On the capacity region of broadcast over wireless erasure networks

In this paper, we consider a special class of wireless networks, called wireless erasure networks. In these networks, each node is connected to a set of nodes by independent erasure channels. The network model incorporates the broadcast nature of the wireless environment in that each node sends out the same signal on its outgoing channels. However, we assume there is no interference in reception. In this paper we first look at the single source single destination unicast problem. We obtain the capacity under the assumption that erasure locations on all the links of the network are provided to the destination. It turns out that the capacity has a nice max-flow min-cut interpretation. The definition of cut-capacity in these network is such that it incorporates the broadcast property of the wireless medium. In the second part of the paper, a time-sharing scheme for broadcast problems over these networks is proposed and its achievable region is analyzed. We show that for some special cases, this time-sharing scheme is optimal.