Extremal Channels of Gallager's $E_{0}$ Under the Basic Polarization Transformations
Mine Alsan · IEEE Transactions on Information Theory · 2014
We study the extremality of the binary erasure channel and the binary symmetric channel for Gallager's reliability function E0of binary input discrete memoryless channels evaluated under the uniform input distribution from the aspect of channel polarization. In particular, we show that amongst all binary discrete memoryless channels of a given E0(ρ) value, for a fixed ρ ≥ 0, the binary erasure channel and the binary symmetric channel are extremal in the evolution of E0under the one-step polarization transformations.