Communications in Information and Systems

Volume 14 (2014)

Number 3

Convergence of fundamental limitations in feedback communication, estimation, and feedback control over Gaussian channels

Pages: 161 – 211



Jialing Liu (Huawei Technologies Co., Ltd., Rolling Meadows, Illinois, U.S.A.)

Nicola Elia (Department of Electrical and Computer Engineering, Iowa State University, Ames, Ia., U.S.A.)


This paper presents a unifying perspective on communication, estimation, and control. A feedback communication system over a Gaussian channel is reformulated as an estimation system (i.e. a Kalman filter) and also as a feedback control system. Therefore, a fundamental limitation applicable in one system can be translated into a fundamental limitation applicable in another system and vice versa. Specifically, the achievable rate in the communication system is equal to half the Cramer-Rao bound decay rate or minimum mean-square error decay rate in the estimation system, and also equal to the Bode integral in the control system. Furthermore, the optimal trade-offs for each of the following three pairs of quantities are equal: first, the pair of power and rate in communication, second, the pair of the (causal) prediction performance and (anticausal) smoothing performance in estimation, and third, the pair of the output regulation performance and disturbance rejection measure in control. All these trade-offs can be interpreted as the trade-off between causality and anti-causality. Extensions to more general channels are briefly discussed.


fundamental limitations, confluence of feedback communication, estimation, and control, Kalman filtering, minimum mean-square error, Bode integral

Published 13 February 2015