Multicast in wireless erasure networks with feedback

This paper studies the lossy, wireless packet network of [1], in the case of a multicast requirement and the availability of feedback. In the unicast case, feedback is sufficient to allow a strategy which achieves the throughput-optimal cut-set capacity without requiring network coding [3]. We provide a counter-example to show that source coding and feedback, without network coding, is insufficient to achieve the cut-set capacity for the multicast wireless erasure network. In particular, we examine a network with one source, one relay, and two destinations. We show that even with the highly optimistic assumption of feedback which provides global packet state awareness, this network still fails to reach capacity. This bridges the gap between two previously known results; one, that network coding can achieve the capacity of the wireless erasure network, and two, that feedback allows a capacity achieving scheme which does not require network coding in the unicast wireless erasure network.