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Communication Dans Un Congrès Année : 2016

On Some Almost Properties

Résumé

Previous works have shown that regular distribu- tions with differential entropy or mean-squared error behavior close to that of the Gaussian are also close to the Gaussian with respect to some distances like Kolmogorov-Smirnov or Wasserstein distances, or vice versa. In keeping with these results, we show that under the assumption of a functional dependence on the Gaussian, any regular distribution that is almost Gaussian in differential entropy has a mean-squared error behavior of an almost linear estimator. A partial converse result is established under the addition of an arbitrary independent quantity: a small mean-squared error yields a small entropy difference. The proofs use basic properties of Shannon’s information measures and can be employed in an alternative solution to the missing corner point problem of Gaussian interference channels.
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Dates et versions

hal-02288458 , version 1 (11-08-2022)

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Olivier Rioul, Max H. M. Costa. On Some Almost Properties. IEEE Information Theory and Applications Workshop (ITA 2016), Jan 2016, San Diego, United States. ⟨10.1109/ITA.2016.7888134⟩. ⟨hal-02288458⟩
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