Error Bounds on a Mixed Entropy Inequality
Information Theory
2018-09-21 v1 math.IT
Probability
Abstract
Motivated by the entropy computations relevant to the evaluation of decrease in entropy in bit reset operations, the authors investigate the deficit in an entropic inequality involving two independent random variables, one continuous and the other discrete. In the case where the continuous random variable is Gaussian, we derive strong quantitative bounds on the deficit in the inequality. More explicitly it is shown that the decay of the deficit is sub-Gaussian with respect to the reciprocal of the standard deviation of the Gaussian variable. What is more, up to rational terms these results are shown to be sharp.
Keywords
Cite
@article{arxiv.1805.11260,
title = {Error Bounds on a Mixed Entropy Inequality},
author = {James Melbourne and Saurav Talukdar and Shreyas Bhaban and Murti V. Salapaka},
journal= {arXiv preprint arXiv:1805.11260},
year = {2018}
}