Elements of Information Theory
The latest edition of this classic is updated with new problem sets and material The Second Edition of this fundamental textbook maintains the book's tradition of clear, thought-provoking instruction. Readers are provided once again with an instructive mix of mathematics, physics, statistics, and information theory. All the essential topics in information theory are covered in detail, including entropy, data compression, channel capacity, rate distortion, network information theory, and hypothesis testing. The authors provide readers with a solid understanding of the underlying theory and applications. Problem sets and a telegraphic summary at the end of each chapter further assist readers. The historical notes that follow each chapter recap the main points. The Second Edition features: Chapters reorganized to improve teaching 200 new problems New material on source coding, portfolio theory, and feedback capacity Updated references Now current and enhanced, the Second Edition of Elements of Information Theory remains the ideal textbook for upper-level undergraduate and graduate courses in electrical engineering, statistics, and telecommunications. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
Why Read This Book
You should read Elements of Information Theory because it gives you the rigorous, unifying theory behind compression, channel capacity, detection, and statistical descriptions of signals — the mathematical foundation that powers modern DSP and communications systems. You will learn how entropy, mutual information, and rate–distortion govern the limits of what any algorithm or system can achieve, and get practice with proofs and problem sets that sharpen intuition for practical design choices.
Who Will Benefit
Advanced undergraduates, graduate students, and practicing engineers or researchers in communications, signal processing, or machine learning who need a deep theoretical foundation for compression, coding, and statistical signal analysis.
Level: Advanced — Prerequisites: Familiarity with probability theory and random variables, multivariable calculus, linear algebra, and basic signals & systems or communications concepts; some exposure to mathematical proofs is highly recommended.
Key Takeaways
- Compute and interpret entropy, conditional entropy, mutual information, and relative entropy for discrete and continuous sources.
- Apply source coding theorems to design and analyze lossless and lossy compression schemes (including rate–distortion theory).
- Evaluate channel capacity for common channel models (e.g., discrete memoryless channels, Gaussian channels) and understand the essentials of channel coding theorems.
- Use typical sequences and asymptotic equipartition properties to analyze the probabilistic behavior of long signal sequences.
- Formulate and solve hypothesis testing and detection problems using information-theoretic measures and error exponents.
- Extend point-to-point results to network settings: multiple access, broadcast, and distributed source coding limits.
Topics Covered
- 1. Introduction and Basic Concepts
- 2. Entropy, Relative Entropy, and Mutual Information
- 3. Properties of Entropy and Information Measures
- 4. Asymptotic Equipartition Property and Typical Sequences
- 5. Lossless Source Coding (Shannon’s Source Coding Theorem)
- 6. Channel Capacity and Channel Coding Theorems
- 7. Continuous Alphabets and Gaussian Channels
- 8. Rate–Distortion Theory and Lossy Compression
- 9. Random Coding, Error Exponents, and Strong Converses
- 10. Channels with Memory and Feedback
- 11. Network Information Theory (Multiple Access, Broadcast, Slepian–Wolf, Wyner–Ziv)
- 12. Hypothesis Testing and Large Deviations
- 13. Universal Coding and Practical Considerations
- Appendices: Mathematical Tools and Historical Notes
Languages, Platforms & Tools
How It Compares
Compared with Gallager's Information Theory and Reliable Communication, Cover & Thomas is broader and more pedagogical with extensive examples and problems; compared with MacKay's Information Theory, Inference and Learning Algorithms, Cover & Thomas emphasizes formal proofs and classical coding theorems while MacKay links information theory more directly to modern inference and coding implementations.
