The Failure Probability at Sink Node of Random Linear Network Coding

TL;DR

This paper analyzes the failure probability at sink nodes in random linear network coding, providing tighter bounds based on network topology knowledge and discussing the asymptotic tightness of these bounds.

Contribution

It offers improved upper bounds on failure probabilities in random linear network coding by leveraging network topology information and establishes asymptotic tightness of these bounds.

Findings

Tighter upper bounds for failure probabilities are derived.

More network topology information leads to better bounds.

Lower bounds are also shown to be asymptotically tight.

Abstract

In practice, since many communication networks are huge in scale or complicated in structure even dynamic, the predesigned network codes based on the network topology is impossible even if the topological structure is known. Therefore, random linear network coding was proposed as an acceptable coding technique. In this paper, we further study the performance of random linear network coding by analyzing the failure probabilities at sink node for different knowledge of network topology and get some tight and asymptotically tight upper bounds of the failure probabilities. In particular, the worst cases are indicated for these bounds. Furthermore, if the more information about the network topology is utilized, the better upper bounds are obtained. These bounds improve on the known ones. Finally, we also discuss the lower bound of this failure probability and show that it is also asymptotically tight.