  Direct application of network coding at the physical layer - physical layer
network coding (PNC) - is a promising technique for two-way relay wireless
networks. In a two-way relay network, relay nodes are used to relay two-way
information flows between pairs of end nodes. This paper proposes a precise
definition for PNC. Specifically, in PNC, a relay node does not decode the
source information from the two ends separately, but rather directly maps the
combined signals received simultaneously to a signal to be relayed. Based on
this definition, PNC can be further sub-classed into two categories - PNCF (PNC
over finite field) and PNCI (PNC over infinite field) - according to whether
the network-code field (or groups, rings) adopted is finite or infinite. For
each of PNCF and PNCI, we consider two specific estimation techniques for
dealing with noise in the mapping process. The performance of the four schemes
is investigated by means of analysis and simulation, assuming symbol-level
synchronization only.
