One example of a non-Abelian group code over AWGN channels

In this work is proposed a definition of G-encoding capacity for G-symmetric channels, where G is a non-Abelian semidirect product of two cyclic p-groups. Then it is shown that the 8PSK constellation transmitted over the AWGN channel has the structure of a G-symmetric channel, where G is the dihedral group of the motions of the square. Also, for the same G, it is conjectured that the G-encoding capacity of this 8PSK-AWGN channel achieves its Shannon capacity.