Yet Another Proof of the Entropy Power Inequality

Yet Another Proof of the Entropy Power Inequality

Yet another simple proof of the entropy power inequality is given, which avoids both the integration over a path of Gaussian perturbation and the use of Young's inequality with sharp constant or Rényi entropies. The proof is based on a simple change of variables, is formally identical in one a...

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Veröffentlicht in:IEEE transactions on information theory 2017-06, Vol.63 (6), p.3595-3599
1. Verfasser: Rioul, Olivier
Format: Artikel
Sprache:eng
Schlagworte:
Context
differential entropy
Entropy
Entropy power inequality
gaussian variables
Indexes
Inequality
Information Theory
Jacobian matrices
Manifolds
Mathematics
Mutual information
optimal transport
Perturbation
Transportation
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Zusammenfassung:Yet another simple proof of the entropy power inequality is given, which avoids both the integration over a path of Gaussian perturbation and the use of Young's inequality with sharp constant or Rényi entropies. The proof is based on a simple change of variables, is formally identical in one and several dimensions, and easily settles the equality case.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2676093