%0 Journal Article
%T Realizable Rate Distortion Function and Bayesian FIltering Theory
%A Photios A. Stavrou
%A Charalambos D. Charalambous
%A Christos K. Kourtellaris
%J Mathematics
%D 2012
%I arXiv
%X 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.
%U http://arxiv.org/abs/1204.2980v1