Conference paper

Ergodic Theory Meets Polarization I: A Foundation of Polarization Theory

An open problem in polarization theory is to determine the binary operations that always lead to polarization when they are used in Ar{\i}kan style constructions. This paper solves this problem by providing a necessary and sufficient condition for a binary operation to be polarizing. The characterization is given in terms of a new mathematical framework that we introduce. We show that a binary operation is polarizing if and only if its inverse is strongly ergodic.

Related material