Parallel Gaussian Interference Channels Are Not Always Separable
Cadambe, V.R.; Jafar, S.A.
Information Theory, IEEE Transactions on
Volume 55, Issue 9, Sept. 2009 Page(s):3983 - 3990
Digital Object Identifier   10.1109/TIT.2009.2025530
Summary:It is known that the capacity of parallel (multicarrier) 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 counterexample is provided in the form of a 3 user interference channel where separate encoding can only achieve a sum capacity of 2 log(1+3 SNR) while the actual capacity, achieved only by joint encoding across carriers, is 3 log(1+2 SNR). As a byproduct of our analysis, we propose a class of multiple-access-outer bounds on the capacity of the 3 user interference channel.

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