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Abstract: We consider the problem of two transmitters wishing to exchange informationthrough a relay in the middle. The channels between the transmitters and therelay are assumed to be synchronized, average power constrained additive whiteGaussian noise channels with a real input with signal-to-noise ratio SNR ofsnr. An upper bound on the capacity is 1-2 log1+ snr bits per transmitter peruse of the medium-access phase and broadcast phase of the bi-directional relaychannel. We show that using lattice codes and lattice decoding, we can obtain arate of 1-2 log0.5 + snr bits per transmitter, which is essentially optimalat high SNRs. The main idea is to decode the sum of the codewords modulo alattice at the relay followed by a broadcast phase which performs Slepian-Wolfcoding with structured codes. For asymptotically low SNR-s, jointly decodingthe two transmissions at the relay MAC channel is shown to be optimal. Wealso show that if the two transmitters use identical lattices with minimumangle decoding, we can achieve the same rate of 1-2 log0.5 + snr. Theproposed scheme can be thought of as a joint physical layer, network layer codewhich outperforms other recently proposed analog network coding schemes.



Author: Makesh Pravin Wilson, Krishna Narayanan, Henry Pfister, Alex Sprintson

Source: https://arxiv.org/







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