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

TL;DR

This paper analyzes a Gaussian interference channel with a shared out-of-band relay, establishing capacity bounds, achievable rates, and demonstrating two-for-one rate gains with specific relay strategies.

Contribution

It provides the first near-complete capacity characterization for low-rate relays in interference channels, introducing a quantize-and-forward scheme and comparing joint and successive decoding.

Findings

Capacity region determined within 1.95 bits for certain relay rates.

Two-for-one rate gains achievable with relay assistance.

Successive decoding approaches joint decoding in some regimes but can be suboptimal.

Abstract

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 $R_0$ 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 $R_0$ values below a certain threshold, which depends on channel parameters, the capacity region of this channel is determined in this paper to within a constant gap of $\Delta=1.95$ 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 show that successive decoding also achieves two-for-one gains asymptotically in regimes where a two-for-one gain is achievable by joint decoding; yet, successive decoding produces unbounded loss asymptotically when compared to joint decoding, in general.