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

Noisy-interference Sum-rate Capacity of Parallel Gaussian Interference Channels