It has recently been recognized that the wireless networks represent a
fertile ground for devising communication modes based on network coding. A
particularly suitable application of the network coding arises for the two--way
relay channels, where two nodes communicate with each other assisted by using a
third, relay node. Such a scenario enables application of \emph{physical
network coding}, where the network coding is either done (a) jointly with the
channel coding or (b) through physical combining of the communication flows
over the multiple access channel. In this paper we first group the existing
schemes for physical network coding into two generic schemes, termed 3--step
and 2--step scheme, respectively. We investigate the conditions for
maximization of the two--way rate for each individual scheme: (1) the
Decode--and--Forward (DF) 3--step schemes (2) three different schemes with two
steps: Amplify--and--Forward (AF), JDF and Denoise--and--Forward (DNF). While
the DNF scheme has a potential to offer the best two--way rate, the most
interesting result of the paper is that, for some SNR configurations of the
source--relay links, JDF yields identical maximal two--way rate as the upper
bound on the rate for DNF.