Geometrical uniformity of a class of space-time trellis codes

The continued relevance of the Euclidean distance in (flat) fading scenarios renders meaning to distance preserving properties for codes designed for fading channels. Geometrical uniformity can shed more light on the structure of various techniques for jointly encoding across multiple transmit antennas, and can assist in the design of, or systematic search for, better coding schemes. In this correspondence, a family of space-time codes introduced by Ionescu et al. is treated as signal space codes, then proved to be generalized coset codes, and thereby geometrically uniform. It is then shown that geometrical uniformity does remain meaningful in fading channels, for an optimally designed space-time code.