Umlaut information
Information Theory
2025-09-03 v2 Mathematical Physics
math.IT
math.MP
Quantum Physics
Abstract
The sphere-packing bound quantifies the error exponent for noisy channel coding for rates above a critical value. Here, we study the zero-rate limit of the sphere-packing bound and show that it has an intriguing single-letter form, which we call the umlaut information of the channel, inspired by the lautum information introduced by Palomar and Verd\'u. Unlike the latter quantity, we show that the umlaut information is additive for parallel uses of channels. We show that it has a twofold operational interpretation: as the zero-rate error exponent of non-signalling-assisted coding on the one hand, and as the zero-rate error exponent of list decoding in the large list limit on the other.
Keywords
Cite
@article{arxiv.2503.18910,
title = {Umlaut information},
author = {Filippo Girardi and Aadil Oufkir and Bartosz Regula and Marco Tomamichel and Mario Berta and Ludovico Lami},
journal= {arXiv preprint arXiv:2503.18910},
year = {2025}
}
Comments
44+7 pages