DESIGN OF ROTATIONALLY INVARIANT C-8 4-PSK TRELLIS CODES/

In recent years, time-variant trellis-coded C-8/4-PSK; modulation sche mes were proposed to improve Ungerboeck's well-known coded 8-PSK becau se of their higher synchronization stability. In addition to the alrea dy known linear C-8/4-PSK codes, new nonlinear ones with 90 degrees ro tational invariance have been designed. The codes result from trellis diagrams which are constructed using a special branch symmetry and sym bol mapping to reach the desired 90 degrees invariance. A special eval uation algorithm for nonlinear codes calculates the coding gain and ex cludes catastrophic trellis diagrams. The new 8- and 16-state codes. f or the repetitive 844-, 884-, and 84-schemes have an asymptotic coding gain of 3 dB over uncoded 4-PSK. The 8-state codes need an additional differential precoder which is not necessary for the 16-state codes.