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Geometrically uniform partitions of L×MPSK constellations and related binary trellis codes

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4 Author(s)
Benedetto, S. ; Dipartimento di Elettronica, Politecnico di Torino, Italy ; Garello, R. ; Mondin, M. ; Montorsi, G.

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

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Information Theory, IEEE Transactions on  (Volume:39 ,  Issue: 6 )