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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{durcik2026weak,
  title = {{A weak Hellinger inequality for noisy Boolean channels}},
  author = {Polona Durcik and Marco Fraccaroli and Joris Roos},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28534},
  eprint = {2609.28534},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28534},
}
RIS
TY  - UNPB
TI  - A weak Hellinger inequality for noisy Boolean channels
AU  - Polona Durcik
AU  - Marco Fraccaroli
AU  - Joris Roos
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.28534
UR  - https://arxiv.org/abs/2609.28534
AB  - 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.
ER  -