Extremality Properties for the Basic Polarization Transformations

Abstract

We study the extremality of the BEC and the BSC for Gallager's reliability function $E_0$ evaluated under the uniform input distribution for binary input DMCs from the aspect of channel polarization. In particular, we show that amongst all B-DMCs of a given $E_0(\rho )$ value, for a fixed $\rho \ge 0$, the BEC and BSC are extremal in the evolution of $E_0$ under the one-step polarization transformations.

Submitted to IEEE Transactions on Information Theory

References in corpus (1)

• Submartingale Property of E_0 Under The Polarization Transformations