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

arXiv: https://arxiv.org/abs/2304.09274 · HTML: https://mlsanity.com/paper/2304.09274/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [KOSS: Kalman-Optimal Selective State Spaces for Long-Term Sequence Modeling](https://mlsanity.com/paper/2512.16723/) (2025)

## Abstract (arXiv)

Fundamental limitations or performance trade-offs/limits are important properties and constraints of both control and filtering systems. Among various trade-off metrics, total information rate that characterizes the sensitivity trade-offs and time-averaged performance of control and filtering systems was 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) relationships 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 explore the trade-off properties of total information rate for a variety of the discrete-time control and filtering systems, e.g., LTI, LTV, and nonlinear, and propose an alternative approach to investigate total information rate via optimal estimation.