Geometrically uniform TCM codes over groups based on L×MPSK constellations

The theory of geometrically uniform signal sets and codes over groups is applied to the case of L×MPSK constellations. Conditions for rotational invariance of group codes are discussed. The tables of geometrically uniform partitions found in Benedetto et al. (1993) are used to construct good geometrically uniform trellis codes over nonbinary Abelian groups. The present authors consider L×4PSK and L×8PSK constellations used to transmit information rates of 1 and 2 bit/two dimensions, respectively; and present tables of good codes over generating groups (Z4)^L and (Z8)^L,for L ranging from 1 to 4. In most cases, they improve the tables of codes known so far. Moreover, the geometrical uniformity of codes allows a very easy performance evaluation, so that the authors also present a complete set of curves of error event probability for the obtained codes