Joint physical layer coding and network coding for bidirectional relaying
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We consider the problem of two transmitters wishing to exchange information through a relay in the middle. The channels between the transmitters and the relay are assumed to be synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. An upper bound on the capacity is 1/2 log(1 + snr) bits per transmitter per use of the medium-access phase and broadcast phase of the bi-directional relay channel. We show that using lattice codes and lattice decoding, we can obtain a rate of 1/2 log(1 + snr) bits per transmitter, which is essentially optimal at high SNR's. The main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs Slepian-Wolf coding with structured codes. For asymptotically low SNR's, jointly decoding the two transmissions at the relay (MAC channel) is shown to be optimal. We conjecture that if the two transmitters use identical lattices, we can achieve a rate of only I log(I + snr) even with maximum likelihood decoding. The proposed scheme can be thought of as a joint physical layer, network layer code which outperforms the recently proposed analog network coding scheme.
author list (cited authors)
Narayanan, K., Wilson, M. P., & Sprintson, A.