TY - GEN
T1 - Directed information and causal estimation in continuous time
AU - Kim, Young Han
AU - Permuter, Haim H.
AU - Weissman, Tsachy
PY - 2009/11/19
Y1 - 2009/11/19
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=70449503463&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2009.5205653
DO - 10.1109/ISIT.2009.5205653
M3 - Conference contribution
AN - SCOPUS:70449503463
SN - 9781424443130
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 819
EP - 823
BT - 2009 IEEE International Symposium on Information Theory, ISIT 2009
T2 - 2009 IEEE International Symposium on Information Theory, ISIT 2009
Y2 - 28 June 2009 through 3 July 2009
ER -