Optimized Filtering and Reconstruction in Predictive Quantization with Losses (WP-P2)

Author(s) : Alyson Fletcher (University of California, Berkeley, USA) Sundeep Rangan (Flarion Technologies, USA) Vivek Goyal (MIT, USA) Kannan Ramchandran (University of California, Berkeley, USA)

Abstract : 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. Furthermore, 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 provided.

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