Extremality Properties for the Basic Polarization Transformations

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 $E_0(ρ)$ value, for a fixed $ρ\geq 0$, the BEC and BSC are extremal in the evolution of $E_0$ under the one-step polarization transformations.

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