On Network Simplification for Gaussian Half-Duplex Diamond Networks

Abstract

This paper investigates the simplification problem in Gaussian Half-Duplex (HD) diamond networks. The goal is to answer the following question: what is the minimum (worst-case) fraction of the total HD capacity that one can always achieve by smartly selecting a subset of $k$ relays, out of the $N$ possible ones? We make progress on this problem for $k=1$ and $k=2$ and show that for $N=k+1,k\in \{1,2\}$ at least $\frac{k}{k+1}$ of the total HD capacity is always {approximately (i.e., up to a constant gap)} achieved. Interestingly, and differently from the Full-Duplex (FD) case, the ratio in HD depends on $N$, and decreases as $N$ increases. For all values of $N$ and $k$ for which we derive worst case fractions, we also show these to be {approximately} tight. This is accomplished by presenting $N$-relay Gaussian HD diamond networks for which the best $k$-relay subnetwork has {an approximate} HD capacity equal to the worst-case fraction of the total {approximate} HD capacity. Moreover, we provide additional comparisons between the performance of this simplification problem for HD and FD networks, which highlight their different natures.

Parts of this work will be presented at ISIT 2016

References in corpus (3)

• Gaussian Half-Duplex Relay Networks: improved constant gap and connections with the assignment problem
• The Approximate Optimality of Simple Schedules for Half-Duplex Multi-Relay Networks
• On Network Simplification for Gaussian Half-Duplex Diamond Networks

Cited by in corpus (1)

• On Network Simplification for Gaussian Half-Duplex Diamond Networks