  In this paper, a compress-and-forward scheme with backward decoding is
presented for the unicast wireless relay network. The encoding at the source
and relay is a generalization of the noisy network coding scheme (NNC). While
it achieves the same reliable data rate as noisy network coding scheme, the
backward decoding allows for a better decoding complexity as compared to the
joint decoding of the NNC scheme. Characterizing the layered decoding scheme is
shown to be equivalent to characterizing an information flow for the wireless
network. A node-flow for a graph with bisubmodular capacity constraints is
presented and a max-flow min-cut theorem is proved for it. This generalizes
many well-known results of flows over capacity constrained graphs studied in
computer science literature. The results for the unicast relay network are
generalized to the network with multiple sources with independent messages
intended for a single destination.
