Abstract: A modem with transmitter and reciever sections. Incoming digital data signals produce successive coordinate signals to define successive transmission points representing a given digital value and to modulate quadrature carrier signals. The coordinate signals have unit values of 0, 1, 2.707, 3 and 5 and together control the amplitude and phase of the modulated carrier signals. The receiver section uses received coordinate signals, after they are properly conditioned, to select a decision region which corresponds to a transmission point to produce the digital data signals. The decision regions have rectilinear boundaries on a Cartesian coordinate system at unit values 0, 1.25, 2 and 4 and each region is either rectangular or non-rectangular. Digital synchronism between separate modems is maintained by transmitting coordinate signals corresponding to a framing point which is separate from the transmission points, but which has the same digital value as a transmission point.