On densifying coding opportunities in instantly decodable network coding graphs

In this paper, we propose a coding strategy that maximizes the density of the coding opportunities in instantly decodable network coding (IDNC). Using the graph representation of IDNC, we derive the expression for the expected evolutions of coding opportunities after the transmission of any arbitrary coded packet and show that serving the maximum number of receivers, with the largest numbers of missing packets and erasure probabilities, tends to both maximize the expected number of coding opportunities and increase the expected coding density almost monotonically. Simulation results justify our theoretical findings and demonstrate the importance of maintaining high coding density when optimizing long-term parameters.