From rate distortion theory to metric mean dimension: variational principle

TL;DR

This paper establishes a novel connection between rate distortion theory in information theory and metric mean dimension in dynamical systems through variational principles, enhancing understanding of data compression and system complexity.

Contribution

It introduces new variational principles linking rate distortion functions to metric mean dimension, bridging two distinct theoretical frameworks.

Findings

Established a variational principle connecting rate distortion and metric mean dimension.

Provided a new perspective on data compression in relation to dynamical system complexity.

Enhanced theoretical understanding of the interplay between information theory and dynamical systems.

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 second we need to describe a dynamical system. The main results are new variational principles connecting rate distortion function to metric mean dimension.