Construction of uniform error property codes for generalized decoding

We consider the general problem of the uniform error property (UEP) for multidimensional coded modulation, transmitted over the AWGN or flat fading channel and received by a generalized decoder. The symbols are restricted to have constant energy. The generalized decoder is a very broad range model for the decoders and receivers which are used in current and proposed communication systems. It operates by maximizing an arbitrary likelihood function the arguments of which are the front-end correlator outputs. The coherent decoder for the AWGN is only a special case. A group code structure which guarantees the UEP is obtained by extending the theory of geometrically uniform codes to the generalized decoder. A discussion on the particular case of noncoherent decoding is presented. It is found that the correlation-based decoder error probability is a function of a pseudo-distance.