A Counterexample to the Vector Generalization of Costa's EPI, and Partial Resolution

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...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-04
Main Authors: Courtade, Thomas A, Han, Guangyue, Wu, Yaochen
Format: Article
Language:English
Subjects:
Covariance
Inequality
Random noise
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422