This text is intended for a one-semester course on the foundations of digital communication. It assumes that the reader has basic knowledge of linear algebra, probability theory, and signal processing, and has the mathematical maturity that is expected from a third-year engineering student.

The text has evolved out of lecture notes that I have written for EPFL students. The first version of my notes greatly profited from three excellent sources, namely the book Principles of Communication Engineering by Wozencraft and Jacobs [1], the lecture notes written by Professor Massey for his ETHZ course Applied Digital Information Theory, and the lecture notes written by Professors Gallager and Lapidoth for their MIT course Introduction to Digital Communication. Through the years the notes have evolved and although the influence of these sources is still recognizable, the text has now its own “personality” in terms of content, style, and organization.

The content is what I can cover in a one-semester course at EPFL. The focus is the transmission problem. By staying focused on the transmission problem (rather than also covering the source digitization and compression problems), I have just the right content and amount of material for the goals that I deem most important, specifically: (1) cover to a reasonable depth the most central topic of digital communication; (2) have enough material to do justice to the beautiful and exciting area of digital communication; and (3) provide evidence that linear algebra, probability theory, calculus, and Fourier analysis are in the curriculum of our students for good reasons. Regarding this last point, the area of digital communication is an ideal showcase for the power of mathematics in solving engineering problems.

The digitization and compression problems, omitted in this text, are also important, but covering the former requires a digression into signal processing to acquire the necessary technical background, and the results are less surprising than those related to the transmission problem (which can be tackled right away, see Chapter 2). The latter is covered in all information theory courses and rightfully so. A more detailed account of the content is given below, where I discuss the text organization.

In terms of style, I have paid due attention to proofs. The value of a rigorous proof goes beyond the scientific need of proving that a statement is indeed true. From a proof we can gain much insight.