Two Birds and One Stone: Gaussian Interference Channel With a Shared Out-of-Band Relay of Limited Rate

The two-user Gaussian interference channel with a shared out-of-band relay is considered. The relay observes a linear combination of the source signals and broadcasts a common message to the two destinations, through a perfect link of fixed limited rate R₀ bits per channel use. The out-of-band nature of the relay is reflected by the fact that the common relay message does not interfere with the received signal at the two destinations. A general achievable rate is established, along with upper bounds on the capacity region for the Gaussian case. For R₀ values below a certain threshold, which depends on channel parameters, in achievable rates asymptotically in regimes where joint a two-for-one gain is achievable by the capacity region of this channel is determined in this paper to within a constant gap of Δ = 1.95 bits. We identify interference regimes where a two-for-one gain in achievable rates is possible for every bit relayed, up to a constant approximation error. Instrumental to these results is a carefully designed quantize-and-forward type of relay strategy along with a joint decoding scheme employed at destination ends. Further, we also study successive decoding strategies with optimal decoding order (corresponding to the order at which common, private, and relay messages are decoded), and identify interference regimes where with an optimal decoding order, successive decoding may also achieve two-for-one gains similar to joint decoding; yet, in general, successive decoding produces unbounded loss asymptotically when compared to joint decoding.