Information Theory and Network Coding

This book is an evolution from my book A First Course in Information Theory published in 2002 when network coding was still at its infancy. The last few years have witnessed the rapid development of network coding into a research ?eld of its own in information science. With its root in infor- tion theory, network coding has not only brought about a paradigm shift in network communications at large, but also had signi?cant in?uence on such speci?c research ?elds as coding theory, networking, switching, wireless c- munications,distributeddatastorage,cryptography,andoptimizationtheory. While new applications of network coding keep emerging, the fundamental - sults that lay the foundation of the subject are more or less mature. One of the main goals of this book therefore is to present these results in a unifying and coherent manner. While the previous book focused only on information theory for discrete random variables, the current book contains two new chapters on information theory for continuous random variables, namely the chapter on di?erential entropy and the chapter on continuous-valued channels. With these topics included, the book becomes more comprehensive and is more suitable to be used as a textbook for a course in an electrical engineering department.

Information Theory and Network Coding consists of two parts: Components of Information Theory, and Fundamentals of Network Coding Theory. Part I is a rigorous treatment of information theory for discrete and continuous systems. In addition to the classical topics, there are such modern topics as the I-Measure, Shannon-type and non-Shannon-type information inequalities, and a fundamental relation between entropy and group theory. With information theory as the foundation, Part II is a comprehensive treatment of network coding theory with detailed discussions on linear network codes, convolutional network codes, and multi-source network coding.

Other important features include:

• Derivations that are from the first principle
• A large number of examples throughout the book
• Many original exercise problems
• Easy-to-use chapter summaries
• Two parts that can be used separately or together for a comprehensive course

Information Theory and Network Coding is for senior undergraduate and graduate students in electrical engineering, computer science, and applied mathematics. This work can also be used as a reference for professional engineers in the area of communications.