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We consider the problem of tracking the state of Gauss-Markov processes overrate-limited erasure-prone links. We concentrate first on the scenario in whichseveral independent processes are seen by a single observer. The observer mapsthe processes into finite-rate packets that are sent over the erasure-pronelinks to a state estimator, and are acknowledged upon packet arrivals. The aimof the state estimator is to track the processes with zero delay and withminimum 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 thecurrent time instant and that of future times. For the case of packet erasureswith delayed acknowledgments, we connect the problem to that of compressionwith side information that is known at the observer and may be known at thestate estimator - where the most recent packets serve as side information thatmay have been erased, and demonstrate that the loss due to a delay by one timeunit is rather small. For the scenario where only one process is tracked by theobserver-state estimator system, we further show that variable-length codingtechniques are within a small gap of the many-process outer bound. Wedemonstrate the usefulness of the proposed approach for the simple setting ofdiscrete-time scalar linear quadratic Gaussian control with a limited data-ratefeedback that is susceptible to packet erasures.

Tracking and Control of Gauss-Markov Processes over Packet-Drop Channels with Acknowledgments