  Despite the simplicity of the scheme of treating interference as noise (TIN),
it was shown to be sum-capacity optimal in the Gaussian interference channel
(IC) with very-weak (noisy) interference. In this paper, the 2-user IC is
altered by introducing an additional transmitter that wants to communicate with
one of the receivers of the IC. The resulting network thus consists of a
point-to-point channel interfering with a multiple access channel (MAC) and is
denoted PIMAC. The sum-capacity of the PIMAC is studied with main focus on the
optimality of TIN. It turns out that TIN in its naive variant, where all
transmitters are active and both receivers use TIN for decoding, is not the
best choice for the PIMAC. In fact, a scheme that combines both time division
multiple access and TIN (TDMA-TIN) strictly outperforms the naive-TIN scheme.
Furthermore, it is shown that in some regimes, TDMA-TIN achieves the
sum-capacity for the deterministic PIMAC and the sum-capacity within a constant
gap for the Gaussian PIMAC. Additionally, it is shown that, even for very-weak
interference, there are some regimes where a combination of interference
alignment with power control and treating interference as noise at the receiver
side outperforms TDMA-TIN. As a consequence, on the one hand treating
interference as noise in a cellular uplink is approximately optimal in certain
regimes. On the other hand those regimes cannot be simply described by the
strength of interference.
