Noisy-Interference Sum-Rate Capacity of Parallel Gaussian Interference Channels

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