Abstract

This paper investigates the problem of finding optimal paths in single-source single-destination accumulative multi-hop networks. We consider a single source that communicates to a single destination assisted by several relays through multiple hops. At each hop, only one node transmits, while all the other nodes receive the transmitted signal, and store it after processing/decoding and mixing it with the signals received in previous hops. That is, we consider that terminals make use of advanced energy accumulation transmission/reception techniques, such as maximal ratio combining reception of repetition codes, or information accumulation with rateless codes. Accumulative techniques increase communication reliability, reduce energy consumption, and decrease latency. We investigate the properties that a routing metric must satisfy in these accumulative networks to guarantee that optimal paths can be computed with Dijkstra’s algorithm. We model the problem of routing in accumulative multi-hop networks, as the problem of routing in a hypergraph. We show that optimality properties in a traditional multi-hop network (monotonicity and isotonicity) are no longer useful and derive a new set of sufficient conditions for optimality. We illustrate these results by studying the minimum energy routing problem in static accumulative multi-hop networks for different forwarding strategies at relays.

Highlights

  • Introducing relay capabilities in a network has a strong effect on the information flow that extends to all communication levels, from the achievable rates to the routing strategy

  • In accumulative multi-hop networks, a single source communicates to a single destination assisted by several relay nodes that can accumulate the received energy/information from previous relay transmissions

  • In accumulative multi-hop (AM) routing, the network is better modeled by a directed hypergraph H(V, E), as the one shown in Figure 1, where V denotes the set of nodes, or vertices, and E denotes the set of hyperedge, or connections between nodes

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Summary

INTRODUCTION

Introducing relay capabilities in a network has a strong effect on the information flow that extends to all communication levels, from the achievable rates to the routing strategy. The problem of routing in a traditional multi-hop (TM) network model, where each relay node only listens to the immediately previous node is quite well understood today. In accumulative multi-hop networks, a single source communicates to a single destination assisted by several relay nodes that can accumulate the received energy/information from previous relay transmissions. We discuss the optimality of Dijkstra’s algorithm for the minimum energy routing in static AM networks. DF relay nodes decode the source message completely by accumulating energy, or information from all previous transmissions. We show the optimality of Dijkstra’s algorithm for DF accumulative networks where nodes decode the source message by only accumulating the energy/information coming from the immediately previous relay, and from the source.

THE ACCUMULATIVE NETWORK MODEL
MINIMUM ENERGY ACCUMULATIVE ROUTING
Decode-and-forward relaying
Cut-set bound
OPTIMALITY OF DIJKSTRA’S ALGORITHM IN ACCUMULATIVE NETWORKS
Optimality Conditions in Traditional Multi-hoping
Optimality Conditions in Accumulative Multi-hoping
Decode-and-Forward Relaying
CONCLUSIONS
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