Network Coded Modulation with partial side-information and hierarchical decode and forward relay sharing in multi-source wireless network

We present a strategy for the relay sharing in the 2-source relay wireless network with the hierarchical decode and forward relaying. It processes both incoming coded symbols through the minimal hierarchical symbol mapping of the same cardinality as the two individual symbol streams and requires a full (perfect) Complementary Side-Information (C-SI) on the other stream available at the destination. This scheme is known to have an advantage in a rectangular shape capacity region which provides higher sum-capacity than the classical MAC. We investigate the capacity region of the case where the destination has only partial C-SI available through a wireless link. We conclude that the overall finite alphabet constrained capacity region including both MAC and BC phase remains rectangular. The BC phase region is limited by the C-SI link capacity and we conjecture that it obeys (in some cases with some small margin) the capacity product law of the individual relay to destination and C-SI links.