Despite the simplicity of the scheme of treating interference as noise (TIN),
it was shown to be sum-capacity optimal in the Gaussian 2-user interference
channel in \cite{ShangKramerChen,MotahariKhandani,AnnapureddyVeeravalli}. In
this paper, an interference network consisting of a point-to-point channel
interfering with a multiple access channel (MAC) is considered, with focus on
the weak interference scenario. Naive TIN in this network is performed by using
Gaussian codes at the transmitters, joint decoding at the MAC receiver while
treating interference as noise, and single user decoding at the point-to-point
receiver while treating both interferers as noise. It is shown that this naive
TIN scheme is never optimal in this scenario. In fact, a scheme that combines
both time division multiple access and TIN outperforms the naive TIN scheme. An
upper bound on the sum-capacity of the given network is also derived.Comment: 5 pages, 3 figures, typos correcte