Sufficient conditions on trellis-coded modulation for code-independent synchronizer performance

The carrier synchronization and symbol timing recovery for two-dimensional trellis-code modulated signals are considered. For many popular carrier and clock synchronizers, and tracking and cycle-slipping performance depends on the trellis code only through the second- and fourth-order moments of the coded channel symbols. For three successively more complicated classes of coded symbol alphabets, simple conditions on the trellis code are derived which are sufficient to yield the same second- and fourth-order moments as for uncoded symbols. For trellis codes satisfying these conditions, the synchronizer performance does not depend on the specific code, and is the same as for uncoded symbols. These sufficient conditions are fulfilled by many codes which have been presented in the literature, some of which are discussed