On Non-Interactive Simulation of Binary Random Variables
Information Theory
2021-01-26 v4 Combinatorics
math.IT
Probability
Abstract
We leverage proof techniques Fourier analysis and an existing result in coding theory to derive new bounds for the problem of non-interactive simulation of binary random variables. Previous bounds in the literature were derived by applying data processing inequalities concerning maximal correlation or hypercontractivity. We show that our bounds are sharp in some regimes. For a specific instance of problem parameters, our main result answers an open problem posed by E. Mossel in 2017. As by-products of our analyses, various new properties of the average distance and distance enumerator of binary block codes are established.
Cite
@article{arxiv.1904.03932,
title = {On Non-Interactive Simulation of Binary Random Variables},
author = {Lei Yu and Vincent Y. F. Tan},
journal= {arXiv preprint arXiv:1904.03932},
year = {2021}
}
Comments
11 pages, 3 figures. IEEE Transactions on Information Theory