Bi-Directional Multi-Hop Wireless Pipeline Using Physical-Layer Network Coding

In this paper, the design of multi-hop physical layer network coding (PNC) is investigated. In the existing multi-hop PNC designs, the effects of error propagation and mutualinterference are not well addressed. Error propagation refers to that the estimation error at any node may propagate to the neighboring nodes, which may result in serious end-to-end bit errors. The impact of the mutual-interference from other transmitting nodes to a receiver determines the upper bound SINR of two neighboring nodes given end-to-end SNR. By carefully addressing these issues, we propose two multi-hop PNC designs, the direct multi-hop PNC (D-MPNC) and the stored multi-hop PNC (S-MPNC), where both designs achieve the throughput upper bound of one symbol per symbol duration, which is the same as that of the traditional PNC with a single relay. There is a tradeoff between the applications of D-MPNC and S-MPNC, which targets for simple-implementation and optimal end-to-end bit error rate (BER), respectively. We provide the detailed designs of D-MPNC and S-MPNC and obtain the end-to-end BER bounds theoretically. Extensive simulation results demonstrate the performance gain of the proposed multi-hop PNC compared with the traditional PNC in terms of end-to-end BER and end-to-end throughout.