  Lattice codes used under the Compute-and-Forward paradigm suggest an
alternative strategy for the standard Gaussian multiple-access channel (MAC):
The receiver successively decodes integer linear combinations of the messages
until it can invert and recover all messages. In this paper, a multiple-access
technique called CFMA (Compute-Forward Multiple Access) is proposed and
analyzed. For the two-user MAC, it is shown that without time-sharing, the
entire capacity region can be attained using CFMA with a single-user decoder as
soon as the signal-to-noise ratios are above $1+\sqrt{2}$. A partial analysis
is given for more than two users. Lastly the strategy is extended to the
so-called dirty MAC where two interfering signals are known non-causally to the
two transmitters in a distributed fashion. Our scheme extends the previously
known results and gives new achievable rate regions.
