A Counterexample to the Vector Generalization of Costa's EPI, and Partial Resolution
Information Theory
2017-04-21 v1 math.IT
Abstract
We give a counterexample to the vector generalization of Costa's entropy power inequality (EPI) due to Liu, Liu, Poor and Shamai. In particular, the claimed inequality can fail if the matix-valued parameter in the convex combination does not commute with the covariance of the additive Gaussian noise. Conversely, the inequality holds if these two matrices commute.
Keywords
Cite
@article{arxiv.1704.06164,
title = {A Counterexample to the Vector Generalization of Costa's EPI, and Partial Resolution},
author = {Thomas A. Courtade and Guangyue Han and Yaochen Wu},
journal= {arXiv preprint arXiv:1704.06164},
year = {2017}
}
Comments
3 pages