  The design of modulation schemes for the physical layer network-coded two way
wireless relaying scenario is considered. It was observed by Koike-Akino et al.
for the two way relaying scenario, that adaptively changing the network coding
map used at the relay according to the channel conditions greatly reduces the
impact of multiple access interference which occurs at the relay during the MA
Phase and all these network coding maps should satisfy a requirement called
exclusive law. We extend this approach to an Accumulate-Compute and Forward
protocol which employs two phases: Multiple Access (MA) phase consisting of two
channel uses with independent messages in each channel use, and Broadcast (BC)
phase having one channel use. Assuming that the two users transmit points from
the same 4-PSK constellation, every such network coding map that satisfies the
exclusive law can be represented by a Latin Square with side 16, and
conversely, this relationship can be used to get the network coding maps
satisfying the exclusive law. Two methods of obtaining this network coding map
to be used at the relay are discussed. Using the structural properties of the
Latin Squares for a given set of parameters, the problem of finding all the
required maps is reduced to finding a small set of maps. Having obtained all
the Latin Squares, the set of all possible channel realizations is quantized,
depending on which one of the Latin Squares obtained optimizes the performance.
The quantization thus obtained, is shown to be the same as the one obtained in
[7] for the 2-stage bidirectional relaying.
