4 problems

Simple-schedule conjecture. Simple schedules suffice for approximate capacity characterization of Gaussian half-duplex relay networks.

Consider a half-duplex Gaussian multi-relay network. A relay schedule is simple if at most $N+1$ of the $2^N$ possible relay listen-transmit configurations have strictly positive p…

Consider a general half-duplex diamond network with $K-2$ relays. For each relay state $s\in[0:2^{K-2}-1]$, let $\lambda_s^\star$ be its optimal probability in the cut-set upper bo…

Consider a general half-duplex diamond network with $K-2$ relays and state probabilities $\lambda_s$, indexed by $s\in[0:2^{K-2}-1]$. Let $\lambda_s^\star$ be optimal state probabi…