  We consider the problem of tracking the state of Gauss-Markov processes over
rate-limited erasure-prone links. We concentrate first on the scenario in which
several independent processes are seen by a single observer. The observer maps
the processes into finite-rate packets that are sent over the erasure-prone
links to a state estimator, and are acknowledged upon packet arrivals. The aim
of the state estimator is to track the processes with zero delay and with
minimum mean square error (MMSE). We show that, in the limit of many processes,
greedy quantization with respect to the squared error distortion is optimal.
That is, there is no tension between optimizing the MMSE of the process in the
current time instant and that of future times. For the case of packet erasures
with delayed acknowledgments, we connect the problem to that of compression
with side information that is known at the observer and may be known at the
state estimator - where the most recent packets serve as side information that
may have been erased, and demonstrate that the loss due to a delay by one time
unit is rather small. For the scenario where only one process is tracked by the
observer-state estimator system, we further show that variable-length coding
techniques are within a small gap of the many-process outer bound. We
demonstrate the usefulness of the proposed approach for the simple setting of
discrete-time scalar linear quadratic Gaussian control with a limited data-rate
feedback that is susceptible to packet erasures.
