A variational perspective over an extremal entropy inequality

Abstract

This paper proposes a novel variational approach for proving the extremal entropy inequality (EEI) [1]. Unlike previous proofs [1], [2], the proposed variational approach is simpler and it does not require neither the classical entropy power inequality (EPI) [1], [2] nor the channel enhancement technique [1]. The proposed approach is versatile and can be easily adapted to numerous other applications such as proving or extending other fundamental information theoretic inequalities such as the EPI, worst additive noise lemma, and Cramér-Rao inequality.