A Theory of Multilevel Information Channel with Gaussian Noise

Abstract

The interval between the “0” level and “1” level of a binary channel with Gaussian noise is subdivided to provide n = 2g levels per symbol. The channel capacity is computed as a function of g and of the signal-noise ratio D of the original binary channel. For a sufficiently large, fixed value of D, if we increase 9 indefinitely, the channel capacity approaches the logarithm of D, as can be expected from continuous channel. For a fixed value of g, if we increase D indefinitely, the channel capacity approaches g. For a given value of D, there is a certain value of g, beyond which the channel capacity does not appreciably increase any longer by increasing g. The problem is first solved by a simplifying model, and then the error introduced by this simplification is estimated. © 1957 IEEE. All rights reserved.