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Demodulation in a random multiple access channel is considered where thesignals are chosen uniformly randomly with unit energy, a model applicable toseveral modern transmission systems. It is shown that by lifting (replicating)the graph of this system and randomizing the graph connections, a simpleiterative cancellation demodulator can be constructed which achieves the sameperformance as an optimal symbol-by-symbol detector of the original system. Theiterative detector has a complexity that is linear in the number of users,while the direct optimal approach is known to be NP-hard. However, the maximalsystem load of this lifted graph is limited to \alpha<2.07, even forsignal-to-noise ratios going to infinity - the system is interference limited.We then show that by introducing spatial coupling between subsequent liftedgraphs, and anchoring the initial graphs, this limitation can be avoided andarbitrary system loads are achievable. Our results apply to severalwell-documented system proposals, such as IDMA, partitioned spreading, andcertain forms of MIMO communications.

Multiple Access Demodulation in the Lifted Signal Graph with Spatial Coupling