Information capacity of the stationary Gaussian channel

The averaged information capacity of the mismatched stationary continuous-time Gaussian channel is considered, in the limit as the observation time becomes infinite. It is required only that the signal satisfy a reproducing kernel Hilbert space constraint on expected energy. This requires the, signal energy to be distributed in regions where the noise energy, is not too small, and is the weakest condition that provides finite capacity. In the case when both the noise covariance and the filter on the message are expressed by rational functions, the results complement those previously obtained by Gallager and Holsinger (1968), and the combination gives a complete solution to the capacity problem. The treatment provides a desirable generality on the class of transmitted signals that is not present in previous treatments