Realizable Rate Distortion Function and Bayesian FIltering Theory

Details Realizable Rate Distortion Function and Bayesian FIltering Theory Realizable Rate Distortion Function and Bayesian FIltering Theory

2012-04-13

arxiv.org/abs/1204.2980v1

Computer Science

Information Theory

5 pages, 3 figures, 1 table, 1 graph, submitted to Information Theory Workshop 2012

Scientific paper

The relation between rate distortion function (RDF) and Bayesian filtering theory is discussed. The relation is established by imposing a causal or realizability constraint on the reconstruction conditional distribution of the RDF, leading to the definition of a causal RDF. Existence of the optimal reconstruction distribution of the causal RDF is shown using the topology of weak convergence of probability measures. The optimal non-stationary causal reproduction conditional distribution of the causal RDF is derived in closed form; it is given by a set of recursive equations which are computed backward in time. The realization of causal RDF is described via the source-channel matching approach, while an example is briefly discussed to illustrate the concepts.

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