Entropy and Information Theory

Preface.- Introduction.- Information Sources.- Pair Processes: Channels, Codes, and Couplings.- Entropy.- The Entropy Ergodic Theorem.- Distortion and Approximation.- Distortion and Entropy.- Relative Entropy.- Information Rates.- Distortion vs. Rate.- Relative Entropy Rates.- Ergodic Theorems for Densities.- Source Coding Theorems.- Coding for Noisy Channels.- Bibliography.- References.- Index

Robert M. Gray is the Alcatel-Lucent Technologies Professor of Communications and Networking in the School of Engineering and Professor of Electrical Engineering at Stanford University. For over four decades he has done research, taught, and published in the areas of information theory and statistical signal processing. He is a Fellow of the IEEE and the Institute for Mathematical Statistics. He has won several professional awards, including a Guggenheim Fellowship, the Society Award and Education Award of the IEEE Signal Processing Society, the Claude E. Shannon Award from the IEEE Information Theory Society, the Jack S. Kilby Signal Processing Medal, Centennial Medal, and Third Millennium Medal from the IEEE, and a Presidential Award for Excellence in Science, Mathematics and Engineering Mentoring (PAESMEM). He is a member of the National Academy of Engineering.

From the reviews of the second edition:

"In Entropy and Information Theory Robert Gray offers an excellent text to stimulate research in this field. ... Entropy and Information Theory is highly recommended as essential reading to academics and researchers in the field, especially to engineers interested in the mathematical aspects and mathematicians interested in the engineering applications. ... it will contribute to further synergy between the two fields and the deepening of research efforts." (Ina Fourie, Online Information Review, Vol. 36 (3), 2012)

"The book offers interesting and very important information about the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The main goal is a general development of Shannon's mathematical theory of communication for single-user systems. ... The author manages to balance the practice with the theory, every chapter is very well structured and has high-value content." (Nicolae Constantinescu, Zentralblatt MATH, Vol. 1216, 2011)

From the book reviews:

"This book is the second edition of the classic 1990 text ... and inherits much of the structure and all of the virtues of the original. ... this is a deep and important book, which would reward further study as the focus of a reading group or graduate course, and comes enthusiastically recommended." (Oliver Johnson, Mathematical Reviews, October, 2014)

"In Entropy and Information Theory Robert Gray offers an excellent text to stimulate research in this field. ... Entropy and Information Theory is highly recommended as essential reading to academics and researchers in the field, especially to engineers interested in the mathematical aspects and mathematicians interested in the engineering applications. ... it will contribute to further synergy between the two fields and the deepening of research efforts." (Ina Fourie, Online Information Review, Vol. 36 (3), 2012)

"The book offers interesting and very important information about the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The main goal is a general development of Shannon's mathematical theory of communication for single-user systems. ... The author manages to balance the practice with the theory, every chapter is very well structured and has high-value content." (Nicolae Constantinescu, Zentralblatt MATH, Vol. 1216, 2011)