Sequential Source Coding for Stochastic Systems Subject to Finite Rate Constraints

TL;DR

This paper develops a new theoretical framework for analyzing the fundamental limits of data-rate constrained stochastic control systems over finite horizons, providing bounds and algorithms for optimal rate-distortion allocation.

Contribution

It introduces a novel characterization of the minimum total rate for sequential source coding under distortion constraints, applicable to finite-time stochastic control scenarios.

Findings

Derived non-asymptotic lower and upper bounds for control systems.

Established the minimum data-rate for stability in finite-horizon LQG control.

Provided algorithms for optimal rate-distortion allocation.

Abstract

In this paper, we revisit the sequential source coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our results is a new characterization of the lower bound on the minimum total-rate achieved by sequential codes subject to a total (across time) distortion constraint and a computational algorithm that allocates optimally the rate-distortion for any fixed finite-time horizon. This characterization facilitates the derivation of analytical, non-asymptotic, and finite-dimensional lower and upper bounds in two control-related scenarios. (a) A parallel time-varying Gauss-Markov process with identically distributed spatial components that is quantized and transmitted through a noiseless channel to a minimum mean-squared error (MMSE) decoder. (b) A time-varying quantized LQG closed-loop control system, with identically distributed spatial components and with a random data-rate allocation. Our non-asymptotic lower bound on the quantized LQG control problem, reveals the absolute minimum data-rates for (mean square) stability of our time-varying plant for any fixed finite time horizon. We supplement our framework with illustrative simulation experiments.