Parallel Gaussian Interference Channels Are Not Always Separable

• Published in: IEEE transactions on information theory Vol. 55; no. 9; pp. 3983 - 3990
• Main Authors: Cadambe, V.R., Jafar, S.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Allocations; Analysis; Applied sciences; Broadcasting; Byproducts; Capacity; Carriers; Channels; Coding, codes; Communication channels; degrees of freedom; Detection, estimation, filtering, equalization, prediction; Encoding; Exact sciences and technology; Frequency; Gaussian; Gaussian channels; Information theory; Information, signal and communications theory; Interference; Interference channels; Intersymbol interference; Multiple access; Multiuser detection; Normal distribution; Power system modeling; Signal and communications theory; Signal, noise; Telecommunications and information theory; Terminology; Time-varying channels; Multiuser detection; Multiple access; Gaussian channel; degrees of freedom; Multicarrier; Power allocation; Channel coding; Counterexample; Capacity; Broadcast channels; interference; Signal detection; Signal to noise ratio
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2009.2025530

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.