  The sum-rate capacity of the parallel Gaussian interference channel is shown
to be achieved by independent transmission across sub-channels and treating
interference as noise in each sub-channel if the channel coefficients and power
constraints satisfy a certain condition. The condition requires the
interference to be weak, a situation commonly encountered in, e.g., digital
subscriber line transmission. The optimal power allocation is characterized by
using the concavity of sum-rate capacity as a function of the power
constraints.
