Open AccessMMSE Bounds for Additive Noise Channels Under Kullback–Leibler Divergence Constraints on the Input Distribution
Author(s) -
Alex Dytso,
Michael Faus,
Abdelhak M. Zoubir,
H. Vincent Poor
Publication year - 2019
Publication title -
ieee transactions on signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.638
H-Index - 270
eISSN - 1941-0476
pISSN - 1053-587X
DOI - 10.1109/tsp.2019.2951221
Subject(s) - mathematics , upper and lower bounds , estimator , minimax , kullback–leibler divergence , divergence (linguistics) , gaussian noise , differential entropy , gaussian , covariance matrix , entropy (arrow of time) , minimax estimator , information theory , cramér–rao bound , chernoff bound , principle of maximum entropy , mathematical optimization , statistics , maximum entropy probability distribution , algorithm , mathematical analysis , minimum variance unbiased estimator , linguistics , philosophy , physics , quantum mechanics
Upper and lower bounds on the minimum mean square error for additive noise channels are derived when the input distribution is constrained to be close to a Gaussian reference distribution in terms of the Kullback-Leibler divergence. The upper bound is tight and is attained by a Gaussian distribution whose mean is identical to that of the reference distribution and whose covariance matrix is define...
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