Optimal Control for Network Coding Broadcast
  Random linear network coding (RLNC) has been shown to efficiently improve the network performance in terms of reducing transmission delays and increasing the throughput in broadcast and multicast communications. However, it can result in increased storage and computational complexity at the receivers end. In our previous work we considered the broadcast transmission of large file to N receivers. We showed that the storage and complexity requirements at the receivers end can be greatly reduced when segmenting the file into smaller blocks and applying RLNC to these blocks. To that purpose, we proposed a packet scheduling policy, namely the Least Received. In this work we will prove the optimality of our previously proposed policy, in terms of file transfer completion time, when N = 2. We will model our system as a Markov Decision Process and prove the optimality of the policy using Dynamic Programming. Our intuition is that the Least Received policy may be optimal regardless of the number of receivers. Towards that end, we will provide experimental results that verify that ntuition. 
Emmanouil Skevakis and Ioannis Lambadaris
cs.SY cs.IT math.IT