Reliability of Multicast under Random Linear Network Coding

TL;DR

This paper analyzes the reliability of multicast networks using Random Linear Network Coding, providing a more accurate lower bound on delivery probability for various network conditions and validating it through extensive simulations.

Contribution

It introduces a new, more precise lower bound on multicast success probability and offers a novel analysis of systematic RLNC performance under realistic conditions.

Findings

Lower bound accuracy with mean square error as low as 9e-5 for ten users.

Performance analysis applicable to arbitrary field sizes and number of destinations.

Validation through extensive Monte Carlo simulations.

Abstract

We consider a lossy multicast network in which the reliability is provided by means of Random Linear Network Coding. Our goal is to characterise the performance of such network in terms of the probability that a source message is delivered to all destination nodes. Previous studies considered coding over large finite fields, small numbers of destination nodes or specific, often impractical, channel conditions. In contrast, we focus on a general problem, considering arbitrary field size and number of destination nodes, as well as a realistic channel. We propose a lower bound on the probability of successful delivery, which is more accurate than the approximation commonly used in the literature. In addition, we present a novel performance analysis of the systematic version of RLNC. The accuracy of the proposed performance framework is verified via extensive Monte Carlo simulations, where the impact of the network and code parameters are investigated. Specifically, we show that the mean square error of the bound for a ten-user network can be as low as $9 \cdot 10^{-5}$ for non-systematic RLNC.