  In this paper, we study a routing problem on the Gaussian multiple relay
channel, in which nodes employ a decode-and-forward coding strategy. We are
interested in routes for the information flow through the relays that achieve
the highest DF rate. We first construct an algorithm that provably finds
optimal DF routes. As the algorithm runs in factorial time in the worst case,
we propose a polynomial time heuristic algorithm that finds an optimal route
with high probability. We demonstrate that that the optimal (and near optimal)
DF routes are good in practice by simulating a distributed DF coding scheme
using low density parity check codes with puncturing and incremental
redundancy.
