  We investigate cooperative wireless relay networks in which the nodes can
help each other in data transmission. We study different coding strategies in
the single-source single-destination network with many relay nodes. Given the
myriad of ways in which nodes can cooperate, there is a natural routing
problem, i.e., determining an ordered set of nodes to relay the data from the
source to the destination. We find that for a given route, the
decode-and-forward strategy, which is an information theoretic cooperative
coding strategy, achieves rates significantly higher than that achievable by
the usual multi-hop coding strategy, which is a point-to-point non-cooperative
coding strategy. We construct an algorithm to find an optimal route (in terms
of rate maximizing) for the decode-and-forward strategy. Since the algorithm
runs in factorial time in the worst case, we propose a heuristic algorithm that
runs in polynomial time. The heuristic algorithm outputs an optimal route when
the nodes transmit independent codewords. We implement these coding strategies
using practical low density parity check codes to compare the performance of
the strategies on different routes.
