Directed Information on Abstract spaces: Properties and Extremum Problems

Details Directed Information on Abstract spaces: Properties and Extremum Problems Directed Information on Abstract spaces: Properties and Extremum Problems

2012-02-05

arxiv.org/abs/1202.0958v1

Computer Science

Information Theory

5 pages,Submitted to International Symposium on Information Theory (ISIT), 2012

Scientific paper

This paper describes a framework in which directed information is defined on abstract spaces. The framework is employed to derive properties of directed information such as convexity, concavity, lower semicontinuity, by using the topology of weak convergence of probability measures on Polish spaces. Two extremum problems of directed information related to capacity of channels with memory and feedback, and causal and sequential rate distortion are extensively analyzed showing existence of maximizing and minimizing solutions, respectively.

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