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arXiv · 2609.28534

A weak Hellinger inequality for noisy Boolean channels

Polona Durcik·Marco Fraccaroli·Joris Roos
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Abstract

A weak form of the Hellinger conjecture of Anantharam, Bogdanov, Chakrabarti, Jayram, and Nair for the binary symmetric channel is proved: dictator functions maximize Hellinger $Φ$-entropy among all Boolean functions of the input and all one-bit statistics of the output of a noisy channel. The technical heart of the matter is an explicit inequality in three real parameters, which is proved using explicit polynomial approximations and computer-assisted positivity checks. The results are also formally verified in Lean 4.

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Polona Durcik, Marco Fraccaroli, Joris Roos. 2026-09-22. A weak Hellinger inequality for noisy Boolean channels. https://arxiv.org/abs/2609.28534

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