  The task of CDMA multiuser detection is to simultaneously estimate binary
symbols of $K$ synchronous users from the received $N$ base-band CDMA signals.
Mathematically, this can be formulated as an inference problem on a complete
bipartite graph. In the research on graphically represented statistical models,
it is known that the belief propagation (BP) can exactly perform the inference
in a polynomial time scale of the system size when the graph is free from
cycles in spite that the necessary computation for general graphs exponentially
explodes in the worst case. In addition, recent several researches revealed
that the BP can also serve as an excellent approximation algorithm even if the
graph has cycles as far as they are relatively long. However, as there exit
many short cycles in a complete bipartite graph, one might suspect that the BP
would not provide a good performance when employed for the multiuser detection.
  The purpose of this paper is to make an objection to such suspicion. More
specifically, we will show that appropriate employment of the central limit
theorem and the law of large numbers to BP, which is one of the standard
techniques in statistical mechanics, makes it possible to develop a novel
multiuser detection algorithm the convergence property of which is considerably
better than that of the conventional multistage detection without increasing
the computational cost significantly. Furthermore, we will also provide a
scheme to analyse the dynamics of the proposed algorithm, which can be
naturally linked to the equilibrium analysis recently presented by Tanaka.
