[Back]


Publications in Scientific Journals:

G. Pichler, P. Piantanida, G. Matz:
"Dictator Functions Maximize Mutual Information";
Annals of Applied Probability, 28 (2018), 5.



English abstract:
Let (Xⁿ,Yⁿ) denote n independent, identically distributed copies of two arbitrarily correlated Rademacher random variables (X,Y). We prove that the inequality I(f(Xⁿ); g(Yⁿ)) ≤ I(X;Y) holds for any two Boolean functions: f,g: {-1,1}ⁿ → {-1,1} (I(;) denotes mutual information). We further show that equality in general is achieved only by the dictator functions f(xⁿ) = g(xⁿ) = xᵢ, i ∈ {1,2,...,n}.

Keywords:
Boolean functions, mutual information, Fourier analysis, binary sequences, binary codes


"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1214/18-AAP1384


Created from the Publication Database of the Vienna University of Technology.