In this paper, a compress-and-forward scheme with backward decoding ispresented for the unicast wireless relay network. The encoding at the sourceand relay is a generalization of the noisy network coding scheme (NNC). Whileit achieves the same reliable data rate as noisy network coding scheme, thebackward decoding allows for a better decoding complexity as compared to thejoint decoding of the NNC scheme. Characterizing the layered decoding scheme isshown to be equivalent to characterizing an information flow for the wirelessnetwork. A node-flow for a graph with bisubmodular capacity constraints ispresented and a max-flow min-cut theorem is proved for it. This generalizesmany well-known results of flows over capacity constrained graphs studied incomputer science literature. The results for the unicast relay network aregeneralized to the network with multiple sources with independent messagesintended for a single destination.
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