Realizable Rate Distortion Function and Bayesian FIltering Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1204.2980,
title = {Realizable Rate Distortion Function and Bayesian FIltering Theory},
author = {Photios A. Stavrou and Charalambos D. Charalambous and Christos K. Kourtellaris},
journal= {arXiv preprint arXiv:1204.2980},
year = {2012}
}
Comments
5 pages, 3 figures, 1 table, 1 graph, submitted to Information Theory Workshop 2012