On optimal coding of non-linear dynamical systems

TL;DR

This paper investigates the minimal channel capacity needed for zero-delay coding of non-linear dynamical systems to achieve low-distortion estimation, linking entropy concepts with information theory.

Contribution

It characterizes the smallest channel capacities required for different estimation criteria in non-linear dynamical systems, connecting topological and metric entropy with information theory.

Findings

Identifies capacity thresholds for low-distortion estimation

Links entropy measures with coding limits

Provides theoretical bounds for system coding

Abstract

We consider the problem of zero-delay coding of a dynamical system over a discrete noiseless channel under three estimation criteria concerned with the low-distortion regime. For these three criteria, formulated stochastically in terms of a probability distribution for the initial state, we characterize the smallest channel capacities above which the estimation objectives can be achieved. The results establish further connections between topological and metric entropy of dynamical systems and information theory.