  Fundamental limitations or performance trade-offs/limits are important
properties and constraints of control and filtering systems. Among various
trade-off metrics, total information rate, which characterizes the sensitivity
trade-offs and average performance of control and filtering systems, is
conventionally studied by using the (differential) entropy rate and
Kolmogorov-Bode formula. In this paper, by extending the famous I-MMSE (mutual
information -- minimum mean-square error) relationship to the discrete-time
additive white Gaussian channels with and without feedback, a new paradigm is
introduced to estimate and analyze total information rate as a control and
filtering trade-off metric. Under this framework, we enrich the trade-off
properties of total information rate for a variety of discrete-time control and
filtering systems, e.g., LTI, LTV, and nonlinear, and also provide an
alternative approach to investigate total information rate via optimal
estimation.
