Fundamental limits of remote estimation of autoregressive Markov processes under communication constraints

TL;DR

This paper investigates the fundamental limits of remote estimation of Markov processes under communication constraints, characterizing optimal trade-offs and strategies for minimizing combined communication and estimation costs.

Contribution

It introduces the first comprehensive analysis of the trade-offs between communication cost and estimation accuracy for Markov processes under various constraints.

Findings

Characterized the minimum combined cost of communication and estimation error.

Identified optimal transmission and estimation strategies that achieve these limits.

Provided fundamental bounds for both discounted and average cost scenarios.

Abstract

The fundamental limits of remote estimation of Markov processes under communication constraints are presented. The remote estimation system consists of a sensor and an estimator. The sensor observes a discrete-time Markov process, which is a symmetric countable state Markov source or a Gauss-Markov process. At each time, the sensor either transmits the current state of the Markov process or does not transmit at all. Communication is noiseless but costly. The estimator estimates the Markov process based on the transmitted observations. In such a system, there is a trade-off between communication cost and estimation accuracy. Two fundamental limits of this trade-off are characterized for infinite horizon discounted cost and average cost setups. First, when each transmission is costly, we characterize the minimum achievable cost of communication plus estimation error. Second, when there is a constraint on the average number of transmissions, we characterize the minimum achievable estimation error. Transmission and estimation strategies that achieve these fundamental limits are also identified.