Equality in the Matrix Entropy-Power Inequality and Blind Separation of Real and Complex sources

Rioul, Olivier; Zamir, Ram

doi:10.1109/isit.2019.8849303

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Otherwise X I Is Gaussian1

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2022

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“…Hence, we might say that the extremizers in (24) are characterized by all present non-recoverable components being Gaussian. This is precisely the statement given by Rioul and Zamir in their recent work [19,Theorem 1], which gave the first characterization of extremizers in the Zamir-Feder inequality.…”

Section: Otherwise X I Is Gaussiansupporting

confidence: 74%

Equality cases in the Anantharam-Jog-Nair inequality

Aras¹,

Courtade²,

Zhang³

2022

Preprint

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Anantharam, Jog and Nair recently unified the Shannon-Stam inequality and the entropic form of the Brascamp-Lieb inequalities under a common inequality. They left open the problems of extremizability and characterization of extremizers. Both questions are resolved in the present paper. PreliminariesWe begin by briefly fixing notation and definitions that will be needed throughout. A Euclidean space E is a finite-dimensional Hilbert space over the real field, equipped with Lebesgue measure. For a probability measure µ on E, absolutely continuous with respect to Lebesgue measure, and a random vector X ∼ µ, we define the Shannon entropy h(X) ≡ h(µ) := − E

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Section: Otherwise X I Is Gaussiansupporting

confidence: 74%