Variational equalities of directed information and applications
Date
2013ISBN
978-1-4799-0446-4Source
IEEE International Symposium on Information Theory - ProceedingsIEEE International Symposium on Information Theory - Proceedings
Pages
2577-2581Google Scholar check
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In this paper we introduce two variational equalities of directed information, which are analogous to those of mutual information employed in the Blahut-Arimoto Algorithm (BAA). Subsequently, we introduce nonanticipative Rate Distortion Function (RDF) Rna o, n(D) defined via directed information introduced in [1], and we establish its equivalence to Gorbunov-Pinsker's nonanticipatory ε-entropy Rε o, n(D). By invoking certain results we first establish existence of the infimizing reproduction distribution for Rna o, n(D), and then we give its implicit form for the stationary case. Finally, we utilize one of the variational equalities and the closed form expression of the optimal reproduction distribution to provide an algorithm for the computation of R na o, n(D). © 2013 IEEE.