number of pages5
ISBN (Electronic)9781509040964
DOIs
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

Conference

Conference2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/TerritoryGermany
CityAachen
Period25/06/1730/06/17

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