PreprintCC BY 4.0arXiv
Polarization on Bounded Euclidean Spaces and More General Compact Groups
Abstract
We establish polarization for memoryless sources taking values on the unit-perimeter circle, or on more general compact groups, under Arıkan's polar transform. For sources with finite differential entropy, all but an O((log N)−1/12) fraction of the conditional differential entropies in successive cancellation order lie within any fixed positive distance of zero, where N is the block length. Examples indicate that the true polarization rate is indeed very slow: an inverse-logarithmic rate does not underestimate the polarization speed at moderate block lengths.
Related
- Bounded curvature manifolds without Euclidean isometric immersions of bounded mean curvature
- An optimal pinching theorem on compact minimal submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices
- An optimal pinching theorem on compact minimal submanifolds in the Euclidean spheres via eigenvalues of fundamental matrices II
- L1-Poincar\'e inequalities for differential forms on Euclidean spaces and Heisenberg groups
- A Frankel type theorem in Euclidean and hyperbolic spaces
BibTeX
@misc{sriramu2026polarization,
title = {{Polarization on Bounded Euclidean Spaces and More General Compact Groups}},
author = {Sharang M. Sriramu and Lampros Gavalakis and Ioannis Kontoyiannis and Aaron B. Wagner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32760},
eprint = {2610.32760},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32760},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Polarization on Bounded Euclidean Spaces and More General Compact Groups
AU - Sharang M. Sriramu
AU - Lampros Gavalakis
AU - Ioannis Kontoyiannis
AU - Aaron B. Wagner
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32760
UR - https://arxiv.org/abs/2610.32760
AB - We establish polarization for memoryless sources taking values on the unit-perimeter circle, or on more general compact groups, under Arıkan's polar transform. For sources with finite differential entropy, all but an O((log N)^−1/12) fraction of the conditional differential entropies in successive cancellation order lie within any fixed positive distance of zero, where N is the block length. Examples indicate that the true polarization rate is indeed very slow: an inverse-logarithmic rate does not underestimate the polarization speed at moderate block lengths.
ER -