Achievable Rate Region for Iterative Multi-User Detection via Low-Cost Gaussian Approximation

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 achievable rate solely determined by the two path terminals. Optimized error correcting 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 MAC capacity-approaching performance, ii) the sum-rate capacity can be achieved independently of the integration path in the MSE fields; and iii) the integration path determining achievable rate tuples of all users can be an extra degree of freedom for code design.