Design procedure for optimum or rotationally invariant trellis codes

The authors present examples for a search-free, step-by-step design procedure for trellis coded modulation that involves both linear and nonlinear convolutional encoders. Such a procedure starts with a derivation of a trellis description of the code and ends with the series combination of a convolutional encoder and a natural bit mapper to modulation symbols to generate the code. The derivation of this structure is obtained from the analytic description of the code, which also could be used as the modulated signal generator. The examples presented include an eight-dimensional PSK (phase-shift keying) code and a nonlinear, rotationally invariant code