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

This paper studies the capacity region of a $K$-user cyclic Gaussian interference channel, where the $k$th user interferes with only the $(k-1)$th user (mod $K$) in the network. Inspired by the work of Etkin, Tse and Wang, which 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, 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 two bits (or one bit per dimension) in the weak interference regime. Finally, the capacity result of the $K$-user cyclic Gaussian interference channel in the strong interference regime is also given.