Proof of the Most Informative Boolean Function Conjecture

Mustafa Kesal

Proof of the Most Informative Boolean Function Conjecture

Information Theory 2017-10-20 v3 math.IT

Authors: Mustafa Kesal

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 $\alpha$ . Recently, Courtade and Kumar postulates that $I(f(\XX{N});\YY{N})\leq 1-\Be(\alpha)$ for any Boolean function $f$ \cite{courtade}. In this paper, we provide a proof of the correctness of this conjecture.

Keywords

boolean functions

Cite

@article{arxiv.1511.01828,
  title  = {Proof of the Most Informative Boolean Function Conjecture},
  author = {Mustafa Kesal},
  journal= {arXiv preprint arXiv:1511.01828},
  year   = {2017}
}

Comments

This paper is withdrawn due to a serious flaw in the proof

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