Claude Shannon, the father of Information Theory, described the fundamental problem of point-to-point communications in his classic 1948 paper as “that of reproducing at one point either exactly or approximately a message selected at another point.” How engineers solve this problem is the subject of this book. But unlike Shannon's general problem, where the message can be an image, a sound clip, or a movie, here we restrict ourselves to bits. We thus envision that the original message is either a binary sequence to start with, or else that it was described using bits by a device outside our control and that our job is to reproduce the describing bits with high reliability. The issue of how images or text files are converted efficiently into bits is the subject of lossy and lossless data compression and is addressed in texts on information theory and on quantization.

The engineering solutions to the point-to-point communication problem greatly depend on the available resources and on the channel between the points. They typically bring together beautiful techniques from Fourier Analysis, Hilbert Spaces, Probability Theory, and Decision Theory. The purpose of this book is to introduce the reader to these techniques and to their interplay.

The book is intended for advanced undergraduates and beginning graduate students. The key prerequisites are basic courses in Calculus, Linear Algebra, and Probability Theory. A course in Linear Systems is a plus but not a must, because all the results from Linear Systems that are needed for this book are summarized in Chapters 5 and 6. But more importantly, the book requires a certain mathematical maturity and patience, because we begin with first principles and develop the theory before discussing its engineering applications. The book is for those who appreciate the views along the way as much as getting to the destination; who like to “stop and smell the roses;” and who prefer fundamentals to acronyms. I firmly believe that those with a sound foundation can easily pick up the acronyms and learn the jargon on the job, but that once one leaves the academic environment, one rarely has the time or peace of mind to study fundamentals.