Abstract: A quotient coding modem comprises a modulator that encodes transmitted symbols by the equation ##EQU1## and a demodulator that decodes received symbols by the equation ##EQU2## where q(t) and q.sub.r (t) are functions of time for transmitted and received symbols s(t) and s.sub.r (t) respectively at time t, P.sub.r (t)=.vertline.q.sub.r (t).vertline..sup.2 is instantaneous received baseband power at time t, .eta. is a function of the two smallest symbol amplitudes, and P.sub.max is peak transmitted power.

Abstract: Equalizer apparatus is provided which includes a number of successively cled lattice stages, each of the stages comprising a selected configuration of adjustable electrical components, the input to the first stage of the successively coupled lattice stages comprising the output of a data transmission channel. The equalizer apparatus further includes a subtractor device coupled to the lattice stages for providing a succession of error terms, each of the error terms comprising an accumulation of the squares of a number of error quantities, each of the error quantities indicating the difference between an undistorted training signal, in a sequence of training signals which are received by the subtractor device, and the same training signal after it has travelled through the data transmission channel and is received by the lattice stages.

Abstract: An improved equalizer receives the output of a data transmission channel at he first stage of a number of successively coupled lattice stages which are each made up of a selected configuration of adjustable electrical components. A subtractor device is coupled to the lattice stages for providing a succession of error terms. The error terms are an accumulation of the squares of a number of error quantities, which are the differences between a sequence of undistorted training signals or estimates of the transmitted signal which are received by the subtractor device, and the same training signals after they have travelled through the data transmission channel. A delayed stage and two dimensional vector matrices are coupled in each of the lattice stages for iteratively adjusting their components in accordance with a least squares procedure, that is, the components are adjusted each time a signal is received and the iterative adjustment continues until a prespecified error limit is reached.