Achievable rates for network coding on the exchange channel

Network coding, where relay nodes combine the information received from multiple links rather than simply replicating and forwarding the received packets, has shown the promise of significantly improving system performance. In very recent works, multiple researchers have presented methods for increasing system throughput by employing network coding inspired methods to mix packets at the physical layer: physical-layer network coding (PNC). A common example used to validate much of this work is that of two sources exchanging information through a single intervening relay - a situation that we denote the "exchange channel". In this paper, achievable rates of various schemes on the exchange channel are considered. Achievable rates for traditional multi-hop routing approaches, network coding approaches, and various PNC approaches are considered. A new method of PNC inspired by Tomlinson-Harashima precoding (THP), where a modulo operation is used to control the power at the relay, is introduced, and shown to have a slight advantage over analogous schemes at high signal-to-noise ratios (SNRs).