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

TL;DR

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

Contribution

It establishes a novel EXIT chart area theorem for IDMA, linking MSE evolution to achievable rates and enabling optimized code design through integration path selection.

Findings

Low-cost GA detection approaches capacity limits.

Sum-rate capacity is independent of MSE integration path.

Path flexibility can be exploited for code optimization.

Abstract

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.