Optimality of codes with respect to error probability in Gaussian noise
Metric Geometry
2017-01-30 v1 Information Theory
math.IT
Abstract
We consider geometrical optimization problems related to optimizing the error probability in the presence of a Gaussian noise. One famous questions in the field is the "weak simplex conjecture". We discuss possible approaches to it, and state related conjectures about the Gaussian measure, in particular, the conjecture about minimizing of the Gaussian measure of a simplex. We also consider antipodal codes, apply the \v{S}id\'ak inequality and establish some theoretical and some numerical results about their optimality.
Cite
@article{arxiv.1701.07986,
title = {Optimality of codes with respect to error probability in Gaussian noise},
author = {Alexey Balitskiy and Roman Karasev and Alexander Tsigler},
journal= {arXiv preprint arXiv:1701.07986},
year = {2017}
}