  The joint design of input constellation and low-density parity-check (LDPC)
codes to approach the symmetric capacity of the two-user Gaussian multiple
access channel is studied. More specifically, multilevel coding is employed at
each user to construct a high-order input constellation and the constellations
of the users are jointly designed so as to maximize the multiuser shaping gain.
At the receiver, each layer of the multilevel coding is jointly decoded among
users, while successive cancellation is employed across layers. The LDPC code
employed by each user in each layer is designed using EXIT charts to support
joint decoding among users for the prescribed per-layer rate and SNR. Numerical
simulations are provided to validate the proposed constellation and LDPC code
designs.
