Information Storage in the Stochastic Ising Model at Low Temperature

Ziv Goldfeld, Guy Bresler, Yury Polyanskiy

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

Abstract

Motivated by questions of data stabilization in emerging magnetic storage technologies, we study the retention of information in interacting particle systems. The interactions between particles adhere to the stochastic Ising model (SIM) on the two-dimensional (2D) \sqrt n × \sqrt n grid. The measure of interest is the information capacity {I-n}\left(t\right) \triangleq {\max -{{p-{{X-0}}}}}I\left({{X-0};{X-t}}\right), where the initial spin configuration X0 is a user-controlled input and the output configuration Xt is produced by running t steps of Glauber dynamics. After the results on the zero-temperature regime reported last year, this work focuses on the positive but low temperature regime. We first show that storing more than a single bit for an exponential time is impossible when the initial configuration is drawn from the equilibrium distribution. Specifically, if X0 is drawn according to the Gibbs measure, then I(X0; Xt) ≤ 1 + o(1) for t \geq \exp \left({c{n^{\frac{1}{4} + \varepsilon }}}\right). On the other hand, when scaling time with β, we propose a stripe-based coding scheme that stores order of \sqrt n bits for exp(β) time. Key to the analysis of the scheme is a new result on the survival time of a single plus-labeled stripe in a sea of minuses. Together, the 1-bit upper bound and the striped-based storage scheme constitute initial steps towards a general analysis of In(t) for β > 0.

Original languageEnglish
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages732-736
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

ASJC Scopus subject areas

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

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