Capacity and Error Bounds for a Time-Continuous Gaussian Channel

A model proposed by Fortet for a time-continuous Gaussian channel is analyzed. The model differs from that of Shannon in that a different constraint is imposed on the allowable input signals, and in addition the transmission of a code word in a given time interval is not assumed to interfere with the transmission of a word in any other interval. The capacity of the Fortet channel is established by proving a coding theorem and its weak converse. It is shown that the probability of error of an optimal code approaches zero exponentially with the time duration of the code words, provided the transmission rate is below channel capacity.