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arXiv · 1704.06164

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

Thomas A. Courtade·Guangyue Han·Yaochen Wu
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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.

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Thomas A. Courtade, Guangyue Han, Yaochen Wu. 2017-04-20. A Counterexample to the Vector Generalization of Costa's EPI, and Partial Resolution. https://arxiv.org/abs/1704.06164

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