Foundations and Trends® in Communications and Information Theory > Vol 2 > Issue 4

# Network Coding Theory Part I: Single Source

• Yeung, Raymond W. 1
• Li, Shuo-Yen Robert 2
• Cai, Ning 3
• Zhang, Zhen 4

[1]Yeung, Raymond W., Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong, whyeung@ie.cuhk.edu.hk [2]Li, Shuo-Yen Robert, Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong, bob@ie.cuhk.edu.hk [3]Cai, Ning, The State Key Lab. of ISN, Xidian University, China, caining@mail.xidian.edu.cn [4]Zhang, Zhen, Department of Electrical Engineering-Systems, University of Southern California, USA, zzhang@milly.usc.edu

### Short description

Network Coding Theory provides a tutorial on the basic of network coding theory. It presents the material in a transparent manner without unnecessarily presenting all the results in their full generality.

## Keywords

1 Introduction
2 Acyclic Networks
3 Cyclic Networks
4 Network Coding and Algebraic Coding
Acknowledgements
References

### Foundations and Trends® in Communications and Information Theory

(Vol 2, Issue 4, 2005, pp 241-329)

### Abstract

Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm for network communications and has generated abundant research interest in information and coding theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix theory.We review the foundational work that has led to the development of network coding theory and discuss the theory for the transmission from a single source node to other nodes in the network. A companion issue discusses the theory when there are multiple source nodes each intending to transmit to a different set of destination nodes.

1. Introduction
Part 1 Single Source
2. Acyclic Networks
3. Cyclic Networks
4. Network Coding and Algebraic Coding
Part 2 Multiple Sources
5. Superposition Coding and Max-Flow Bound
6. Network Codes for Acyclic Networks
7. Fundamental Limits of Linear Codes
Appendix A. Global Linearity versus Nodal Linearity

### Network Coding Theory

154 pages

DOI: 10.1561/9781933019758

E-ISBN: 978-1-933019-75-8

ISBN: 978-1-933019-24-6

### Description

Network Coding Theory provides a tutorial on the basic of network coding theory. It presents the material in a transparent manner without unnecessarily presenting all the results in their full generality. Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network coding theory. Network coding offers a new paradigm for network communications and has generated abundant research interest in information and coding theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix theory. The tutorial is divided into two parts. Part I is devoted to network coding for the transmission from a single source node to other nodes in the network. Part II deals with the problem under the more general circumstances when there are multiple source nodes each intending to transmit to a different set of destination nodes. Network Coding Theory presents a unified framework for understanding the basic notions and fundamental results in network coding. It will be of interest to students, researchers and practitioners working in networking research.

Companion

Network Coding Theory Part II: Multiple Source, Foundations and Trends® in Communications and Information Theory, Volume 2 Issue 5 DOI: 10.1561/0100000007II