Tracking an Auto-Regressive Process with Limited Communication

Samples from a high-dimensional AR[1] process are quantized and sent over a time-slotted communication channel of finite capacity. The receiver seeks to form an estimate of the process in real-time. We consider the slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to update the estimates of the latest sample. We show that there exist quantizers that render the fast but loose version of this scheme, which updates estimates in every slot, universally optimal asymptotically. However, we provide evidence that most practical quantizers will require a judiciously chosen update frequency.