  We study the capacity of discrete memoryless many-to-one interference
channels, i.e., K user interference channels where only one receiver faces
interference. For a class of many-to-one interference channels, we identify a
noisy interference regime, i.e., a regime where random coding and treating
interference as noise achieves sum-capacity. Specializing our results to the
Gaussian MIMO many-to-one interference channel, which is a special case of the
class of channels considered, we obtain new capacity results. Firstly, we
extend the noisy interference regime, previously studied for (many-to-one)
interference channels with average power constraints on the inputs, to a more
general class of inputs. This more general class includes the practical
scenario of inputs being restricted to fixed finite-size constellations such as
PSK or QAM. Secondly, we extend noisy interference results previously studied
in SISO interference channels with full channel state information (CSI) at all
nodes, to MIMO and parallel Gaussian many-to-one interference channels, and to
fading Gaussian many-to-one interference channels without CSI at the
transmitters. While the many-to-one interference channel requires interference
alignment, which in turn requires structured codes in general, we argue that in
the noisy interference regime, interference is implicitly aligned by random
coding irrespective of the input distribution. As a byproduct of our study, we
identify a second class of many-to-one interference channels (albeit
deterministic) where random coding is optimal (though interference is not
treated as noise). The optimality of random coding in this second class of
channels is due to an interference resolvability condition which precludes
interference alignment and hence obviates the need of structured codes.
