The Capacity of the Band-Limited Gaussian Channel

Shannon's celebrated formula W ln(1 + Po/NoW) for the capacity of a time-continuous communication channel with bandwidth W cps, average signal power Po, and additive Gaussian noise with flat spectral density Nohas never been justified by a coding theorem (and “converse”). Such a theorem is necessary to establish W ln(1 + Po/NoW) as the supremum of those transmission rates at which one may communicate over this channel with arbitrarily high reliability as the coding and decoding delay becomes large. In this paper, a number of physically consistent models for this time-continuous channel are proposed. For each model the capacity is established as W ln(1 + Po/NoW) by means of a coding theorem and converse.