Building Blocks of Physical-Layer Network Coding

This paper investigates the fundamental building blocks of physical-layer network coding (PNC). Most prior work on PNC focused on its application in a simple two-way-relay channel (TWRC) consisting of three nodes only. Studies of the application of PNC in general networks are relatively few. This paper is an attempt to fill this gap. We put forth two ideas: a general network can be decomposed into small building blocks of PNC, referred to as the PNC atoms, for scheduling of PNC transmissions; and we identify nine PNC atoms, with TWRC being one of them. Three major results are as follows. First, using the decomposition framework, the throughput performance of PNC is shown to be significantly better than those of the traditional multi-hop scheme and the conventional network coding scheme. For example, under heavy traffic volume, PNC can achieve 100% throughput gain relative to the traditional multi-hop scheme. Second, PNC decomposition based on a variety of different PNC atoms can yield much better performance than PNC decomposition based on the TWRC atom alone. Third, three out of the nine atoms are most important to good performance. Specifically, the decomposition based on these three atoms is good enough most of the time, and it is not necessary to use the other six atoms.