Reminiscent of the parity function in network coding for the butterflynetwork, it is shown that forwarding an even/odd indicator bit for a scalarquantization of a relay observation recovers 1 bit of information at the twodestinations in a noiseless interference channel where interference is treatedas noise. Based on this observation, a coding strategy is proposed to improvethe rate of both users at the same time using a relay node in an interferencechannel. In this strategy, the relay observes a linear combination of the twosource signals, and broadcasts a common message to the two destinations over ashared out-of-band link of rate R0 bits per channel use. The relay messageconsists of the bin index of a structured binning scheme obtained from a2^R0-way partition of the squared lattice in the complex plane. We show thatsuch scalar quantization-binning relay strategy asymptotically achieves thecut-set bound in an interference channel with a common out-of-band relay linkof limited rate, improving the sum rate by two bits for every bit relayed,asymptotically at high signal to noise ratios (SNR) and when interference istreated as noise. We then use low-density parity-check (LDPC) codes along withbit-interleaved coded-modulation (BICM) as a practical coding scheme for theproposed strategy. We consider matched and mismatched scenarios, depending onwhether the input alphabet of the interference signal is known or unknown tothe decoder, respectively. For the matched scenario, we show the proposedstrategy results in significant gains in SNR. For the mismatched scenario, weshow that the proposed strategy results in rate improvements that, without therelay, cannot be achieved by merely increasing transmit powers. Finally, we usegeneralized mutual information analysis to characterize the theoreticalperformance of the mismatched scenario and validate our simulation results.
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