Monotonicity of the Rényi channel capacity under non-signaling assisted channel simulation
Abstract
We give an alternative variational proof that non-signaling correlations shared between the sender and receiver cannot increase the Rényi capacity of a classical channel. This monotonicity follows from the data-processing inequality for channel divergences established by Oufkir, Yao and Berta. Our approach works directly with the information-radius representation of the capacity. The constraints defining non-signaling boxes are linear in the box, while the Rényi capacity depends on the channel nonlinearly. We use a Legendre transform to express the capacity as an extremum over a family of affine functionals in which the channel appears linearly. Combining this method with separate arguments for the Shannon capacity and endpoint orders, we recover monotonicity at every order from zero to infinity. We then derive consequences for standard coding exponent functions: non-signaling simulation cannot increase the random-coding or sphere-packing exponent below capacity, or decrease the strong-converse exponent above capacity.
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BibTeX
@misc{shariat2026monotonicity,
title = {{Monotonicity of the Rényi channel capacity under non-signaling assisted channel simulation}},
author = {Tina Shariat and Matt Hoogsteder-Riera and Marco Tomamichel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.34213},
eprint = {2609.34213},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34213},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Monotonicity of the Rényi channel capacity under non-signaling assisted channel simulation
AU - Tina Shariat
AU - Matt Hoogsteder-Riera
AU - Marco Tomamichel
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2609.34213
UR - https://arxiv.org/abs/2609.34213
AB - We give an alternative variational proof that non-signaling correlations shared between the sender and receiver cannot increase the Rényi capacity of a classical channel. This monotonicity follows from the data-processing inequality for channel divergences established by Oufkir, Yao and Berta. Our approach works directly with the information-radius representation of the capacity. The constraints defining non-signaling boxes are linear in the box, while the Rényi capacity depends on the channel nonlinearly. We use a Legendre transform to express the capacity as an extremum over a family of affine functionals in which the channel appears linearly. Combining this method with separate arguments for the Shannon capacity and endpoint orders, we recover monotonicity at every order from zero to infinity. We then derive consequences for standard coding exponent functions: non-signaling simulation cannot increase the random-coding or sphere-packing exponent below capacity, or decrease the strong-converse exponent above capacity.
ER -