Real-time Estimation of a Markov Process Over a Noisy Digital Communication Channel

The contents of this report reflect the views of the authors who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the State of California. This report does not constitute a standard, specification , or regulation. Abstract We study the real-time estimation of a Markov process over a memoryless noisy digital communication channel. The goal of system design is to minimize the mean squared estimation error. We first show the optimal encoder and decoder can be memoryless in terms of the source symbols. We then prove the optimal encoder separates the real space with hyperplanes. In the case of the binary symmetric channel and scalar source, the optimal encoder can be a threshold. A recursive algorithm is given to jointly find a locally optimal encoder and decoder for the binary symmetric channel. For a memoryless Gaussian vector source and a binary symmetric channel, we show the optimal policy is to encode the principal component. We derive the minimum mean squared error as a function of the variance of source and the channel noise.