2016 Volume E99.A Issue 12 Pages 2107-2115
We investigate the coding scheme and error probability in information transmission over continuous-time additive Gaussian noise channels with feedback. As is known, the error probability can be substantially reduced by using feedback, namely, under the average power constraint, the error probability may decrease more rapidly than the exponential of any order. Recently Gallager and Nakiboğlu proposed, for discrete-time additive white Gaussian noise channels, a feedback coding scheme such that the resulting error probability Pe(N) at time N decreases with an exponential order αN which is linearly increasing with N. The multiple-exponential decay of the error probability has been studied mostly for white Gaussian channels, so far. In this paper, we treat continuous-time Gaussian channels, where the Gaussian noise processes are not necessarily white nor stationary. The aim is to prove a stronger result on the multiple-exponential decay of the error probability. More precisely, for any positive constant α, there exists a feedback coding scheme such that the resulting error probability Pe(T) at time T decreases more rapidly than the exponential of order αT as T→∞.
