ON MULTIDIMENSIONAL CODED MODULATIONS HAVING UNIFORM ERROR PROPERTY FOR GENERALIZED DECODING AND FLAT-FADING CHANNELS

We consider the problem of uniform error property (UEP) for a coded mo dulation with constant energy multidimensional symbols, transmitted ov er the additive white Gaussian noise (AWGN) or fading channels and rec eived by a broad class of decoders, This class includes coherent, part ially coherent, double differential, and noncoherent decoders, decoder s designed for fading channels, decoders using one or multiple-symbol observations, and many more, These decoders are described as special c ases of a general decoder model, This decoder operates by maximizing a n arbitrary likelihood function that its arguments are front-end corre lator (matched-filter) outputs, A group code structure that guarantees UEP is developed by using the theory of geometrically uniform codes a nd applying it to the general decoder. These codes are defined over gr oups (commonly nonbinary) with isometric mapping to channel symbols, W e show the code construction for the specific case of L th-dimensional M-ary phase-shift keying (MPSK), An additional interesting property o f these general uniform error codes is related to the case of noncoher ent decoding, We show that when using codes of this family, if a code is noncoherently catastrophic, then it is also rotationally invariant, Then, the use of preceding of the input such that the code becomes ro tationally transparent will also make it noncatastrophic.