The authors analyse a new topology for designing ring-TCM schemes over N-di
mensional constellations. The squared free distance of these codes is optim
ised, thus optimisation is performed for AWGN channels. The generalised top
ology is studied for M-PSK and N-dimensional constellations. An improvement
is obtained by using an N-dimensional constellation, in comparison with it
s M-PSK constellation counterpart. This improvement is more evident for hig
her level constellations.