Coding Opportunity Densification Strategies for Instantly Decodable Network Coding

In this paper, we aim to identify the strategies that maximize and monotonically increase the density of coding opportunities in instantly decodable network coding (IDNC). Using the graph representation of IDNC, we first derive an expression for the exact evolution of the edge set size after the transmission of any arbitrary coded packet. From the derived expression, we show that sending commonly wanted packets for all the receivers can maximize the number of coding opportunities. Since guaranteeing such property in IDNC is usually impossible, this strategy does not guarantee the achievement of our target. Consequently, we further investigate the problem by deriving an expression for the expected edge set size evolution after ignoring the identities of the packets requested by the different receivers and considering only their numbers. This expression was then employed to show that serving the maximum number of receivers with largest numbers of missing packets and erasure probabilities tends to maximize and monotonically increase the expected density of coding opportunities. Simulation results justify our theoretical findings. Finally, we validate the importance of our work through two case studies showing that our\ignore{ identified} strategy outperforms several well-known IDNC solutions in optimizing the IDNC completion delay and receiver goodput.