ECE630 - Spring 2007

STATISTICAL COMMUNICATION THEORY

Professor Yariv Ephraim

STII Room 221

 

Time:              Thursday 4:30-7:10 pm 

 

Place:              Enterprise Hall 174

 

Final Exam:     Exam will be assigned on Thursday, 3 May, and will be due Thursday, 10 May by 5:00pm.

 

Office Hours:            

Tuesday: 4:15-5:15 pm 

Thursday 1:45-2:45 pm 

Other time by appointment

 

To contact me please use yephraim AT gmu DOT edu

 

Course Description:

 

The two designable components of any modern communication system are the source coder/decoder and the channel coder/decoder. From Shannonís theory, optimal design of these two components may be performed independently.  The principles of source coding are covered in several ECE courses; for example, in Information Theory (ECE751) and Data Compression (ECE735). The primary focus of ECE 630 is on the principles of channel coding for digital communication. We shall first develop the optimal receiver, and study its performance, for communicating a sequence of bits over an additive white Gaussian noise channel. Then we impose time-bandwidth constraints and prove the existence of optimal codes for rates smaller than some critical rates of the channel. Next we study implementable channel coding schemes in the form of linear codes and Convolutional codes.  Probability theory in the ECE528 level is essential for understanding the material in this course.

 

Course Outline:

 

  • Introduction  (Chap. 1, week 1)
    • Canonical communication system
    • Overview of topics for this course
  • Review of probability theory  (Chap. 2-3, week 2)
    • Random processes
    • Mean, autocorrelation, power spectral density, bandwidth
    • Transfer of random processes through linear filters
    • The Gaussian process
  • Principles of Optimum Receivers (Chap. 4, weeks 3-6)
    • The maximum a-posteriori decision rule
    • Vector channels
    • Waveform channels with additive Gaussian white noise
    • The matched filter
    • Probability of error:
      1. Signals with rectangular decision regions
      2. Orthogonal, Biorthogonal and Simplex signals
  • Mid-term (week 7)
  • Efficient signaling  (Chap. 5 - weeks 8-9)
    • Bit-by-bit and block orthogonal signaling
    • Upper bounds on the probability of error for block codes
    • Channel rate, time duration, bandwidth, and dimensionality
    • Random coding
    • Existence of optimal codes, critical rates
    • Channel capacity
  • Implementation of Coded Systems (Chap. 6 - week 10-12)
    • Linear block codes
    • Convolutional codes
      1. State and trellis diagrams
      2. Transfer function
      3. Bound on the probability of error
    • Introduction to turbo codes
  • Important channel models  (Chap. 7 - week 12-14)
    • Effects of filtering (non-white noise)
    • Bandpass channels
    • Random amplitude and phase
    • Fading channel

 

Text Book:

 

  • J. M. Wozencraft and I. M. Jacobs, Principles of Communication Engineering. Waveland Press, 1990.

Other References:

 

J. G. Proakis and M. Salehi, Communication Systems Engineering. Prentice-Hall, 2001.

 

J. Proakis, Digital Communications. McGraw-Hill Science/Engineering/Math; 4th edition, 2000.
 

Prerequisite:

 

ECE-528 or instructor permission

 

Communication:

 

Course announcements, assignments and homework solutions will be emailed to you. I will use your email addresses which are on file at the GMU Registrar. If you wish to have your course material delivered to another email address, you may include a .forward command in your GMU directory. It is important that your mail box does not reach its capacity at any time during the semester.

 

Grading:

 

Homework 15%, Mid-term 40%, final 45%

 

The two exams are take-home exams. For these exams you may use the text book, your class notes, and assigned homework solutions.  No other material is allowed.

 

Solutions to homework problems and other assignments in this course may be found on the internet or in course material from previous semesters. Students are not allowed to use these solutions before they submit their homework/assignments. Using such material will constitute a violation of the university honor code.