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 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.Comment: 32 pages, 8 figures, submitted to IEEE trans. on Information Theory in Fe

Multiple Access Outerbounds and the Inseparability of Parallel Interference Channels

Abstract — It is known that the capacity of parallel (multi-carrier) Gaussian point-to-point, multiple access and broadcast channels can be achieved by separate encoding for each subchannel (carrier) subject to a power allocation across carriers. In this paper we show that such a separation does not apply to parallel Gaussian interference channels in general. A counter-example is provided in the form of a 3 user interference channel where separate encoding can only achieve a sum capacity of log(SNR)+o(log(SNR)) per carrier while the actual capacity, achieved only by jointencoding across carriers, is 3/2 log(SNR)) + o(log(SNR)) per carrier. As a byproduct of our analysis, we propose a class of multiple-access-outerbounds on the capacity of the 3 user interference channel. I