When an Energy-Efficient Scheduling is Optimal for Half-Duplex Relay Networks?.

This paper considers a diamond network with $\N$ interconnected relays, namely a network where a source communicates with a destination by hopping information through $\N$ communicating/interconnected relays. Specifically, the main focus of the paper is on characterizing sufficient conditions under which the $\N+1$ states (out of the $2^{\N}$ possible ones) in which at most one relay is transmitting suffice to characterize the approximate capacity, that is the Shannon capacity up to an additive gap that only depends on $\N$. Furthermore, under these sufficient conditions, closed form expressions for the approximate capacity and scheduling (that is, the fraction of time each relay should receive and transmit) are provided. A similar result is presented for the dual case, where in each state at most one relay is in receive mode.