Abstract-Physical-layer network coding is considered for the two-way relay network with realistic assumptions on the coherence of the channel. In contrast to analog network coding, which relays received analog signals plus noise, our system relays digital network codewords, obtained by digital demodulation and channel decoding. By using binary frequency-shift keying and noncoherent reception, the relay may operate without knowledge of the phases of the signals transmitted simultaneously by the two sources. The channels between the end nodes and the relay are modeled as noncoherent block fading channels, and an outer turbo code is used. A noncoherent receiver is formulated for the relay, which estimates the fading amplitudes but not the phases. Several block sizes are considered, and the effect of block size on error-rate performance is investigated. As a baseline for performance comparison, the system is also simulated using perfect knowledge of the fading amplitudes, and it is observed that the performance lost to channel estimation is negligible for sufficiently large blocks. An example realization of the proposed system demonstrates a 32.4% throughput improvement compared to a similar system that performs network coding at the link layer.
I. INTRODUCTIONNetwork coding is a relaying technique that increases throughput over traditional store-and-forward relaying [1]. The two-way relay channel (TWRC) is the most fundamental topology that can exploit network coding techniques [2]. The TWRC is a three-terminal network consisting of a pair of source nodes N 1 and N 2 that exchange information via a single relay node R. Information is exchanged, making N j the destination of node N i , i = j. In this topology, network coding can be applied at either the link layer or the physical layer [3]. Information may be protected by using an errorcorrecting channel code, which is applied either on a linkby-link basis or on an end-to-end basis [4]. Using link-bylink channel coding, both the end nodes and the relay apply channel codes to the data. The channel codes applied by the end nodes and the relay may be different. Using end-to-end coding, only nodes N 1 and N 2 perform channel decoding, not the relay. Because the decoding operation at the relay minimizes error propagation and noise accumulation over the two links, link-by-link channel coding offers potentially better performance than end-to-end coding at the cost of increased complexity.In Fig. 1, link-layer network coding (LNC) is compared against physical-layer network coding (PNC) in the channelcoded TWRC. Let u i indicate the message of source node N i . The modulated and channel-coded signal transmitted by N i is denoted by Γ S (u i ). With LNC, which is shown in Fig. 1(a), nodes N 1 and N 2 transmit their signals during two disjoint time slots. Using link-by-link channel coding, the two signals are demodulated and channel-decoded at the relay to obtain estimatesû 1 andû 2 . Assuming the network code is defined over finite field GF(2), a network codeword u =û 1 ⊕û 2 is