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The Capacity of the White Gaussian Noise Channel

Published online by Cambridge University Press:  27 July 2009

Jerome R. Bretienbach
Jerome R. Bretienbach
Affiliation:
Department of Electronic and Electrical EngineeringCailfornia Polytechnic State University San Luis Obispo, California 93407
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Abstract

The capacity of the white Gaussian noise (WGN) channel is widely stated as S/N0 nats/unit time. This conclusion is commonly derived either formally, or from the capacity, W ln(l + S/N0W), of the corresponding band-limited channel with bandwidth W, by taking W→8. In this paper, the WGN channel capacity is instead found directly by treating WGN as an arbitrary noise sequence that whitens in a general sense. In addition, the coding theorems proved make explicit the class of allowable receivers, either finite- or infinite-dimensional correlation receivers, or unconstrained. The capacities for these three receiver classes are found to be, respectively: S/N0 for S> 0, and 0 for S = 0; and 8 for all S ≥ 0. In those cases where the capacity is infinite, actual transmitter–receiver pairs are specified that achieve capacity.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 3 , July 1990 , pp. 345 - 353
Copyright
Copyright © Cambridge University Press 1990

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