Transmission of multi-level digital signals through noise-free distorting channels

The transmission of digital information by variation of the energy level of pulses of fixed shape is limited by channel distortion even in the absence of noise. For a fixed number of levels there is a maximum rate at which information can be transmitted without error—a rate which depends, in general, on the number of levels chosen. The nature of this dependence is examined for several classes of received pulse-shape. It is not generally true that the maximum rate increases with the number of levels, although this result can be obtained with a proper choice of received pulse-shape. The case of a channel with an exponentially decaying impulse characteristic, for which the maximum rate is independent of the number of levels, is of special interest as a large class of passive linear networks has this characteristic at least asymptotically. The RC transmission line when resistively terminated is a member of this class and the maximum rate of transmission over it is in fact approximately independent of the number of levels; when reflectionlessly terminated, however, it behaves in a quite different way.