Random delay in network coding for bidirectional relaying

Consider the problem of exchanging information in a wireless network with random transmission delays. While the broadcast nature of the wireless medium presents many challenges, it also affords novel coding opportunities when exchanging information. However, straightforward network coding schemes do not perform well under random delay. In this paper, we rigorously define Real Time (RT) coding and introduce a novel RT coding scheme for bidirectional relaying in wireless networks that obviates the need for synchronicity. The construction is based on introducing practical coding schemes with minimal delay for both 'line' and 'star' topologies, and then using these constructions as building blocks for general networks. Specifically, we show that a general topology with up to three users and equal rate demands can be decomposed to these two canonical topologies without any loss of optimality. Consequently, the proposed scheme achieves the maximum transmission rate for wireless networks with random (yet bounded) transmission delays using a small overhead.