Delivery delay analysis of network coded wireless broadcast schemes

In this paper we study in-order packet delivery delay of two recently proposed network coded transmission schemes with applications in wireless broadcast. Unlike previous works where asymptotic behaviour of decoding or delivery delay was presented, we provide a general analysis of the three conditions under which in-order packet delivery is possible at a receiver: by 1) catching up with the sender, 2) receiving while a leader, and 3) chance decoding. We use a Markov model to represent the difference between the knowledge space of the sender and a receiver. For the first condition, we calculate the expected distribution of decoding cycle lengths under the Markov model. For the second condition, we propose to use a simplifying independent Markov model among receivers to shed light on the factors that determine the probability of receiving while a leader. Finally, we compare the chance decoding probabilities of two transmission schemes and a baseline random transmission algorithm to show that surprisingly (and fortunately) the probability of chance decoding is significant in one of the transmission schemes. We verify our analysis by extensive simulations and discuss the usefulness of our study for understanding and design of better transmission algorithms.