  We study adaptive network coding (NC) for scheduling real-time traffic over a
single-hop wireless network. To meet the hard deadlines of real-time traffic,
it is critical to strike a balance between maximizing the throughput and
minimizing the risk that the entire block of coded packets may not be decodable
by the deadline. Thus motivated, we explore adaptive NC, where the block size
is adapted based on the remaining time to the deadline, by casting this
sequential block size adaptation problem as a finite-horizon Markov decision
process. One interesting finding is that the optimal block size and its
corresponding action space monotonically decrease as the deadline approaches,
and the optimal block size is bounded by the "greedy" block size. These unique
structures make it possible to narrow down the search space of dynamic
programming, building on which we develop a monotonicity-based backward
induction algorithm (MBIA) that can solve for the optimal block size in
polynomial time. Since channel erasure probabilities would be time-varying in a
mobile network, we further develop a joint real-time scheduling and channel
learning scheme with adaptive NC that can adapt to channel dynamics. We also
generalize the analysis to multiple flows with hard deadlines and long-term
delivery ratio constraints, devise a low-complexity online scheduling algorithm
integrated with the MBIA, and then establish its asymptotical
throughput-optimality. In addition to analysis and simulation results, we
perform high fidelity wireless emulation tests with real radio transmissions to
demonstrate the feasibility of the MBIA in finding the optimal block size in
real time.
