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Parallel Gaussian Interference Channels Are Not Always Separable

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2 Author(s)
Cadambe, V.R. ; Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Irvine, CA, USA ; Jafar, S.A.

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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Information Theory, IEEE Transactions on  (Volume:55 ,  Issue: 9 )