Nonanticipative Rate Distortion Function and Filtering Theory: A weak Convergence Approach

TL;DR

This paper explores the connection between nonanticipative rate distortion functions and Bayesian filtering, establishing existence of optimal solutions and demonstrating real-time joint source-channel coding with linear encoders.

Contribution

It introduces a weak convergence approach to relate nonanticipative RDF with filtering, proving existence of optimal distributions and applying results to real-time source-channel coding.

Findings

Existence of optimal nonanticipative RDF established.

Linear encoders are optimal for joint source-channel coding.

Application to multidimensional sources over Gaussian channels.

Abstract

In this paper the relation between nonanticipative rate distortion function (RDF) and Bayesian filtering theory is further investigated on general Polish spaces. The relation is established via an optimization on the space of conditional distributions of the so-called directed information subject to fidelity constraints. Existence of the optimal reproduction distribution of the nonanticipative RDF is shown using the topology of weak convergence of probability measures. Subsequently, we use the solution of the nonanticipative RDF to present the realization of a multidimensional partially observable source over a scalar Gaussian channel. We show that linear encoders are optimal, establishing joint source-channel coding in real-time.