# Decoding Delay Performance of Random Linear Network Coding for Broadcast

## TL;DR

This paper analyzes the delay performance of random linear network coding in broadcast systems with transmission deadlines, providing closed-form expressions and bounds to optimize system parameters for reliable service.

## Contribution

It introduces a new framework that accounts for transmission deadlines in network coding delay analysis and derives tighter bounds on decoding delay.

## Key findings

- Closed-form expressions for average packet transmissions per generation.
- A tighter upper bound on average decoding delay.
- Framework for tuning system parameters to balance delay and transmission efficiency.

## Abstract

Characterization of the delay profile of systems employing random linear network coding is important for the reliable provision of broadcast services. Previous studies focused on network coding over large finite fields or developed Markov chains to model the delay distribution but did not look at the effect of transmission deadlines on the delay. In this work, we consider generations of source packets that are encoded and transmitted over the erasure broadcast channel. The transmission of packets associated to a generation is taken to be deadline-constrained, that is, the transmitter drops a generation and proceeds to the next one when a predetermined deadline expires. Closed-form expressions for the average number of required packet transmissions per generation are obtained in terms of the generation size, the field size, the erasure probability and the deadline choice. An upper bound on the average decoding delay, which is tighter than previous bounds found in the literature, is also derived. Analysis shows that the proposed framework can be used to fine-tune the system parameters and ascertain that neither insufficient nor excessive amounts of packets are sent over the broadcast channel.