Joint Physical Layer Coding and Network Coding for Bidirectional Relaying

• Published in: IEEE transactions on information theory 2010-11, Vol.56 (11), p.5641-5654
• Main Authors: Wilson, Makesh Pravin, Narayanan, Krishna, Pfister, Henry D, Sprintson, Alex
• Format: Article
• Language: English
• Subjects: Applied sciences; Bi-directional relaying; Bidirectional; Channels; Codes; Coding; Coding, codes; Decoding; Encoding; Exact sciences and technology; Exchange rates; Information systems; Information theory; Information, signal and communications theory; Lattices; minimum angle decoding; nested lattice decoding; Networks; Normal distribution; Radiocommunications; Relay; Relays; Signal and communications theory; Signal to noise ratio; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitters; Transmitters. Receivers; Upper bound
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2010.2068750

We consider a communication system where two transmitters wish to exchange information through a central relay. The transmitter and relay nodes exchange data over 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 multiple access phase and broadcast phase of the bidirectional relay channel. We show that, using lattice codes and lattice decoding, we can obtain a rate of 1/2 log(1/2 + snr) bits per transmitter, which is essentially optimal at high SNR. 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. 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(1/2 + 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.