Incoherent detection based on differential encoding has been successfully applied to phase-shift-keying (PSK) signals because it eliminates the need for carrier phase acquisition and tracking at the receiver. This paper generalizes the idea of differential encoding by using a nonlinear transformation called multilag high-order instantaneous moment (ml-HIM). The ml-HIM decoder is capable of removing the effects of phase ambiguity, Doppler frequency, Doppler rate, and even higher order phase distortions. The degrees of freedom offered by the different lags is exploited to optimize system performance. In addition to the classical M-ary PSK, the generalized differential encoding idea is also applied to nonconstant modulus constellations, such as M-ary QAM and AM-PM.