On the Queueing Behavior of Random Codes over a Gilbert-Elliot Erasure Channel

TL;DR

This paper analyzes the queueing performance of coded data transmission over a Gilbert-Elliot erasure channel, providing a rigorous framework to evaluate and optimize system parameters for delay-sensitive applications.

Contribution

It introduces a Markov chain model combining queue length and channel state, enabling analysis of queue behavior as a function of code rate, unlike prior models that ignore block-length or assume error-free communication.

Findings

Provides a framework to analyze queue behavior with finite block-length codes.

Shows how channel variability impacts queue performance and system delay.

Offers methods to optimize coding parameters for delay-sensitive systems.

Abstract

This paper considers the queueing performance of a system that transmits coded data over a time-varying erasure channel. In our model, the queue length and channel state together form a Markov chain that depends on the system parameters. This gives a framework that allows a rigorous analysis of the queue as a function of the code rate. Most prior work in this area either ignores block-length (e.g., fluid models) or assumes error-free communication using finite codes. This work enables one to determine when such assumptions provide good, or bad, approximations of true behavior. Moreover, it offers a new approach to optimize parameters and evaluate performance. This can be valuable for delay-sensitive systems that employ short block lengths.