Incremental Redundancy, Fountain Codes and Advanced Topics

TL;DR

This paper reviews and compares linear fountain codes, focusing on incremental redundancy and theoretical fundamentals, providing a unified framework and reference for researchers and students in coding theory.

Contribution

It offers a comprehensive, unified framework for analyzing linear fountain codes, consolidating theoretical fundamentals and serving as a reference for future research.

Findings

Reviewed theoretical fundamentals of fountain codes

Compared various linear fountain code schemes

Provided exercises for understanding

Abstract

This document is written in order to establish a common base ground on which the majority of the relevant research about linear fountain codes can be analyzed and compared. As far as I am concerned, there is no unified approach that outlines and compares most of the published linear fountain codes in a single and self-contained framework. This written document has not only resulted in the review of theoretical fundamentals of efficient coding techniques for incremental redundancy and linear fountain coding, but also helped me have a comprehensive reference document and hopefully for many other graduate students who would like to have some background to pursue a research career regarding fountain codes and their various applications. Some background in information, coding, graph and probability theory is expected. Although various aspects of this topic and many other relevant research are deliberately left out, I still hope that this document shall serve researchers' need well. I have also included several exercises to warm up. The presentation style is usually informal and the presented material is not necessarily rigorous. There are many spots in the text that are product of my coauthors and myself, although some of which have not been published yet.