Some Relations between Signal Detection and the Capacity of Communication Channels

摘要

The theme of the ComCon conferences is the unification of communications and control. Thus, methods and results that are common to the two areas are of central interest. This paper contains a discussion of a topic that is in this general spirit: relations that exist between signal detection and information theory and/or signal detection. They have bee developed in recent years as a result of specific needs: They have been developed in recent years as a result of specific needs: they are essential in obtaining solutions to channel capacity problems when the noise sample paths comprise an infinite-dimensional linear manifold. Channel capacity is one of the most basic problems of information theory. In many setups, such as that of the DMC (discrete memoryless channel), the basic mathematical structure is so simple that measure-theoretic questions do not arise. The situation changes radically when one considers more complicated channels, such as the continuous-time Gaussian channel with memory. (rh)