  Numerous applications demand communication schemes that minimize the
transmission delay while achieving a given level of reliability. An extreme
case is high-frequency trading whereby saving a fraction of millisecond over a
route between Chicago and New York can be a game-changer. While such
communications are often carried by fiber, microwave links can reduce
transmission delays over large distances due to more direct routes and faster
wave propagation. In order to bridge large distances, information is sent over
a multihop relay network.
  Motivated by these applications, this papers present an information-theoretic
approach to the design of optimal multihop microwave networks that minimizes
end-to-end transmission delay. To characterize the delay introduced by coding,
we derive error exponents achievable in multihop networks. We formulate and
solve an optimization problem that determines optimal selection of
amplify-and-forward and decode-and-forward relays. We present the optimal
solution for several examples of networks. We prove that in high SNR the
optimum transmission scheme is for all relays to perform amplify-and-forward.
We then analyze the impact of deploying noisy feedback
