An Improved Physical Layer Network Coding Scheme for Two-Way Relay Systems Yidong Lang, Dirk W¨ ubben and Karl-Dirk Kammeyer Department of Communications Engineering, University of Bremen Otto-Hahn-Allee NW1, D-28359 Bremen, Germany Email: {lang, wuebben, kammeyer}@ant.uni-bremen.de Abstract—In this paper we consider a two-way relaying system with two sources A, B and one relay R, where the two sources desire to exchange information through the relay. The transmission consists of two states: multiple access (MAC) stage, where A and B transmit the channel-coded signals to R simultaneously, and broadcast (BC) stage, where R transmits towards both A and B. One critical process at R is to decode the superimposed signal from A and B in such a way that A and B could decode the information from each other reliably at the BC stage. Instead of decoding the individual information belonging to A and B separately, R aims to decode the superimposed signal to the network-coded combination of the two source information, i.e., the binary XOR of the two source information. We refer this decoding process as the joint channel decoding and physical network encoding (JCNC). In this paper, a novel iterative decoding algorithm is presented for the physical network coding scheme, which is applicable to any linear channel code, e.g. Low-Density Parity-Check (LDPC) code. Furthermore, the two-way relaying scheme is extended to distributed multiple input multiple output (MIMO) multi-hop networks. Based on an antenna selection criterion within each virtual antenna array (VAA), the end-to-end (e2e) BER of the multi-hop system can be further reduced. Simulation results show that the proposed scheme outperforms other recently proposed network coding schemes with slightly increased complexity. Index Terms—Physical network coding, relay, iterative decod- ing, distributed MIMO, antenna selection, sum product algo- rithm. I. I NTRODUCTION AND SYSTEM MODEL Network coding has been shown to improve the network throughput significantly, which was first proposed in [1]. The network coding scheme was originally considered as a network-layer technique for wired networks. In wireless network, the broadcast nature of the wireless physical medium is usually considered to cause enormous interference if sev- eral nodes transmit simultaneously. On the contrary, physical network coding (PNC) can employ this broadcast nature as a capacity-boosting approach for two-way or multi-way communication network, [2], [3], [4], [5]. Especially, a direct application of physical network coding arises for the two-way (or bi-directional) point-to-point communication. A simple two-way relay system with two sources A and B, and one relay R is depicted in Fig. 1. Source A and source B wish to exchange information between each other through the relay R. We denote b A ∈{0, 1} K and b B ∈{0, 1} K as the This work was supported in part by the Central Research Funding, University of Bremen under grant 01/129/07. A A B B R R Stage I: MAC Stage II: BC y R = x A + x B + n R x A x B x R y A = x R + n A y B = x R + n B Fig. 1. Two source A and B wish to exchange information through the relay R, which consists of two stages: multiple access (MAC) stage, where A and B transmit the signals x A and x B to R simultaneously, and broadcast (BC) stage, where R transmits x R towards both A and B. information vector of source A and source B. The information is encoded by the same linear code with a code rate of R c = K N into the codeword vectors c A ∈{0, 1} N and c B ∈{0, 1} N at the sources A and B, respectively. The encoded vectors are BPSK-modulated to x A ∈ {-1, 1} N and x B ∈ {-1, 1} N according to the mapping rule 0 → 1 and 1 →-1. The communication consists of two stages: multiple access (MAC) and broadcast (BC). In the MAC stage, the two source A and B transmit their information x A and x B to the relay simultaneously over an AWGN channel. Under the assumption of perfect synchro- nization, the received signal at the relay R is y R = x A + x B + n R , (1) where the elements of n R are identically distributed (i.i.d) zero-mean Gaussian random variables with variance σ 2 n . We assume that both sources A and B have the same power con- straint E{||x A || 2 }≤ P and E{||x B || 2 }≤ P . According to the physical network coding scheme introduced in [2], the XOR of the source information denoted by b A⊕B = b A ⊕b B ∈{0, 1} K can be estimated at the relay from the received signal y R , i.e., b R = ˆ b A⊕B ∈{0, 1} K . Then, b R is encoded by the same channel code, and the code vector c R BPSK-modulated to x R . In the BC stage, the relay R broadcasts x R to both A and B. It is assumed that the relay R has the same power constraint 2010 International ITG Workshop on Smart Antennas (WSA 2010) 978-1-4244-6072-4/10/$26.00 ©2010 IEEE 107