On the Capacity of the $K$-User Cyclic Gaussian Interference Channel

Details On the Capacity of the $K$-User Cyclic Gaussian Interference Channel On the Capacity of the $K$-User Cyclic Gaussian Interference Channel

2010-10-06

arxiv.org/abs/1010.1044v2

Computer Science

Information Theory

33 pages including 3 figures. Submitted to IEEE Trans on IT

Scientific paper

This paper studies the capacity region of a $K$-user cyclic Gaussian interference channel, where the $k$th user interfers with only the $(k-1)$th user (mod $K$) in the network. Inspired by the work of Etkin, Tse and Wang, who derived a capacity region outer bound for the two-user Gaussian interference channel and proved that a simple Han-Kobayashi power splitting scheme can achieve to within one bit of the capacity region for all values of channel parameters, this paper shows that a similar strategy also achieves the capacity region for the $K$-user cyclic interference channel to within a constant gap in the weak interference regime. Specifically, it is shown that for a special symmetric case where all direct links share the same channel gain and all cross links share another channel gain, the symmetric capacity can be achieved to within one bit in the weak interference regime. For the general (nonsymmetric) $K$-user cyclic Gaussian interference channel, a compact representation of the Han-Kobayashi achievable rate region using Fourier-Motzkin elimination is first derived, a capacity region outer bound is then established. It is shown that the Etkin-Tse-Wang power splitting strategy gives a constant gap of at most 2 bits in the weak interference regime. For the special 3-user case, this gap can be sharpened to $1 {1}{2}$ bits by time sharing of several different strategies. Finally, the capacity result of the $K$-user cyclic Gaussian interference channel in the strong interference regime is also given.

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