DeepAI

# An Elementary Proof of a Classical Information-Theoretic Formula

A renowned information-theoretic formula by Shannon expresses the mutual information rate of a white Gaussian channel with a stationary Gaussian input as an integral of a simple function of the power spectral density of the channel input. We give in this paper a rigorous yet elementary proof of this classical formula. As opposed to all the conventional approaches, which either rely on heavy mathematical machineries or have to resort to some "external" results, our proof, which hinges on a recently proven sampling theorem, is elementary and self-contained, only using some well-known facts from basic calculus and matrix theory.

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12/24/2019

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### Information Theory in Density Destructors

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### There are EXACTLY 1493804444499093354916284290188948031229880469556 Ways to Derange a Standard Deck of Cards (ignoring suits) [and many other such useful facts]

In this memorial tribute to Joe Gillis, who taught us that Special Funct...
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### Representative elementary volume via averaged scalar Minkowski functionals

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