Extremality for Gallager’s Reliability Function

We describe certain extremalities for Gallager´s E₀ function evaluated under the uniform input distribution over the class of binary input discrete memoryless channels; The results characterize the extremality of the E₀(ρ) curves of the binary erasure channel and the binary symmetric channel among all the E₀(ρ) curves that can be generated by the class of binary discrete memoryless channels whose E₀(ρ) curves pass through a given point (ρ₀, ε₀), for some ρ₀ > -1.