Delay-Constrained Network Information Flow

Joint work with Chih-Chun Wang from Purdue University and Ye Tian from Nanjing University

This project aims to study a fundamental problem in delay-constrained network communication: determining and achieving (exactly or approximately) the maximum throughput of streaming perishable information with hard deadlines over networks.

We first 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 rightarrow infty) 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.

Recently, we have developed an algebraic approach to characterize the coding capacity for single-source unicast and multicast, as the rank difference between an information space and a deadline-induced interference space. The results allow us to numerically compute the NC capacity for any given graph, serving as a benchmark for existing and future solutions on improving delay-constrained throughput.


  • C. Wang and M. Chen, “Sending Perishable Information: Coding Improves Delay-Constrained Throughput Even for Single Unicast”, IEEE Transactions on Information Theory, vol. 63, no. 1, pp. 252 - 279, January 2017. [PDF] (Its conference version appeared in IEEE ISIT 2014.)

  • M. Chen, Y. Tian, and C. Wang, “On Coding Capacity of Delay-constrained Network Information Flow: An Algebraic Approach”, in Proceedings of 2016 IEEE International Symposium on Information Theory (IEEE ISIT 2016), Barcelona, Spain, July 10-15, 2016. [PDF]


  • M. Chen, “Sending Perishable Messages: Delay-Constrained Network Information Flow”. [PowerPoint]