An achievable rate region for certain noisy three-user-pair interference channels is proposed. The channel class under consideration generalizes the three-pair deterministic interference channel (3-DIC) in the same way as the Telatar-Tse noisy two-pair interference channel generalizes the El Gamal-Costa injective channel. Specifically, arbitrary noise is introduced that acts on the combined interference signal before it affects the desired signal. This class of channels includes the Gaussian case. The rate region includes the best-known inner bound on the 3-DIC capacity region, dominates treating interference as noise, and subsumes the Han-Kobayashi region for the two-pair case.

9 pages, 3 figures; abbreviated version to be presented at IEEE International Symposium on Information Theory (ISIT 2012)