On the Error Probability of Optimal Codes in Gaussian Channels under Maximal Power Constraint

Abstract

978-1-5386-9291-2/19/$31.00 ©2019 IEEEFor an additive white Gaussian noise channel, we prove that Th. 41 in [Polyanskiy, Poor, Verdú 2010] is a lower bound to the error probability of any channel code satisfying the maximal power constraint. In contrast, the (tighter) lower bound to the error probability in Eq. (20) in [Shannon 1959] only holds under equal power constraint.