Nonanticipative Rate Distortion Function and Relations to Filtering Theory
Abstract
The relation between nonanticipative Rate Distortion Function (RDF) and filtering theory is discussed on abstract spaces. The relation is established by imposing a realizability constraint on the reconstruction conditional distribution of the classical RDF. Existence of the extremum solution of the nonanticipative RDF is shown using weak-convergence on appropriate topology. The extremum reconstruction conditional distribution is derived in closed form, for the case of stationary processes. The realization of the reconstruction conditional distribution which achieves the infimum of the nonanticipative RDF is described. Finally, an example is presented to illustrate the concepts.
Cite
@article{arxiv.1210.1266,
title = {Nonanticipative Rate Distortion Function and Relations to Filtering Theory},
author = {Charalambos D. Charalambous and Photios A. Stavrou and Nasir U. Ahmed},
journal= {arXiv preprint arXiv:1210.1266},
year = {2016}
}
Comments
41 pages,5 figures, Provisionally Accepted Version of the manuscript submitted to IEEE Transactions on Automatic Control; Part of this work was presented in 20th International Symposium on Mathematical Theory of Networks and Systems (MTNS '12)