Joint Physical Layer Coding and Network Coding for Bi-Directional Relaying

TL;DR

This paper introduces a joint physical and network coding scheme using lattice codes for bi-directional relaying, achieving near-optimal rates at high SNRs and outperforming existing analog network coding methods.

Contribution

It proposes a novel lattice coding and decoding approach for bi-directional relaying that combines physical and network layer coding, improving achievable rates.

Findings

Achieves near-capacity rates at high SNRs using lattice codes.

Optimal decoding strategies vary with SNR levels.

Outperforms recent analog network coding schemes.

Abstract

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(0.5 + snr) bits per transmitter, which is essentially optimal at high SNRs. 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 also show that if the two transmitters use identical lattices with minimum angle decoding, we can achieve the same rate of 1/2 log(0.5 + snr). The proposed scheme can be thought of as a joint physical layer, network layer code which outperforms other recently proposed analog network coding schemes.