Work

Polarization on Bounded Euclidean Spaces and More General Compact Groups

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.32760

Authors: Sriramu, Sharang M., Gavalakis, Lampros, Kontoyiannis, Ioannis, Wagner, Aaron B.

Institutions: Fraunhofer Institute for Telecommunications, Heinrich Hertz Institute, University of Cambridge, Cornell University

Language: English

Topic: Error Correcting Code Techniques

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223672380

Cites: 1

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Related to: 10