A generalisation of the Gaussian doubly dirty multiple access channel to a Gaussian triply dirty multiple access chan- nel (GTD-MAC) is considered, where there are three additive interference signals, each one non-causally known to only associated transmitter. Same as in the Gaussian doubly dirty multiple access channel, Costa’s strategy (i.e. random bin- ning scheme) cannot achieve positive rates in the limit of strong interferences. In contrast, it is shown that positive rates independent of the interferences can be achieved by lattice strategies. In fact in some cases—which depend on the noise variance and power constraints—lattice strategies are optimal, in particular, in the high signal-to-noise ratio (SNR) regime. For the GTD-MAC, two models are considered, full side information and partial side information at the transmitters. The results show that partiality in side information reduces the achievable rates as numerical illustrations confirm. Also, the results for the GTD-MAC can be extended to the K-user case. Copyright © 2013 John Wiley & Sons, Ltd.

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