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This paper studies incremental relay strategies for a two-user Gaussianrelay-interference channel with an in-band-reception andout-of-band-transmission relay, where the link between the relay and the tworeceivers is modelled as a degraded broadcast channel. It is shown thatgeneralized hash-and-forward (GHF) can achieve the capacity region of thischannel to within a constant number of bits in a certain weak relay regime,where the transmitter-to-relay link gains are not unboundedly stronger than theinterference links between the transmitters and the receivers. The GHF relayingstrategy is ideally suited for the broadcasting relay because it can beimplemented in an incremental fashion, i.e., the relay message to one receiveris a degraded version of the message to the other receiver. Ageneralized-degree-of-freedom (GDoF) analysis in the high signal-to-noise ratio(SNR) regime reveals that in the symmetric channel setting, each common relaybit can improve the sum rate roughly by either one bit or two bitsasymptotically depending on the operating regime, and the rate gain can beinterpreted as coming solely from the improvement of the common message rates,or alternatively in the very weak interference regime as solely coming from therate improvement of the private messages. Further, this paper studies anasymmetric case in which the relay has only a single single link to one of thedestinations. It is shown that with only one relay-destination link, theapproximate capacity region can be established for a larger regime of channelparameters. Further, from a GDoF point of view, the sum-capacity gain due tothe relay can now be thought as coming from either signal relaying only, orinterference forwarding only.

Incremental Relaying for the Gaussian Interference Channel with a Degraded Broadcasting Relay