THE recent development of various methods of modulation such as PCM and PPM which exchange

bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. A

basis for such a theory is contained in the important papers of Nyquist1 and Hartley2 on this subject. In the

present paper we will extend the theory to include a number of new factors, in particular the effect of noise

in the channel, and the savings possible due to the statistical structure of the original message and due to the

nature of the final destination of the information.