Multiple Access Demodulation in the Lifted Signal Graph with Spatial Coupling

Demodulation in a random multiple access channel is considered where the signals are chosen uniformly randomly with unit energy, a model applicable to several modern transmission systems. It is shown that by lifting (replicating) the graph of this system and randomizing the graph connections, a simple iterative cancellation demodulator can be constructed which achieves the same performance as an optimal symbol-by-symbol detector of the original system. The iterative 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 maximal system load of this lifted graph is limited to \alpha<2.07, even for signal-to-noise ratios going to infinity - the system is interference limited. We then show that by introducing spatial coupling between subsequent lifted graphs, and anchoring the initial graphs, this limitation can be avoided and arbitrary system loads are achievable. Our results apply to several well-documented system proposals, such as IDMA, partitioned spreading, and certain forms of MIMO communications.