Optimization of directed information and relations to filtering theory

@article{Charalambous2014OptimizationOD,
  title={Optimization of directed information and relations to filtering theory},
  author={Charalambos D. Charalambous and Photios A. Stavrou},
  journal={2014 European Control Conference (ECC)},
  year={2014},
  pages={1385-1390}
}
In this paper we generalize the relation between nonanticipative Rate Distortion Function (RDF) and filtering theory, to processes which are affected by the reproduction process, by utilizing the topology of weak convergence of probability measures. Specifically, this generalization is established via an optimization on the space of conditional distributions of the so-called directed information, subject to a fidelity constraint. Existence of the optimal reproduction distribution of the general… CONTINUE READING

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