Geometrically uniform partitions of L*MPSK constellations and related binary trellis codes
Sergio Benedetto, Roberto Garello, M. Mondin, G. Montorsi · IEEE Transactions on Information Theory · 1993
The theory of geometrically uniform trellis codes is applied to the case of multidimensional PSK (phase shift keying) constellations. The symmetry group of an L*MPSK (M-ary PSK) constellation is completely characterized. Conditions for rotational invariance of geometrically uniform partitions of a signal constellation are given. Through suitable algorithms, geometrically uniform partitions of L*MPSK (M=4,8,16 and L=1,2,3,4) constellations are found, which present good characteristics in terms of the set of distances at a given partition level, the maximum obtainable rotational invariance, and the isomorphism of the quotient group associated with the partition. These partitions are used as starting points in a search for good geometrically uniform trellis codes based on binary convolutional codes.>