Introduction to Single-User Information Theory

This book provides a concise and rigorous treatment of Shannons information theory, covering key concepts and results in information measures, lossless and lossy data compression, channel coding, and joint source-channel coding. It is ideal for a one-semester course on information theory for students in mathematics, statistics, engineering, and computing.

Format: Hardback
Length: 323 pages
Publication date: 07 May 2018
Publisher: Springer Verlag, Singapore

This comprehensive textbook delves into the core principles of Shannons information theory, providing a concise and mathematically rigorous exploration of its fundamental concepts and indispensable results. Spanning five meticulously crafted core chapters, accompanied by comprehensive problem sets, it emphasizes key topics such as information measures, lossless and lossy data compression, channel coding, and joint source-channel coding for single-user (point-to-point) communications systems. Additionally, two appendices offer essential background material in real analysis, probability theory, and stochastic processes. Designed as a foundational course for upper-level undergraduate and entry-level graduate students in mathematics, statistics, engineering, computing, and information sciences, this book offers a valuable resource for understanding the foundations of information theory. An accompanying instructors solutions manual is also available to support teaching and learning.

Information theory is a fundamental branch of mathematics that deals with the transmission and processing of information in various systems. It emerged in the early 20th century as a way to analyze and optimize communication systems, such as telecommunication networks and computer networks. Shannons information theory is a mathematical framework that was developed by Claude Shannon in the 1940s and 1950s. It is based on the concept of entropy, which measures the amount of uncertainty or randomness in a message. Shannons information theory has had a profound impact on the development of communication systems and has led to the invention of many technologies that we use today, such as digital communication, data compression, and wireless communication.

One of the key concepts of Shannons information theory is the concept of entropy. Entropy is a measure of the amount of information that is contained in a message. It is defined as the average amount of uncertainty or randomness in a message, measured in bits. The higher the entropy of a message, the more information it contains. Shannons information theory also introduced the concept of channel coding, which is used to improve the reliability of communication systems. Channel coding is a technique that adds redundancy to a message to ensure that it can be successfully transmitted over a noisy channel. There are two types of channel coding: source coding and channel coding. Source coding is used to compress the information before it is transmitted, while channel coding is used to recover the information after it has been transmitted.

Shannons information theory has also been used to develop data compression algorithms, such as JPEG and MP3. These algorithms are used to reduce the size of digital images and audio files, making them easier to store and transmit. Shannons information theory has also been used to develop wireless communication systems, such as Wi-Fi and cellular networks. These systems use channel coding and modulation techniques to transmit data over a wireless channel. In conclusion, Shannons information theory is a fundamental branch of mathematics that has had a profound impact on the development of communication systems and technology. It has led to the invention of many technologies that we use today, such as digital communication, data compression, and wireless communication. Shannons information theory is still an active area of research, and new discoveries and applications are being made all the time.

Weight: 672g
Dimension: 242 x 162 x 26 (mm)
ISBN-13: 9789811080005
Edition number: 1st ed. 2018