Optimized filtering and reconstruction in predictive quantization with losses

Consider a communication system in which a filtered and quantized signal is sent over a channel with erasures and (potentially) additive noise. Linear MMSE estimation is achieved in such a system by Kalman filtering. Allowing any Markov erasure process and any Markov-state jump linear signal generation model, it is shown that the estimation performance at the receiver can be computed as a deterministic optimization with linear matrix inequality (LMI) constraints rather than a pseudorandom simulation. Further-more, in contrast to the case without erasures, the filtering in the transmitter should not necessarily be MMSE prediction (whitening); a procedure is given to find a locally optimal prefilter. The main tools are recent LMI characterizations of asymptotic state estimation error covariance and output estimation error variance for discrete-time jump linear systems in which the discrete portion of the system state is a Markov chain. As another application of this framework, a novel analysis and optimization of a "streaming" version of multiple description coding based on subsampling is outlined.