On scalability of physical layer network coding with modulo‐sum mapping overN‐way relay channels

Abstract

Summary In this manuscript, fundamental limits of physical layer network coding with modulo‐sum mapping (to avoid of large cardinality), in terms of the number of superimposed signals that still render an acceptable probability of error, are studied. It is expected that (1) for a given bit error rate or throughput, an upper bound on the number of superimposed signals may exist and (2) if a large network is considered as a set of small subnetworks, and the proposed network code is used in each subnetwork, a significant increase in network throughput can be achieved. Answering these questions sheds light on the scalability of multiuser physical layer network coding with bit error rate or throughput constraints. Theoretical calculations, as well as simulation results, indicate the extraction of network coded signal from more than 2 (which is special case known as 2‐way relay channel) superimposed signals can be practical and lucrative.