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arXiv · 1511.01828

Proof of the Most Informative Boolean Function Conjecture

Mustafa Kesal
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Abstract

Suppose $\XX{N}$ is a uniformly distributed $N$-dimensional binary vector and $\YY{N}$ is obtained by passing $\XX{N}$ through a binary symmetric channel with crossover probability $α$. Recently, Courtade and Kumar postulates that $I(f(\XX{N});\YY{N})\leq 1-\Be(α)$ for any Boolean function $f$ \cite{courtade}. In this paper, we provide a proof of the correctness of this conjecture.

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Mustafa Kesal. 2017-10-18. Proof of the Most Informative Boolean Function Conjecture. https://arxiv.org/abs/1511.01828

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