The Failure Probability of Random Linear Network Coding for Networks

TL;DR

This paper analyzes the failure probabilities of random linear network coding in large or complex networks, providing tight bounds and showing how additional topological information improves performance.

Contribution

It offers new upper and lower bounds on failure probabilities for random linear network coding based on network topology.

Findings

Tight upper bounds on failure probabilities are derived.

More topological information leads to better failure probability bounds.

Worst-case networks meet the bounds with equality.

Abstract

In practice, since many communication networks are huge in scale, or complicated in structure, or even dynamic, the predesigned linear network codes based on the network topology is impossible even if the topological structure is known. Therefore, random linear network coding has been proposed as an acceptable coding technique for the case that the network topology cannot be utilized completely. Motivated by the fact that different network topological information can be obtained for different practical applications, we study the performance analysis of random linear network coding by analyzing some failure probabilities depending on these different topological information of networks. We obtain some tight or asymptotically tight upper bounds on these failure probabilities and indicate the worst cases for these bounds, i.e., the networks meeting the upper bounds with equality. In addition, if the more topological information of the network is utilized, the better upper bounds are obtained. On the other hand, we also discuss the lower bounds on the failure probabilities.