  We consider multiple access communication on a binary input additive white
Gaussian noise channel using randomly spread code division. For a general class
of symmetric distributions for spreading coefficients, in the limit of a large
number of users, we prove an upper bound on the capacity, which matches a
formula that Tanaka obtained by using the replica method. We also show
concentration of various relevant quantities including mutual information,
capacity and free energy. The mathematical methods are quite general and allow
us to discuss extensions to other multiuser scenarios.
