2211.15466
Metric entropy of causal, discrete-time LTI systems
Clemens Hutter, Thomas Allard, Helmut Bölcskei
correcthigh confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves E(ε; C(a,b), ρ) ∼ (log2 e)/(2b)·(log(a/ε))^2 via explicit packing and covering (Theorem 2.4, with Lemmas 3.1 and 3.3 providing the matching bounds) . The candidate solution derives the same asymptotic by reducing to bounded analytic functions on the smaller disc and invoking the Kolmogorov–Tikhomirov entropy, yielding the identical constant. Hence, both are correct, but by different methods.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper cleanly establishes the sharp constant in the metric entropy for exponentially decaying LTI systems under H∞, correcting a prior constant. The argument is constructive and accessible, with clear covering and packing schemes. Minor clarifications could further situate the result within the classical theory of metric entropy for analytic function classes.