Joint Nonanticipative Rate Distortion Function for a Tuple of Random Processes with Individual Fidelity Criteria

TL;DR

This paper characterizes the joint nonanticipative rate distortion function for multiple processes with individual fidelity constraints, providing structural insights and explicit solutions for Gaussian Markov processes.

Contribution

It derives structural properties of optimal test channels and explicitly characterizes the joint NRDF for Gaussian Markov processes with individual square-error criteria.

Findings

Optimal test channel structures are identified.

Explicit joint NRDF formulas for Gaussian Markov processes are provided.

Illustrative example demonstrates key challenges and solutions.

Abstract

The joint nonanticipative rate distortion function (NRDF) for a tuple of random processes with individual fidelity criteria is considered. Structural properties of optimal test channel distributions are derived. Further, for the application example of the joint NRDF of a tuple of jointly multivariate Gaussian Markov processes with individual square-error fidelity criteria, a realization of the reproduction processes which induces the optimal test channel distribution is derived, and the corresponding joint NRDF is characterized. The analysis of the simplest example, of a tuple of scalar correlated Markov processes, illustrates many of the challenging aspects of such problems.