6.450 | Fall 2006 | Graduate

Principles of Digital Communications I


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


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 (digital communications II), 6.452 (wireless communications), and 6.441 (information theory).


6.011. 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.

Text and Handouts

The only required text for the course is the provided manuscript in the lecture notes section.

Course Handouts

Handouts and graded problem sets not picked up during lecture can be found on the cabinet in front of the TA’s office.

Problem Sets

There will be 14 problem sets, corresponding to a weekly schedule, though 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 end of the class in which they are due. Problem set solutions will usually be available at the end of the due date lecture.

The grades assigned to problems 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.


There will be two quizzes during the semester. A final exam will be given during the scheduled final exam period. The quizzes and final will be closed book, but you may bring three double sided 8.5" by 11" pages of notes to each of the quizzes. You may bring five double sided 8.5" by 11" pages of notes to the final. Most people find that the preparing of such notes helps them much more than their use.

The quizzes will be scheduled as shown in the calendar. The final exam will be scheduled by the registrar for 3 hours. We will attempt to make each quiz and the final a test 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. This assessment is based on four noisy measurements: the problem sets, the mini-quizzes, the midterm, and the final. The different measurements have different noise levels, and the final grade will be thus a weighted average, roughly according to the following rule:

Problem sets 15%
Quizzes 50% (each quiz 25%)
Final exam 35%

Reference Texts

The class notes cover all the material in the course, but the following references can provide enrichment and additional examples.

Proakis, John G. Digital Communications. 4th ed. New York, NY: McGraw-Hill, 2000. ISBN: 9780072321111.
This has a larger variety of systems than the class notes, but in less depth.

Proakis, John G., and Masoud Salehi. Communication Systems Engineering. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2001. ISBN: 9780130617934.
This is an undergraduate version of the above text.

Wozencraft, John M., and Irwin Mark Jacobs. Principles of Communication Engineering. Reprint ed. Long Grove, IL: Waveland Press, 1990. ISBN: 9780881335545.
Classic text that first developed the signal space view of communication.

Wilson, Stephen G. Digital Modulation and Coding. Upper Saddle River, NJ: Prentice Hall, 1996. ISBN: 9780132100717.
Another text covering mostly the material of the last two thirds of the course.

Gallager, Robert G. Information Theory and Reliable Communication. New York, NY: John Wiley & Sons, 1968. ISBN: 9780471290483.
Treats most of the topics here in a more advanced information theoretic treatment.

Cover, Thomas M., and Joy A. Thomas. Elements of Information Theory. 2nd ed. New York, NY: Wiley Interscience, 2006. ISBN: 9780471241959.
An excellent text on information theory.

Tse, David, and Pramod Viswanath. Fundamentals of Wireless Communication. Cambridge, UK: Cambridge University Press, 2005. ISBN: 9780521845274.
Excellent Coverage of many topics in the last third of the course.

Goldsmith, Andrea. Wireless Communications. Cambridge, UK: Cambridge University Press, 2005. ISBN: 9780521837163.
An up-to-date of wireless channels.

Strang, Gilbert. Introduction to Linear Algebra. 3rd ed. Wellesley, MA: Wellesley-Cambridge Press, 2003. ISBN: 9780961408893.
Gives clear explanations of many standard linear algebra results.


1 Introduction: A layered view of digital communication

2 Discrete source encoding

3 Memory-less sources, prefix free codes, and entropy

4 Entropy and asymptotic equipartition property

5 Markov sources and Lempel-Ziv universal codes

6 Quantization

7 High rate quantizers and waveform encoding

8 Measure, fourier series, and fourier transforms

9 Discrete-time fourier transforms and sampling theorem Quiz 1 taken 2 days after Ses #9
10 Degrees of freedom, orthonormal expansions, and aliasing

11 Signal space, projection theorem, and modulation

12 Nyquist theory, pulse amplitude modulation (PAM), quadrature amplitude modulation (QAM), and frequency translation

13 Random processes

14 Jointly Gaussian random vectors and processes and white Gaussian noise (WGN)

15 Linear functionals and filtering of random processes

16 Review; introduction to detection Quiz 2 taken 2 days after Ses #16
17 Detection for random vectors and processes

18 Theorem of irrelevance, M-ary detection, and coding

19 Baseband detection and complex Gaussian processes

20 Introduction of wireless communication

21 Doppler spread, time spread, coherence time, and coherence frequency

22 Discrete-time baseband models for wireless channels

23 Detection for flat rayleigh fading and incoherent channels, and rake receivers

24 Case study — code division multiple access (CDMA)

25 Review Final exam taken 7 days after Ses #25

Course Info

Learning Resource Types
Lecture Videos
Problem Sets
Exams with Solutions
Lecture Notes