Directed information, causal estimation, and communication in continuous time

Young Han Kim, Haim H. Permuter, Tsachy Weissman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

The notion of directed information is introduced for stochastic processes in continuous time. Properties and operational interpretations are presented for this notion of directed information, which generalizes mutual information between stochastic processes in a similar manner as Massey's original notion of directed information generalizes Shannon's mutual information in the discrete-time setting. As a key application, Duncan's theorem is generalized to estimation problems in which the evolution of the target signal is affected by the past channel noise, and the causal minimum mean squared error estimation is related to directed information from the target signal to the observation corrupted by additive white Gaussian noise. An analogous relationship holds for the Poisson channel. The notion of directed information as a characterizing of the fundamental limit on reliable communication for a wide class of continuous-time channels with feedback is discussed.

Original languageEnglish
Title of host publicationFinal Proceedings of the 2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2009
DOIs
StatePublished - 1 Dec 2009
Event2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2009 - Seoul, Korea, Republic of
Duration: 23 Jun 200927 Jun 2009

Publication series

NameFinal Proceedings of the 2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2009

Conference

Conference2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks, WiOpt 2009
Country/TerritoryKorea, Republic of
CitySeoul
Period23/06/0927/06/09

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