From Rate Distortion Theory to Metric Mean Dimension: Variational Principle

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.