  We establish a multiuser extrinsic information transfer (EXIT) chart area
theorem for the interleave-division multiple access (IDMA) scheme, a special
form of superposition coding, in multiple access channels (MACs). A low-cost
multi-user detection (MUD) based on the Gaussian approximation (GA) is assumed.
The evolution of mean-square errors (MSE) of the GA-based MUD during iterative
processing is studied. We show that the K-dimensional tuples formed by the MSEs
of K users constitute a conservative vector field. The achievable rate is a
potential function of this conservative field, so it is the integral along any
path in the field with value of the integral solely determined by the two path
terminals. Optimized codes can be found given the integration paths in the MSE
fields by matching EXIT type functions. The above findings imply that i)
low-cost GA detection can provide near capacity performance, ii) the sum-rate
capacity can be achieved independently of the integration path in the MSE
fields; and iii) the integration path can be an extra degree of freedom for
code design.
