English

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