On the intersymbol interference problem for the Gaussian channel

In this paper we are concerned with the Holsinger–Gallager model for the continuous-time Gaussian channel. Gallager1 proved a coding theorem for this channel, and Cordaro and Wagner2 showed that the 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, the proof here 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.