An Optimal Adaptive Network Coding Scheme for Minimizing Decoding Delay in Broadcast Erasure Channels

We are concerned with designing feedback-based adaptive network coding schemes with the aim of minimizing decoding delay in each transmission in packet-based erasure networks. We study systems where each packet brings new information to the destination regardless of its order and require the packets to be instantaneously decodable. We first formulate the decoding delay minimization problem as an integer linear program and then propose efficient algorithms for finding its optimal solution(s). We show that our problem formulation is applicable to memoryless erasures as well as Gilbert-Elliott erasures with memory. We then propose a number of heuristic algorithms with worst case linear execution complexity that can be used when an optimal solution cannot be found in a reasonable time. We verify the delay and speed performance of our techniques through numerical analysis. This analysis reveals that by taking channel memory into account in network coding decisions, one can considerably reduce decoding delays.