Multiple access outerbounds and the inseparability of parallel interference channels

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 joint- encoding across carriers, is 3/2log(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.