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. Previous treatments of this channel have assumed an integrability and boundedness condition on the filter producing the transmitted signal. These conditions are omitted here; 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 given here complement those previously obtained by Gallager and Holsinger, and the combination gives a complete solution to the capacity problem. The class of admissible signals under the constraints given here admits more variability in the signal characteristics, which will generally result in a higher capacity than that obtained under the assumptions of previous treatments. As part of the development, it is shown that attention can be restricted to stationary signal processes.