Sparse graph codes for the two-way relay network with correlated sources

We consider the two-way relay network where two nodes communicate via a relay. We assume that the data at the nodes are correlated (e.g., measurements in a sensor network) and that there is no direct communication between the nodes. The nodes communicate via the relay using a two-phase protocol consisting of an uplink part over an orthogonal multiple access channel and a downlink part over a broadcast channel. The individual codes as well as the overall system can be represented by a joint factor graph consisting of a source code at each node, a channel code for the each uplink and a channel code for the downlink. The optimality of separation of source and channel coding implies that it is optimal to individually design these codes. We focus on low-density parity-check codes where code design corresponds to the optimisation of their degree distributions.