Lattice Strategies for the Dirty Multiple Access Channel

TL;DR

This paper demonstrates that lattice strategies can effectively handle interference in a multiple access channel, outperforming traditional methods like Costa's binning, especially at high SNR, and provides near-capacity results.

Contribution

It introduces lattice precoding as a superior approach for the dirty MAC, showing its optimality in high SNR and deriving conditions for asymmetric and common interference cases.

Findings

Lattice strategies achieve positive rates independent of interference strength.

In high SNR, lattice strategies are optimal for the dirty MAC.

The gap between achievable rates and capacity is at most 0.167 bits.

Abstract

A generalization of the Gaussian dirty-paper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa's strategies (i.e. by a random binning scheme induced by Costa's auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies ("lattice precoding") can achieve positive rates independent of the interferences, and in fact in some cases - which depend on the noise variance and power constraints - they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the Korner-Marton modulo-two sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a "helper" to the other user), and for the "common interference" case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit.