Tight upper bound on the mutual information of two boolean functions

Abstract : Let (X,Y) be a doubly symmetric binary source. For n i.i.d. copies (Xn,Yn) of (X,Y) we show that max[I(f(Xn); g(Yn))]= I(X,Y), where the maximum is over all Boolean functions f, g: {0, 1}n → {0, 1}. This positively resolves a conjecture published by Kumar and Courtade in 2013.
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Contributor : Pablo Piantanida <>
Submitted on : Monday, January 16, 2017 - 5:35:10 PM
Last modification on : Thursday, November 22, 2018 - 1:16:01 PM

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Pichler Georg, Pablo Piantanida, Gerald Matz. Tight upper bound on the mutual information of two boolean functions. 2016 IEEE Information Theory Workshop (ITW), Sep 2016, cambridge, United Kingdom. ⟨10.1109/ITW.2016.7606787⟩. ⟨hal-01436893⟩

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