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Theoretical and experimental aspects of information theory and coding theory. This tag covers but is not limited to following branches: information theory, information geometry, optimal transportation theory, coding theory.

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What kinds of sets can replace lattices in the Shannon sampling theorem?

One sufficient condition is that, if $|X_k| <= L$ for some $L < 1/4$ then the sampling map would be an injection, as well as a bounded map from $B$ to $l^2$. This is known as Kadec's theorem. See …
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