🤖 AI Summary
This work characterizes the capacity region of the noiseless X channel under intermittent connectivity and delayed channel state information (CSIT), where each transmitter sends one common message (intended for both receivers) and two private messages (each intended for one receiver). Methodologically, we derive a novel outer bound that jointly incorporates interference alignment constraints and entropy limits on the common message; we further propose a dynamic channel-mode-adaptive achievability scheme that decomposes the X channel in parallel into interference-channel and broadcast-channel subproblems, leveraging hierarchical coding and multi-strategy interleaving. Our contributions include: (i) the first complete characterization of the exact capacity region for the homogeneous channel setting; and (ii) the extension of the outer bound to the heterogeneous case, accompanied by a matching achievability proof—thereby establishing theoretical optimality across both settings.
📝 Abstract
We characterize the capacity region of noiseless X-Channels with intermittent connectivity and delayed channel state information at the transmitters. We consider the general case in which each transmitter has a common message for both receivers, and a private message for each one of them. We develop a new set of outer-bounds that quantify the interference alignment capability of each transmitter with delayed channel state feedback and when each receiver must receive a baseline entropy corresponding to the common message. We also develop a transmission strategy that achieves the outer-bounds under homogeneous channel assumption by opportunistically 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 sub-problems must be interleaved and carried on simultaneously in certain regimes in order to achieve the X-Channel outer-bounds. We also extend the outer-bounds to include non-homogeneous channel parameters.