On the capacity of 2-user 1-hop relay erasure networks — The union of feedback, scheduling, opportunistic routing, and network coding

This work studies the capacity of 2-user 1-hop relay networks, for which the sources, destinations, and the common relay are interconnected by broadcast packet erasure channels. In contrast with the existing results, this paper allows (i) transmission from a source being heard directly by its 2-hop-away destination, the so-called opportunistic routing scenario, (ii) instant channel status feedback among all network nodes, and (iii) per-slot scheduling decisions that are functions of the traffic loads and the past channel status. A new pair of inner and outer bounds is provided, and a condition is identified for the scenario in which the bounds coincide. Numerical experiments show that for commonly encountered scenarios, the gap between the inner and the outer bounds is less than 0.2%, which demonstrates the effectiveness of the proposed bounding techniques.