Coding Opportunity Densification Strategies for Instantly Decodable Network Coding

TL;DR

This paper develops strategies to maximize and monotonically increase coding opportunities in instantly decodable network coding, improving efficiency and performance in data transmission.

Contribution

It introduces a novel approach to densify coding opportunities in IDNC by analyzing the evolution of the graph's edge set and proposing an effective transmission strategy.

Findings

Maximizing common wanted packets increases coding opportunities.

Serving receivers with the most missing packets enhances opportunity density.

Strategy outperforms existing methods in reducing delay and increasing goodput.

Abstract

In this paper, we aim to identify the strategies that can maximize and monotonically increase the density of the coding opportunities in instantly decodable network coding (IDNC).Using the well-known graph representation of IDNC, first derive an expression for the exact evolution of the edge set size after the transmission of any arbitrary coded packet. From the derived expressions, 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 the expectation of the edge set size evolution after ignoring the identities of the packets requested by the different receivers and considering only their numbers. We then employ this expected expression to show that serving the maximum number of receivers having the largest numbers of missing packets and erasure probabilities tends to both 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 identified strategy outperforms the step-by-step service maximization solution in optimizing both the IDNC completion delay and receiver goodput.