On the synchronization of physical-layer network coding

When data are transmitted in a wireless network, they reach the target receiver as well as other receivers in the neighborhood. Rather than a blessing, this attribute is treated as an interference-inducing nuisance in most wireless networks today (e.g., IEEE 802.11). Physical-laver network coding (PNC), however, has been proposed to take advantage of this attribute. Unlike "conventional" network coding which performs coding arithmetic on digital bit streams after they are decoded, PNC makes use of the additive nature of simultaneously arriving electromagnetic (EM) waves and applies the network coding arithmetic at the physical layer. As a result, the destructive effect of interference is eliminated and the capacity of networks is boosted significantly. A key requirement of PNC is synchronization among nodes, which has not been addressed previously. This is the focus of this paper. Specifically, we investigate the impact of imperfect synchronization (i.e., finite synchronization errors) on PNC. We show that with BPSK modulation, PNC still yields significantly higher capacity than straightforward network coding when there are synchronization errors. And interestingly, this remains to be so even in the extreme case where synchronization is not performed at all.