On second-order asymptotics of AWGN channels with feedback under the expected power constraint

Abstract

In this paper, we analyze the asymptotic expansion for additive white Gaussian noise (AWGN) channels with feedback under an expected power constraint and the average error probability formalism. We show that the ε-capacity depends on ε in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that the second-order term is bounded between -ln ln n and a term that is proportional to +√(n ln n). The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available.