Transcription of Entropy and Information Theory - Stanford EE
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Entropy and Information Theory - Stanford EE
Entropy and Information Theory First Edition, Corrected March 3, 2013. ii Entropy and Information Theory First Edition, Corrected Robert M. Gray Information Systems Laboratory Electrical Engineering Department Stanford University Springer-Verlag New York c 1990 by Springer Verlag. Revised 2000, 2007, 2008, 2009, 2013 by Robert M. Gray iv to Tim, Lori, Julia, Peter, Gus, Amy Elizabeth, and Alice and in memory of Tino Contents Prologue ix 1 Information Sources 1. Introduction .. 1. Probability Spaces and Random Variables .. 1. Random Processes and Dynamical Systems .. 5. Distributions .. 6. Standard Alphabets .. 10. Expectation .. 11. Asymptotic Mean Stationarity .. 14. Ergodic Properties .. 15. 2 Entropy and Information 17. Introduction .. 17. Entropy and Entropy Rate .. 17. Basic Properties of Entropy .. 20. Entropy Rate .. 31. Conditional Entropy and Information .
ical aspects and general models of the theory and mathematicians in some of the important engineering applications of performance bounds and code design for communication systems. Information theory, the mathematical theory of communication, has two primary goals: The rst is the development of the fundamental theoretical lim-
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