On the Intersymbol Interference Problem for the Gaussian Channel

In this paper we are concerned with the Holsinger-Gallager model of the continuous-time Gaussian channel. Gallager 1 proved a coding theorem for this channel, and Corado and Wagner 2 showed that this theorem remains valid when the effect of intersymbol interference from previous channel uses is taken into account. We show here that the Cordaro-Wagner result holds under somewhat weaker hypotheses. Further, our proof is more elementary, since it does not depend on reproducing kernel Hilbert space theory. Finally, we pose what we feel is an important open problem concerning the stability of the model. In the Holsinger-Gallager 1 model, the channel output is -- 00 where x(t) is the channel input, h^t) is the impulse response of a causal linear filter, and z(t) is a sample from a stationary Gaussian process with two-sided spectral density N(f). A code (M, T, S, A) for this channel is a set of M functions {rc, (i)} f = x with support on the interval [0, T) which satisfy 2355 2356 T H E BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER