On the Degrees-of-Freedom of the K-User Gaussian Interference Channel

Details On the Degrees-of-Freedom of the K-User Gaussian Interference Channel On the Degrees-of-Freedom of the K-User Gaussian Interference Channel

2009-01-13

arxiv.org/abs/0901.1695v1

Computer Science

Information Theory

submitted to IEEE Transactions on Information Theory, June 18, 2008

Scientific paper

The degrees-of-freedom of a K-user Gaussian interference channel (GIFC) has been defined to be the multiple of (1/2)log_2(P) at which the maximum sum of achievable rates grows with increasing P. In this paper, we establish that the degrees-of-freedom of three or more user, real, scalar GIFCs, viewed as a function of the channel coefficients, is discontinuous at points where all of the coefficients are non-zero rational numbers. More specifically, for all K>2, we find a class of K-user GIFCs that is dense in the GIFC parameter space for which K/2 degrees-of-freedom are exactly achievable, and we show that the degrees-of-freedom for any GIFC with non-zero rational coefficients is strictly smaller than K/2. These results are proved using new connections with number theory and additive combinatorics.

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