Conditional Information Inequalities for Entropic and Almost Entropic Points
Information Theory
2013-10-30 v4 Discrete Mathematics
math.IT
Probability
Abstract
We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be extended to any unconditional linear inequalities. Some of these conditional inequalities hold for almost entropic points, while others do not. We also discuss some counterparts of conditional information inequalities for Kolmogorov complexity.
Keywords
Cite
@article{arxiv.1207.5742,
title = {Conditional Information Inequalities for Entropic and Almost Entropic Points},
author = {Tarik Kaced and Andrei Romashchenko},
journal= {arXiv preprint arXiv:1207.5742},
year = {2013}
}
Comments
Submitted to the IEEE Transactions on Information Theory