Relations between Information and Estimation in the presence of Feedback

We discuss some of the recent literature on relations between information and estimation theoretic quantities. We begin by exploring the connections between mutual information and causal/non-causal, matched/mismatched estimation for the setting of a continuous source corrupted by white Gaussian noise. Relations involving causal estimation, in both matched and mismatched cases, and mutual information persist in the presence of feedback. We present a new unified framework, based on Girsanov theory and Itô’s Calculus, to derive these relations. We conclude by deriving some new results using this framework.