  Constellation Constrained (CC) capacity regions of a two-user SISO Gaussian
Multiple Access Channel (GMAC) with finite complex input alphabets and
continuous output are computed in this paper. When both the users employ the
same code alphabet, it is well known that an appropriate rotation between the
alphabets provides unique decodability to the receiver. For such a set-up, a
metric is proposed to compute the angle(s) of rotation between the alphabets
such that the CC capacity region is maximally enlarged. Subsequently, code
pairs based on Trellis Coded Modulation (TCM) are designed for the two-user
GMAC with $M$-PSK and $M$-PAM alphabet pairs for arbitrary values of $M$ and it
is proved that, for certain angles of rotation, Ungerboeck labelling on the
trellis of each user maximizes the guaranteed squared Euclidean distance of the
\textit{sum trellis}. Hence, such a labelling scheme can be used systematically
to construct trellis code pairs for a two-user GMAC to achieve sum rates close
to the sum capacity of the channel. More importantly, it is shown for the first
time that ML decoding complexity at the destination is significantly reduced
when $M$-PAM alphabet pairs are employed with \textit{almost} no loss in the
sum capacity. \indent A two-user Multiple Input Multiple Output (MIMO) fading
MAC with $N_{t}$ antennas at both the users and a single antenna at the
destination has also been considered with the assumption that the destination
has the perfect knowledge of channel state information and the two users have
the perfect knowledge of only the phase components of their channels. For such
a set-up, two distinct classes of Space Time Block Code (STBC) pairs derived
from the well known class of real orthogonal designs are proposed such that the
STBC pairs are information lossless and have low ML decoding complexity.
