## Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

## Description

This course is a graduate level introduction to the basic principles of digital communication systems. A digital communication system is one that transmits a source (voice, video, data, etc.) from one point to another, by first converting it into a stream of bits, and then into symbols that can be transmitted over channels (cable, wireless, storage, etc.). The use of the digital bit-stream as the interface between the source and the channel is universal regardless of what kind of source and channel are involved. Digital communication principle, with "bit" as the most important concept of the information age, and applications in computer science, Internet, wireless, etc, is one of the most successful stories of applying mathematics in engineering designs.

The course gives an overview of the designs of digital communication systems. We explain the mathematical foundation of decomposing the systems into separately designed source codes and channel codes. We introduce the principles and some commonly used algorithms in each component, to convert continuous time waveforms into bits, and vice versa. We give a comprehensive introduction to the basics of information theory, a rather thorough treatment of Fourier transforms and the sampling theorem, and an overview of the use of vector spaces in signal processing.

The course would be beneficial particularly to students who are interested in doing research in fields related to communications, networks, and signal processing. The general principle and philosophy of the engineering designs discussed in this course are inspiring to all engineering majors. As a Technical Qualifying Exam (TQE) course, we also try to offer some rigorous mathematical training. The materials of this course are the baselines of further studies in *6.451 Principles of Digital Communication II*, *6.452 Principles of Wireless Communication*, and *6.441 Information Theory*.

## Prerequisites

The prerequisite for this course is *6.011 Introduction to Communication, Control and Signal Processing*. Students are expected to have a good undergraduate background in probability and linear systems. Some maturity and patience in looking carefully at fundamental issues is also needed.

## Required Text

Gallager, Robert G. *Principles of Digital Communication*. New York, NY: Cambridge University Press, 2008. ISBN: 9780521879071.

## Handouts

Handouts of the lecture slides will be given out at the beginning of lectures.

## Problem Sets

There will be 11 weekly problem sets posted online. The final problem set will not be collected. Problem sets will be shorter in weeks involving either quizzes or holidays. You are expected to do all the assigned problems, and we will assume that in making up the quizzes and final. We encourage you to cooperate with each other in doing the problem sets. The problem sets are vehicles for learning, and whatever maximizes learning for you is desirable. This usually includes discussion, teaching of others, and learning from others. You are not competing for grades with your classmates.

Problem sets must be handed in by the beginning of the class in which they are due. Graded problem sets will be returned in class. The grades assigned to problem sets will be 0, 1, or 2. Usually only one or two of the problems on a set will be graded, and you are responsible for asking about points of confusion. You are also welcome to flag confusing topics in the problem sets; this will not lower your grade. It will usually be more efficient, however, for you to ask one of us directly about such issues.

## Exams

There will be one midterm exam during the semester and a final exam during the finals week. The exams will be closed book, but you may bring three double-sided 8.5" by 11" pages of notes to each of the tests. Most people find that the preparation of such notes helps them much more than the actual use.

The midterm is scheduled as shown in the calendar. The final exam is 3 hours long and will be scheduled by the registrar. We will attempt to make the midterm and final exam tests of understanding rather than of speed-writing.

## Course Grade

The final grade in the course is based upon our best assessment of your understanding of the material. The final grade is given roughly according to the following rule:

ACTIVITIES | PERCENTAGES |
---|---|

Problem sets | 15% |

Quizzes | 35% |

Final exam | 50% |