Remote-state estimation with packet drop

In the remote estimation system, a transmitter observes a discrete-time symmetric countable state Markov process and decides to either transmit the current state of the Markov process or not transmit. The transmitted packet gets dropped in the communication channel with a probability ε. An estimator estimates the Markov process based on the received observations. When each transmission is costly, we characterize the minimum achievable cost of communication plus estimation error. 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.