Sending perishable information: Coding improves delay-constrained throughput even for single unicast

We consider a delay-constrained unicast scenario, where a source node streams perishable information to a destination node over a directed acyclic graph subject to a delay constraint. Transmission along any edge incurs unit delay, and we require that every information bit generated at the source in the beginning of time t to be received and recovered by the destination in the end of time t + D - 1 where D > 0 is the maximum allowed communication delay. We study the corresponding delay-constrained (d-cn) unicast capacity problem. When only routing is allowed, [Ying, et al. 2011] showed that the aforementioned d-cn unicast routing capacity can be characterized and computed efficiently. However, the d-cn capacity problem changes completely when network coding (NC) is allowed. In this work, we construct the first example showing that NC can achieve strictly higher d-cn throughput than routing even for the single unicast setting and the NC gain can be arbitrarily close to 2 in some instances. This is in sharp contrast to the delay-unconstrained (D → ∞) single-unicast case where the classic min-cut/max-flow theorem implies that coding cannot improve throughput over routing. Finally, we propose a new upper bound on the d-cn unicast NC capacity and elaborate its connections to the existing routing-based results [Ying, et al. 2011]. Overall, our results suggest that d-cn communication is fundamentally different from the well-understood delay-unconstrained one and call for investigation participation.