  We consider a sensor scheduling and remote estimation problem with one sensor
and one estimator. At each time step, the sensor makes an observation on the
state of a source, and then decides whether to transmit its observation to the
estimator or not. The sensor is charged a cost for each transmission. The
remote estimator generates a real-time estimate on the state of the source
based on the messages received from the sensor. The estimator is charged for
estimation error. As compared with previous works from the literature, we
further assume that there is an additive communication channel noise. As a
consequence, the sensor needs to encode the message before transmitting it to
the estimator. For some specific distributions of the underlying random
variables, we obtain the optimal solution to the problem of minimizing the
expected value of the sum of communication cost and estimation cost over the
time horizon.
