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Fundamental limitations or performance trade-offs/limits are importantproperties and constraints of control and filtering systems. Among varioustrade-off metrics, total information rate, which characterizes the sensitivitytrade-offs and average performance of control and filtering systems, isconventionally studied by using the (differential) entropy rate andKolmogorov-Bode formula. In this paper, by extending the famous I-MMSE (mutualinformation -- minimum mean-square error) relationship to the discrete-timeadditive white Gaussian channels with and without feedback, a new paradigm isintroduced to estimate and analyze total information rate as a control andfiltering trade-off metric. Under this framework, we enrich the trade-offproperties of total information rate for a variety of discrete-time control andfiltering systems, e.g., LTI, LTV, and nonlinear, and also provide analternative approach to investigate total information rate via optimalestimation.

An Information-Theoretic Analysis of Discrete-Time Control and Filtering Limitations by the I-MMSE Relationships