From Rate Distortion Theory to Metric Mean Dimension: Variational Principle

Elon Lindenstrauss, Masaki Tsukamoto

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

Abstract

The purpose of this paper is to point out a new connection between information theory and dynamical systems. In the information theory side, we consider rate distortion theory, which studies lossy data compression of stochastic processes under distortion constraints. In the dynamical systems side, we consider mean dimension theory, which studies how many parameters per iterate we need to describe a dynamical system. The main results are new variational principles connecting rate distortion function to metric mean dimension.

Original languageAmerican English
Pages (from-to)3590-3609
Number of pages20
JournalIEEE Transactions on Information Theory
Volume64
Issue number5
DOIs
StatePublished - May 2018

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

  • Dynamical system
  • invariant measure
  • metric mean dimension
  • rate distortion function
  • variational principle

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