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PreprintCC BY 4.0arXiv

Beyond Hypercontractivity: Stronger Communication Converses via Rényi Contraction

  • Ryo Hommura Moore
  • Amedeo Roberto Esposito
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Abstract

We study the relationship between strong data-processing inequalities for Rényi divergences and hypercontractivity. For Rényi divergences of order greater than one, we characterize the contraction of Rényi divergences through a property of the dual Markov operator that we name power contraction. Using the contraction coefficient, we derive an upper bound on rectangle probabilities in terms of their marginals that is at least as strong as the corresponding bound obtained via hypercontractivity. Combining this result with inversion of the binary Rényi divergence, we derive communication lower bounds for one-way communication-assisted agreement distillation. Examples involving binary symmetric and rare-event Z-channels illustrate the improvements over standard hypercontractive converses.

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Cite

BibTeXRIS
BibTeX
@misc{moore2026beyond,
  title = {{Beyond Hypercontractivity: Stronger Communication Converses via Rényi Contraction}},
  author = {Ryo Hommura Moore and Amedeo Roberto Esposito},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13030},
  eprint = {2610.13030},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13030},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Beyond Hypercontractivity: Stronger Communication Converses via Rényi Contraction
AU  - Ryo Hommura Moore
AU  - Amedeo Roberto Esposito
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13030
UR  - https://arxiv.org/abs/2610.13030
AB  - We study the relationship between strong data-processing inequalities for Rényi divergences and hypercontractivity. For Rényi divergences of order greater than one, we characterize the contraction of Rényi divergences through a property of the dual Markov operator that we name power contraction. Using the contraction coefficient, we derive an upper bound on rectangle probabilities in terms of their marginals that is at least as strong as the corresponding bound obtained via hypercontractivity. Combining this result with inversion of the binary Rényi divergence, we derive communication lower bounds for one-way communication-assisted agreement distillation. Examples involving binary symmetric and rare-event Z-channels illustrate the improvements over standard hypercontractive converses.
ER  -