Recoverable systems on lines and grids

Alexander Barg, Ohad Elishco, Ryan Gabrys, Eitan Yaakobi

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

Abstract

A storage code is an assignment of symbols to the vertices of a connected graph G(V, E) with the property that the value of each vertex is a function of the values of its neighbors, or more generally, of a certain neighborhood of the vertex in G. Under the name of recoverable systems, a class of storage codes on Z was recently studied relying on methods from constrained systems and ergodic theory. In this work, we address the question of the maximum capacity of recoverable systems on Z and Z2 from a combinatorial perspective. We establish a closed form formula for the capacity of several one- and two-dimensional systems, depending on their recovery set, using connections between storage codes, graphs, anticodes, and difference-avoiding sets.

Original languageEnglish
Title of host publication2022 IEEE International Symposium on Information Theory, ISIT 2022
PublisherInstitute of Electrical and Electronics Engineers
Pages2637-2642
Number of pages6
ISBN (Electronic)9781665421591
DOIs
StatePublished - 1 Jan 2022
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: 26 Jun 20221 Jul 2022

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2022-June
ISSN (Print)2157-8095

Conference

Conference2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/TerritoryFinland
CityEspoo
Period26/06/221/07/22

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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