Information Capacity of Gaussian Channels

i Information capacity of Gaussian channels is one of the basic problems of information theory. Shannon's results for white Gaussian channels and Fano's "waterfilling" analysis of stationary Gaussian channels are two of the best-known works of early information theory. Results are given here which extend to a general framework these results and others due to Gallager and to Kadota, Zakai, and Ziv. The development applies to arbitrary Gaussian channels when the channel noise has sample paths in a separable Banach sp»ace, and to a large class of Gaussian channels when the noise has sample paths in a linear topological vector space. Solutions for the capacity are given for both matched and mismatched channels.