On the Delay Advantage of Coding in Packet Erasure Networks

TL;DR

This paper demonstrates that network coding offers a significant delay advantage over routing in packet erasure networks, with the delay benefit scaling at least as the square root of the number of packets, supported by exact analysis and concentration results.

Contribution

The paper provides the first exact characterization of the maximum of two negative binomial variables and proves the unbounded delay gap between network coding and routing in erasure networks.

Findings

Delay benefit of network coding scales at least as √n.

Exact characterization of the maximum of two negative binomial variables.

Delay delay is tightly concentrated around its expectation.

Abstract

We consider the delay of network coding compared to routing with retransmissions in packet erasure networks with probabilistic erasures. We investigate the sub-linear term in the block delay required for unicasting $n$ packets and show that there is an unbounded gap between network coding and routing. In particular, we show that delay benefit of network coding scales at least as $\sqrt{n}$. Our analysis of the delay function for the routing strategy involves a major technical challenge of computing the expectation of the maximum of two negative binomial random variables. This problem has been studied previously and we derive the first exact characterization which may be of independent interest. We also use a martingale bounded differences argument to show that the actual coding delay is tightly concentrated around its expectation.