Extremality for Gallager's Reliability Function $E_0$

Abstract

We describe certain extremalities for Gallager's $E_0$ function evaluated under the uniform input distribution for binary input discrete memoryless channels. The results characterize the extremality of the $E_0(\rho )$ curves of the binary erasure channel and the binary symmetric channel among all the $E_0(\rho )$ curves that can be generated by the class of binary discrete memoryless channels whose $E_0(\rho )$ curves pass through a given point $({\rho }_0,e_0)$, for some ${\rho }_0>-1$.

39 pages, submitted to IEEE Transactions on Information Theory

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