1. A modem system comprising: a signal mapper having digital symbols applied to the mapper at a digital port and analog signal samples applied to the mapper at an analog port, for developing mapper output signals that represent the digital symbols and the analog samples; a modulator, responsive to the signal mapper output signals, for developing a modulated output signal at an output port of the modulator representable by a N-dimensional signal space that is composed of a plurality of N-dimensional sub-spaces, where N is an integer greater than 1, the sub-spaces are areas when N is 2 and volumes when N is greater than 2, a predetermined point in each of the sub-spaces being associated with a predetermined digital symbol applied to said mapper in each of the N dimensions, with a zero level analog sample in each of the N dimensions, and other points in each of the volumes associated with the predetermined digital symbols in each of the N dimensions and a non-zero level analog sample in at least one of the N dimensions, and the analog samples in each of the N dimensions form a mutually exclusive set; and means for coupling the output port of the modulator to an output port of the modem.