Course Syllabus - Spring 2016

This is the first graduate course covering the principles of digital transmission of information. ECE 535 introduces a notion of information. We rigorously define the amount of information, introduce information measures and explain how to extract a pure information from a source and how to protect information during transmission. The largest portion of the course is devoted to studying how to translate information into a digital signal to be transmitted, and how to retrieve the information back from the received signal. We study in depth various digital modulation schemes through a concept of signal space. We build analytical and simulation models for digital modulation systems in presence of noise, and define the performances of digital communication systems through a probability of reliable transmission of information. We also build optimal receiver models for digital base-band and band-pass modulation schemes.

The successful student will be able to:

  1. understand and compute Shannon capacity of various communications, channels.
  2. write a software and analyze source coding algorithms such as: Huffman, arithmetic and Ziv-Lempel coding, and channel coding schemes as convolutional codes and linear block codes.
  3. rigorously analyze and develop simulation models for coded digital communications systems, such as PSK, ASK, QAM etc…
  4. design optimal detectors in presence of AWGN.

Class Information

Instructor: Dr. Bane Vasić
Phone: (520) 626-5550
Office Hours: TBA, and by appointment.
Textbook: None required
References: J. G. Proakis, Digital Communications, 4th Edition, McGraw-Hill, 2000.
S. G. Wilson, Digital Modulation and Coding, Prentice-Hall, 1995.
R. Blahut, Digital Transmission of Information, Addison-Wesley, 1990.
J. Wozencraft and I. Jacobs, Principles of Communication Engineering, Wiley, 1965 S. Haykin, Introduction to Communication Systems, 4rd ed., Wiley, 2000.
Credits: ECE 535 is a three-unit, A-E based graduate course.
TA/Grader: Mohsen Bahrami (

Administrative Details and Policies

Prerequisites: 1. ECE 340 (Engineering Systems Analysis) (signal characterization in frequency domain, Fourier transform, discrete-time systems)
2. ECE 529 (Digital Signal Processing)
3. ECE 503 (Random Processes for Engineering Applications)
Attendance: Optional, but recommended.
Punctuality: Entering the classroom after the instructor is strongly discouraged!
Participation: Students are encouraged to take part in general class discussions.
Student Questions: The instructor will not be able to answer questions submitted by e-mail or phone, nor to accept student visits out of the office hours.
Projects and Homework: There will be no homework in this class, i.e., homework if assigned will be graded as a reference to the final grade. Solved problems will be posted on the instructor’s web page. There will be couple of medium size computer projects instead.
Exams: There will be two mid-term exams, one final written examination. The final exam schedule can be found here. Exams may include material/topics not contained in the text, but which are discussed in class. The final exam is mandatory.
Computer problems: These will be integrated with your regular homework. Students may use any convenient math software.
Grading policy: Graded work includes exams and projects. Final grades will be determined by your total number of points compared to an absolute scale. The course grade will be percentage based and I guarantee the following minimum cutoffs for grades:
The weights below will be used to determine your point total and your final grade.
Academic Integrity: All submitted work must be original. The minimum penalty for plagiarism and cheating on exams and quizzes is an E grade of failing.

Course Outline

Review of mathematical tools: Orthogonal functions, probability theory, random processes, Markov processes.
Information theory: Information measures (self information, mutual information, channel capacity), looseless source coding, Huffman codes, channel coding, Shannon coding theorems.
Representation of band-pass signals and systems: Band-pass signals and noise representation (Hilbert transform); signal space representation.
Digital modulation schemes: Memoryless digital modulation methods (ASK, PSK, FSK, QPSK), modulation with memory (base-band and band-pass), spectra of digitally modulated signals.
Optimum receivers for additive white Gaussian noise (AWGN) channel: Maximum a posteriori and maximum likelihood detection, matched filter demodulation, sequence detectors, symbol by symbol MAP detector for channels with memory, receiver performance.
Error control coding fundamentals: Finite fields, generator and parity check matrices block and convolutional codes, Hamming codes, syndrome decoding.
Codes on graphs and iterative decoding: Probabilistic graphical models, exact and approximate inference, belief propagation, low-density parity check (LDPC) codes, iterative decoding, linear programming decoding.
Viterbi algorithm.
Gallager algorithms for decoding of LDPC codes.
Belief propagation.
LDPC code construction.