Lov\'asz's Theta Function, R\'enyi's Divergence and the Sphere-Packing Bound
Information Theory
2013-05-21 v2 math.IT
Quantum Physics
Abstract
Lov\'asz's bound to the capacity of a graph and the the sphere-packing bound to the probability of error in channel coding are given a unified presentation as information radii of the Csisz\'ar type using the R{\'e}nyi divergence in the classical-quantum setting. This brings together two results in coding theory that are usually considered as being of a very different nature, one being a "combinatorial" result and the other being "probabilistic". In the context of quantum information theory, this difference disappears.
Keywords
Cite
@article{arxiv.1301.6339,
title = {Lov\'asz's Theta Function, R\'enyi's Divergence and the Sphere-Packing Bound},
author = {Marco Dalai},
journal= {arXiv preprint arXiv:1301.6339},
year = {2013}
}
Comments
An excerpt from arXiv:1201.5411v3 (with a different notation) accepted at ISIT 2013