Geometrically uniform TCM codes over groups based on multidimensional 4-PSK and 8-PSK signals

The theory of geometrically uniform (GU) signal constellations and linear codes over groups is applied to the case of multidimensional phase shift keying (PSK) signals. Tables of GU partitions of multidimensional PSK constellations are used to construct good GU codes over nonbinary abelian groups. The authors consider L × 4 PSK and L × 8 PSK constellations used to transmit information rates of 1 and 2 bits per signaling interval, respectively, and present a systematic constructive procedure to search for good codes over generating groups (Z₄)^L and (Z₈)^L . Rotational invariance conditions for the codes are easily incorporated into the search algorithm. In some cases, the codes found improve over the codes known so far. The geometrical uniformity of codes allows a very easy performance evaluation. A set of curves of error event probability for some selected codes is presented