Claude Elwood Shannon, the giant who ignited the digital revolution, is the father of information theory and a hero for many engineers and scientists. There are many excellent textbooks describing the many facets of his work, so why add another one? The ambitious goal is to provide a completely different perspective. The writing reflects my desire to abhor duplication and to attempt to break through the compartmentalized walls of several disciplines. Rather than copying a Picasso, I have tried to frame it and place it in a broader context.

The motivation also came from my experience as a teacher. The Electrical and Computer Engineering Department of the University of California at San Diego, in the spotlight of its annual workshop on information theory and applications, attracting several hundred participants from around the world, may be considered a holy destination for graduate students in information theory. Many gifted young minds join our department every year with the ultimate goal of earning a PhD in this venerable subject. Here, thanks to the work of many esteemed colleagues, they can become experts in coding and communication theories, point-to-point and network information theories, and wired and wireless information systems. Over my years of teaching, however, I have noticed that sometimes students are missing the master plan for how these topics are tied together and how are they related to the fundamental sciences. Some questions that may catch them off guard are: How much information can be radiated by a waveform at the most fundamental level? How is the physical entropy related to the information-theoretic limits of communication? How does the energy and the quantum nature of radiation limit information? How is information theory related to other branches of mathematics besides probability theory, like functional analysis and approximation theory? On top of these, there is the overarching question, of paramount importance for the engineer, of how communication technologies are influenced by fundamental limits in a practical setting. To fill these gaps, this book focuses on information theory from the point of view of wave theory, and describes connections with different branches of physics and mathematics.