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The fundamental limits of remote estimation of Markov processes undercommunication constraints are presented. The remote estimation system consistsof a sensor and an estimator. The sensor observes a discrete-time Markovprocess, which is a symmetric countable state Markov source or a Gauss-Markovprocess. At each time, the sensor either transmits the current state of theMarkov process or does not transmit at all. Communication is noiseless butcostly. The estimator estimates the Markov process based on the transmittedobservations. In such a system, there is a trade-off between communication costand estimation accuracy. Two fundamental limits of this trade-off arecharacterized for infinite horizon discounted cost and average cost setups.First, when each transmission is costly, we characterize the minimum achievablecost of communication plus estimation error. Second, when there is a constrainton the average number of transmissions, we characterize the minimum achievableestimation error. Transmission and estimation strategies that achieve thesefundamental limits are also identified.

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