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The concept of physical-layer network coding (PNC) was proposed in 2006 forapplication in wireless networks. Since then it has developed into a subfieldof network coding with wide followings. The basic idea of PNC is to exploit thenetwork coding operation that occurs naturally when electromagnetic (EM) wavesare superimposed on one another. This simple idea turns out to have profoundand fundamental ramifications. Subsequent works by various researchers have ledto many new results in the domains of 1) wireless communication; 2) wirelessinformation theory; and 3) wireless networking. The purpose of this paper isfourfold. First, we give a brief tutorial on the basic concept of PNC. Second,we survey and discuss recent key results in the three aforementioned areas.Third, we examine a critical issue in PNC: synchronization. It has been acommon belief that PNC requires tight synchronization. Our recent resultssuggest, however, that PNC may actually benefit from asynchrony. Fourth, wepropose that PNC is not just for wireless networks; it can also be useful inoptical networks. We provide an example showing that the throughput of apassive optical network (PON) could potentially be raised by 100% with PNC.

Physical-Layer Network Coding: Tutorial, Survey, and Beyond