Achievable rates for Gaussian relay networks with a supplementary non-broadcast link

Abstract

Large system analysis has shown that per-node throughput in purely wireless networks goes to zero as the network size increases. Thus it appears the world will never be totally wireless. This motivates the study of a new kind of hybrid network composed both of purely broadcast wireless (RF) nodes and what we call multi modal nodes, i.e., nodes that can transmit simultaneously over broadcast wireless and other non-broadcast nodes, e.g., wires, infrared, or acoustic links. Here we present achievable rates for three terminal networks using DF, CF, and partial DF when one additional non-broadcast mode is available.We also provide rates for the special case of Gaussian channels. I. INTRODUCTIONThe difficulties encountered when trying to extend point point information theory to networks have motivated the study of large systems, where the capacity region can be collapsed to a single point. The results have been largely pessimistic, indicating that per-node throughout goes to zero as the network size increases [ 1], [2]. Even worse, the problem appears to be physical in nature and cannot be over come by clever protocols, codes, and modulations, i.e., it appears space itself is a capacity bearing object [3].Here we consider networks with both purely wireless nodes and multimodal nodes, i.e., nodes that can transmit simultane ously over broadcast wireless and other non-broadcast odes, e.g., wires, infrared, or acoustic links. Note that in contrast to existing hybrid wireless/wired networks, including cellular networks and infrastructure-aided ad hoc networks, where networks are designed through separate optimization followed by a joining, we are interested here in joint optimization and simultaneous communication across multiple modes of communication. Thus we call these networks multimodal net works to distinguish them from conventional hybrid networks. Previous results on multimodal networks include information outage probability using an extension of the Laneman protocol [4] to quantify the energy-savings available when additional modes are available in flat-fading channels [5], traffic opti mization over multimodal networks [6], and achievable rates for multiple-level relay networks [7] using a generalization of [8] appear. Some of these last results we include here for comparison purposes.Our contribution here is a set of achievable rates for single relay networks with one supplementary non-broadcast mode between the source and the relay. The channel is assumed static and the non-broadcast mode is assumed unidirectional