Geometrically uniform trellis codes for the Rayleigh-fading channel

We have applied the theory of geometrically uniform (GU) codes to search for good PSK trellis codes for the Rayleigh flat fading channel. It is now well established that the code parameter to be optimised for the Rayleigh fading channel is the diversity (Hamming distance) of the code. We have derived an upper bound on the diversity of multiple symbol per branch trellis codes in terms of the number of states and the spectral efficiency of the code. Many of the GU codes discovered meet this bound with equality and improve upon the PSK trellis codes presented in the current literature. GU trellis codes have the advantage of a reduced code search and a reduced decoding complexity.