Trellis Coded Modulation for Two-User Unequal-Rate Gaussian MAC

TL;DR

This paper introduces trellis coded modulation schemes for a two-user Gaussian multiple access channel, optimizing constellation rotation and labeling to maximize capacity and approach any rate pair within the capacity region.

Contribution

It proposes a systematic trellis coding method with optimal labeling and rotation to enhance capacity and decoding in two-user Gaussian MACs.

Findings

Maximizes minimum Euclidean distance in sum trellis

Enlarges the constellation constrained capacity region

Enables approaching any rate pair within capacity region

Abstract

In this paper, code pairs based on trellis coded modulation are proposed over PSK signal sets for a two-user Gaussian multiple access channel. In order to provide unique decodability property to the receiver and to maximally enlarge the constellation constrained (CC) capacity region, a relative angle of rotation is introduced between the signal sets. Subsequently, the structure of the \textit{sum alphabet} of two PSK signal sets is exploited to prove that Ungerboeck labelling on the trellis of each user maximizes the guaranteed minimum squared Euclidean distance, $d^{2}_{g, min}$ in the \textit{sum trellis}. Hence, such a labelling scheme can be used systematically to construct trellis code pairs for a two-user GMAC to approach \emph{any rate pair} within the capacity region.