  Consider a discrete-time remote estimation system formed by an encoder, a
transmission policy, a channel, and a remote estimator. The encoder assesses a
random process that the remote estimator seeks to estimate based on information
sent to it by the encoder via the channel. The channel is affected by Bernoulli
drops. The instantaneous probability of a drop is governed by a finite state
machine (FSM). The state of the FSM is denoted as the channel state. At each
time step, the encoder decides whether to attempt a transmission through the
packet-drop link. The sequence of encoder decisions is the input to the FSM.
This paper seeks to design an encoder, transmission policy and remote estimator
that minimize a finite-horizon mean squared error cost. We present two
structural results. The first result in which we assume that the process to be
estimated is white and Gaussian, we show that there is an optimal transmission
policy governed by a threshold on the estimation error. The second result
characterizes optimal symmetric transmission policies for the case when the
measured process is the state of a scalar linear time-invariant plant driven by
white Gaussian noise. Use-dependent packet-drop channels can be used to
quantify the effect of transmission on channel quality when the encoder is
powered by energy harvesting. An application to a mixed initiative system in
which a human operator performs visual search tasks is also presented.
