From Rate Distortion Theory to Metric Mean Dimension: Variational Principle

Elon Lindenstrauss; Masaki Tsukamoto

doi:10.1109/TIT.2018.2806219

From Rate Distortion Theory to Metric Mean Dimension: Variational Principle

Elon Lindenstrauss, Masaki Tsukamoto

Research output: Contribution to journal › Article › peer-review

39 Citations (Scopus)

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 language	English
Pages (from-to)	3590-3609
Number of pages	20
Journal	IEEE Transactions on Information Theory
Volume	64
Issue number	5
DOIs	https://doi.org/10.1109/TIT.2018.2806219
Publication status	Published - May 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

10.1109/TIT.2018.2806219

Cite this

@article{d64fe1a5f0eb43d497457b950d6b968a,

title = "From Rate Distortion Theory to Metric Mean Dimension: Variational Principle",

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.",

author = "Elon Lindenstrauss and Masaki Tsukamoto",

note = "Funding Information: Manuscript received March 10, 2017; revised October 28, 2017; accepted January 30, 2018. Date of publication February 28, 2018; date of current version April 19, 2018. E. Lindenstrauss was supported in part by the European Research Council Advanced Research under Grant 267259 and in part by ISF under Grant 891/15. M. Tsukamoto was supported by the John Mung Program of Kyoto University. Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2018",

month = may,

doi = "10.1109/TIT.2018.2806219",

language = "English",

volume = "64",

pages = "3590--3609",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "5",

}

TY - JOUR

T1 - From Rate Distortion Theory to Metric Mean Dimension

T2 - Variational Principle

AU - Lindenstrauss, Elon

AU - Tsukamoto, Masaki

N1 - Funding Information: Manuscript received March 10, 2017; revised October 28, 2017; accepted January 30, 2018. Date of publication February 28, 2018; date of current version April 19, 2018. E. Lindenstrauss was supported in part by the European Research Council Advanced Research under Grant 267259 and in part by ISF under Grant 891/15. M. Tsukamoto was supported by the John Mung Program of Kyoto University. Publisher Copyright: © 1963-2012 IEEE.

PY - 2018/5

Y1 - 2018/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85042855898&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042855898&partnerID=8YFLogxK

U2 - 10.1109/TIT.2018.2806219

DO - 10.1109/TIT.2018.2806219

M3 - Article

AN - SCOPUS:85042855898

SN - 0018-9448

VL - 64

SP - 3590

EP - 3609

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 5

ER -

From Rate Distortion Theory to Metric Mean Dimension: Variational Principle

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this