Routing in Accumulative Multi-Hop Networks

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.