Foundations and Trends in Signal Processing has published a book co-authored by Dongning Guo, Associate Professor, Shlomo Shamai, Distinguished Professor, Israel Institute of Technology, and Sergio Verdu, Faculty, Princeton, titled "The Interplay Between Information and Estimation Measures."
The publication is a handbook of known formulas which directly relate to information measures and estimation measures. It provides intuition and draws connections between these formulas, highlights some important applications, and motivates further explorations.
Abstract: This monograph surveys the interactions between information measures and estimation measures as well as their applications. The emphasis is on formulas that express the major information measures, such as entropy, mutual information and relative entropy in terms of the minimum mean square error achievable when estimating random variables contaminated by Gaussian noise. These relationships lead to wide applications ranging from a universal relationship in continuous time nonlinear filtering to optimal power allocation in communication systems, to the simplified proofs of important results in information theory such as the entropy power inequality and converses in multiuser information theory.
The 214-page book is currently for sale available on Amazon.