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

TL;DR

This paper proves an EXIT chart area theorem for IDMA in MACs, showing that low-cost Gaussian approximation-based multi-user detection can achieve near capacity rates and that the sum-rate capacity is path-independent in the MSE field.

Contribution

It establishes a novel EXIT chart area theorem for IDMA with Gaussian approximation, linking MSE evolution to achievable rates and enabling optimized code design.

Findings

GA-based MUD can approach capacity performance

Sum-rate capacity is independent of the integration path

Path flexibility can be exploited for code optimization

Abstract

We establish a multi-user 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-based MUD can provide near capacity performance; ii) the sum-rate capacity (region) 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.