We derive inner and outer bounds on the capacity region for a class of three-user partially connected interference channels. We focus on the impact of topology, interference alignment, and interplay between interference and noise. The representative channels we consider are the ones that have clear interference alignment gain. For these channels, Z-channel type outer bounds are tight to within a constant gap from capacity. We present near-optimal achievable schemes based on rate-splitting and lattice alignment.
The @math -user cyclic Gaussian interference channel is considered in @cite_6 where an approximate capacity for the weak interference regime ( @math for all @math ) and the exact capacity for the strong interference regime ( @math for all @math ) are derived. Our type 4 and 5 channels are @math cases in interference regimes, which were not considered in @cite_6 .
@cite_6
2568383335
This paper studies the capacity region of a K-user cyclic Gaussian interference channel, where the kth user interferes 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 of the K-user cyclic interference channel to within a constant gap in the weak interference regime. Specifically, for the 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 three-user case, this gap can be sharpened to 1 ½ bits by time-sharing of several different strategies. The capacity result of the K-user cyclic Gaussian interference channel in the strong interference regime is also given. Further, based on the capacity results, this paper studies the generalized degrees of freedom (GDoF) of the symmetric cyclic interference channel. It is shown that the GDoF of the symmetric capacity is the same as that of the classic two-user interference channel, no matter how many users are in the network.