Information Theory MATH-474* Textbook: Elements of Information
ties of information measures; the data processing theorem; Fano's inequality. 2. ... memoryless sources, asymptotic equipartition property (AEP), block or fixed- ...
Textbook: Elements of Information Theory by T. M. Cover and J. A. Thomas (John Wiley & Sons) Class Notes Prerequisite: STAT-251* or 356*. Corequisite: STAT-455* or permission of the instructor. Instructor: F. Alajaji Evaluation:
Final Examination Midterm Examination Homework
60% 30% 10%
Outline: The reliable transmission of information bearing signals over a noisy communication channel is at the heart of what we call communication. Information theory – founded by Claude E. Shannon in 1948 – provides a mathematical framework for the theory of communication; it describes the fundamental limits to how efficiently one can encode information and still be able to recover it with negligible loss. This course will examine the basic concepts of this theory. What follows is a list of topics to be covered. 1. Shannon’s Measures of Information: entropy, divergence, mutual information; properties of information measures; the data processing theorem; Fano’s inequality. 2. Fundamentals of Fixed-Length Lossless Source Coding (Data Compression): discrete memoryless sources, asymptotic equipartition property (AEP), block or fixed-length coding, fixed-length source coding theorem for discrete memoryless sources; entropy rate of stationary sources with memory, Markov sources, stationary ergodic sources, fixed-length source coding theorem for stationary ergodic sources; source modeling and computation of data redundancy. 3. Fundamentals of Variable-Length Lossless Source Coding: variable-length encoding, unique decodability, Kraft inequality, prefix codes, variable-length source coding theorem for discrete memoryless sources and for stationary sources with memory; design and construction of data compression codes: Shannon-Fano and arithmetic codes, optimal Huffman codes, adaptive Huffman codes. 4. Fundamentals of Channel Coding: discrete memoryless channels, channel capacity and properties; noisy channel coding theorem for discrete memoryless channels; the lossless joint source-channel coding theorem; channel coding techniques. 5. Information Theory for Continuous Alphabet Systems: differential entropy, divergence and mutual information; differential entropy of the multivariate Gaussian distribution; AEP for continuous alphabet memoryless sources, capacity of discrete-time and bandlimited continuous-time memoryless Gaussian channels; parallel Gaussian channels and waterfilling.
Information theory provides basic tools and understanding in many fields. ⢠Information theory is applied mathematics and statistics rather than pure engineering.
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