Joint Physical Layer Coding and Network Coding for Bidirectional Relaying

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( 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 with structured codes. For asymptotically low SNR, joint decoding of 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( 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.

Energy Efficiency Maximization of Full-Duplex Two-Way Relay With Non-Ideal Power Amplifiers and Non-Negligible Circuit Power

“…half-duplex (HD) relay [7], [8]. Physical-layer network coding (PNC) has been proposed to achieve the minimum number of two slots under HD settings [8].…”

“…Physical-layer network coding (PNC) has been proposed to achieve the minimum number of two slots under HD settings [8]. TWR also has the advantage of improving energy efficiency (EE), as extensively studied in [9]- [12].…”

Impact of Interference in Coexisting Wireless Networks with Applications to Arbitrarily Varying Bidirectional Broadcast Channels

“…Besides the decode-and-forward protocol [20][21][22][23][24][25][26][27][28][29][30][31][32] there are also amplify-and-forward [32][33][34][35][36] or compress-and-forward [37][38][39] approaches similarly as for the classical relay channel. A newer approach is compute-and-forward [40][41][42][43][44][45][46], where the relay decodes a certain function of both individual messages. Another approach is given in [47] which is based on the noisy network coding idea [48][49][50].…”

“…Then it suffices to show that for every small δ > 0 and sufficiently large n there exist M 1,n M 2,n codewords x n m 1 ,m 2 (on the unit sphere) with M 1,n = exp(nR 2 ) and M 2,n = exp(nR 1 ) and (41), such that the average probability is arbitrarily small for all j n i satisfying (40). To ensure that the probability of error gets arbitrarily small, the codewords must possess certain properties which are guaranteed by the following lemma.…”

Symbol error rate analysis for M-QAM modulated physical-layer network coding with phase errors

“…Although there is also some work focusing on asynchronous PNC [8]- [10], synchronous PNC still has advantages because it allows more efficient constellation design [4] and can make use of capacity-approaching channel codes [6]. The capacity region of the Gaussian two-way relay channel can also be reached with synchronous PNC [7].…”