Communication in the Presence of Noise

TLDR

Messages and signals are points in two function spaces, with modulation mapping one space into the other. The authors develop a geometric representation method for any communication system. This method maps messages and signals between function spaces to represent communication systems geometrically. The representation yields results on bandwidth expansion/compression, threshold effects, maximum binary transmission rates under various noise types, properties of ideal systems at that rate, and equivalent binary digits per second for certain information sources.

Abstract

A method is developed for representing any communication system geometrically. Messages and the corresponding signals are points in two "function spaces," and the modulation process is a mapping of one space into the other. Using this representation, a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect. Formulas are found for the maxmum rate of transmission of binary digits over a system when the signal is perturbed by various types of noise. Some of the properties of "ideal" systems which transmit at this maxmum rate are discussed. The equivalent number of binary digits per second for certain information sources is calculated.