On the capacity of the K-user cyclic Gaussian interference channel

Abstract

This paper studies the capacity region of a Kuser 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, 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.

Superposition Signaling in Broadcast Interference Networks

“…A similar result for the K-user cyclic GIN was obtained in [18]. It was also shown in [19]- [21] that using non-Gaussian inputs (or in [22] with Gaussian inputs) and treating interference as noise achieves the capacity region of some special SISO GINs within a constant gap.…”

On the Optimality of Treating Interference as Noise

“…1 demonstrates that for the two-user symmetric Gaussian interference channel, when the strengths of both direct channels are assumed as SNR and the interference channels are not stronger than √ SNR, TIN achieves the symmetric GDoF for each user. This result is generalized to K-user fully-connected symmetric Gaussian interference channels in [8] and to cyclic asymmetric Gaussian interference channels in [9]. However, not much is known about the regime where TIN is GDoF-optimal for the general fully-connected, fully-asymmetric K-user Gaussian interference channel.…”

“…Following the same definition as in [7] and [9], an achievable region is said to be within x bits of the capacity region if for any rate tuple (R 1 , R 2 , ..., R K ) on the boundary of the achievable region, the rate tuple (R 1 + x, R 2 + x, ..., R K + x) is outside the channel capacity region.…”

“…The significance of our dual characterization is the elimination of power allocation variables in the characterization. Finally, we use the outer bounds developed in [9] to establish the optimality of polyhedral TIN in the regime of interest. Since TIN performs no worse than polyhedral TIN, this proves that TIN is optimal in that regime in the GDoF sense.…”

Sum-capacity of a class of K-user Gaussian interference channels within O(K) bits

“…Even for some linear deterministic 3-user ICs with specific connectivity [14], [15], sum-capacity itself is not fully characterized. Recently, the approximate capacity was derived for a K-user Gaussian IC with specific cyclic interference pattern [19]. However, in this kind of interference channel, the key problem of interference alignment does not arise.…”