We consider the design of a simple but powerful space-time trellis coding scheme.While delay diversity can be viewed as the combination of repetition code and delay element

GDDC(Generalized Delay Diversity Code) replaces the repetition code with some other simple block code in order to achieve higher coding gain.The necessary and sufficient condition for GDDCs to achieve full diversity advantage is given.It is proved that all the full diversity GDDCs on BPSK(Binary Phase-Shift Keying) constellation have the same coding gain.We have also thoroughly studied the coding gain of full diversity GDDCs on QPSK (Quadriphase Shift Keying) constellation and the optimal GDDC is given.The strategy can also be applied to the analysis of the coding gain of full diversity GDDCs defined on other constellations.