Network coding schemes for data exchange networks with arbitrary transmission delays

In this paper, we introduce construction techniques for network coding in bidirectional networks with arbitrary transmission delays. These coding schemes reduce the number of transmissions and achieve the optimal rate region in the corresponding broadcast model for both multiple unicast and multicast cases with up to three users, under the equal rate constraint. The coding schemes are presented in two phases; first, coding schemes for line, star and line-star topologies with arbitrary transmission delays are provided and second, any general topology with multiple bidirectional unicast and multicast sessions is shown to be decomposable into these canonical topologies to reduce the number of transmissions. As a result, the coding schemes developed for the line, star, and line-star topologies serve as building blocks for the construction of more general coding schemes for all networks. The proposed schemes are proved to be real time in the sense that they achieve the minimum decoding delay. With a negligible size header, these coding schemes are shown to be applicable to unsynchronized networks, i.e., networks with arbitrary transmission delays. Finally, we demonstrate the applicability of these schemes by extensive simulations. The implementation of such coding schemes on a wireless network with arbitrary transmission delays can improve performance and power efficiency.