Semidefinite Programming Approach to Gaussian Sequential Rate-Distortion Trade-offs

TL;DR

This paper introduces a semidefinite programming method to analyze the fundamental trade-offs between data rate and quality in real-time communication of Gaussian processes, extending SRD theory.

Contribution

It develops a semidefinite programming framework for optimal sensor-estimator design in Gaussian SRD problems, providing a new computational approach.

Findings

Semidefinite representation of SRD function derived

Optimal joint sensor-estimator design via SDP established

Implications for zero-delay source coding and networked control discussed

Abstract

Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between data-rate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional time-varying Gauss-Markov processes under mean-square distortion criteria. We first revisit the sensor-estimator separation principle, which asserts that considered SRD problem is equivalent to a joint sensor and estimator design problem in which data-rate of the sensor output is minimized while the estimator's performance satisfies the distortion criteria. We then show that the optimal joint design can be performed by semidefinite programming. A semidefinite representation of the corresponding SRD function is obtained. Implications of the obtained result in the context of zero-delay source coding theory and applications to networked control theory are also discussed.