Trellis-based equalization schemes for physical layer network coding

In this paper, we consider two-way relaying in a physical layer network coded system in a scenario where transmissions are subject to frequency-selective fading. Physical Layer Network Coding (PNC) enabled single-carrier transmission systems operating in flat fading environments have been subjected to scrutiny extensively, yet approaches for tackling the problem of extending them to environments causing multi-path fading are quite limited. We present three equalization schemes that can be used at the relay nodes to retrieve the data to be relayed in the presence of intersymbol interference (ISI). The most basic scheme jointly estimates both data streams and combines them afterwards. Furthermore, a scheme that already combines state and transition probabilities inside the trellis diagram is devised. Finally, we present a complexity-reduced algorithm where state combinations that yield the same bit to be relayed can be combined into a single state. All of the three algorithms can be regarded as different types of a decode-and-forward (DF) scheme.