LDPC Coded Multiuser Shaping for the Gaussian Multiple Access Channel

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.