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arXiv · 2610.32760

Polarization on Bounded Euclidean Spaces and More General Compact Groups

Sharang M. Sriramu·Lampros Gavalakis·Ioannis Kontoyiannis·Aaron B. Wagner
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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.

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Sharang M. Sriramu, Lampros Gavalakis, Ioannis Kontoyiannis, Aaron B. Wagner. 2026-10-23. Polarization on Bounded Euclidean Spaces and More General Compact Groups. https://arxiv.org/abs/2610.32760

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