  In this paper, achievable rates regions are derived for power constrained
Gaussian broadcast channel of two users using finite dimension constellations.
Various transmission strategies are studied, namely superposition coding (SC)
and superposition modulation (SM) and compared to standard schemes such as time
sharing (TS). The maximal achievable rates regions for SM and SC strategies are
obtained by optimizing over both the joint probability distribution and over
the positions of constellation symbols. The improvement in achievable rates for
each scheme of increasing complexity is evaluated in terms of SNR savings for a
given target achievable rate or/and percentage of gain in achievable rates for
one user with reference to a classical scenario.
