Abstract: A signal system for use in a communication system for reducing intersymbol interference to increase the data rate per cycle of bandwidth, comprising a plurality of digital channel signal states each representing a channel symbol having a plurality of bits, the channel signal states being related in accordance with the simultaneous solution of a number of equations which are the first derivatives of mean squared channel error with respect to each signal state, each equation being set equal to zero and the equations being solved simultaneously to provide the related signal states.