Capacity Results for Finite-Field X-Channels with Delayed CSIT

We establish the capacity region of the two-user Finite-Field Fading X-Channel with delayed channel state information at the transmitters. We consider the most general case in which each transmitter has a common message for both receivers and a private message for each one of them. We derive a new set of outer-bounds for this problem that rely on an extremal entropy inequality. This inequality quantifies the ability of each transmitter in favoring one receiver over the other in terms of the delivered entropy when both receivers must obtain a baseline entropy. We show that the outer-bounds can be achieved by treating the X-Channel as a combination of a number of well-known problems such as the interference channel and the multicast channel. The capacity-achieving strategies of these subproblems must be interleaved and carried on simultaneously in certain regimes in order to achieve the X-Channel outer-bounds. Index Terms X-Channel, finite-field model, channel capacity region, interference channel, delayed CSIT.