Trellis-Coded Multidimensional Phase Modulation

A 2L -dimensional multiple phase-shift keyed MPSK (1.X MPSK) signal set is obtained by forming the Cartesian product of L two-dimensional MPSK signal sets. A systematic approach to partitioning L X MPSK signal sets is used that is based on block coding. An encoder system approach is developed which incorporates the design of a differential precoder, a systematic convolutional encoder, and a signal set mapper. Trellis-coded /. X 4PSK, L X 8PSK, and L X16PSK modulation schemes are found for 1 < L < 4 and a variety of code rates and decoder complexities, many of which are fully transparent to discrete phase rotations of the signal set. The new codes achieve asymptotic coding gains up to 5.85 dB. © 1990 IEEE