|
Back to overview over all lectures...
Information Theory Spring 2007
News
- Class Evaluation: There will be a class evaluation online between June 18 and June 29. I would very much like to encourage all students to participate! Thanks!
- Final Grade: You will receive your final grade of this course together with your results from the final exam (the final grade will be depicted beside the grade of the final exam). The final exams will be returned and discussed on June 25 during normal class hours. If you cannot make it, contact the Teaching Assistant Lin Ding-Jie.
- Final Exam: The final exam will take place on
- Wednesday, June 20, 15:40-18:30 (Note that this is one hour longer than usual!)
Regulations:
- open book: any book is allowed
- not allowed are: any telecommunication devices like mobile phones, any "friend" or other help from outside...
- covered material: everything we covered in class
- Mid-Term Exam: The mid-term exam will take place on
- Wednesday, April 25, 15:40-18:30 (Note that this is one hour longer than usual!)
Regulations:
- open book: any book is allowed
- not allowed are: any telecommunication devices like mobile phones, any "friend" or other help from outside...
- covered material: everything covered in class until (and including) April 9, i.e., everything up to the definition of information capacity, and strongly and weakly symmetric DMCs
Instructor
Stefan M. Moser
Engineering Building IV, Room 727
phone: 03-571 21 21 ext. 54548
e-mail:
Teaching Assistant
In case you would like to discuss some questions in Chinese, you might contact my TA:
Room: Engineering Building IV, Room 711 (ED711)
Phone: 03-571 21 21 ext. 54628
Time and Place
The course is scheduled for 4 hours per week:
- Monday, 15:40-17:30, Engineering Building IV, Room 021 (ED021)
- Wednesday, 15:40-17:30, Engineering Building IV, Room 021 (ED021)
On Wednesday, the second hour is reserved for exercises. The mid-term and final exams will be 3 hours.
Course Objectives
This course is an introduction to Information Theory. We will cover
the most important results concerning data compression and reliable
communication over a communication channel. The course will follow
approximately the following schedule:
- Introduction and basic definitions:
- entropy
- mutual information
- relative entropy
- Source coding: how to compress data efficiently?
- Kraft inequality
- source coding theorem for a single random variable
- Shannon-Fano codes
- Huffman codes
- source coding theorem for a discrete memoryless source
- Tunstall codes
- universal codes
- Channel coding: how to transmit data reliably?
- Fano's inequality and data processing lemma
- converse to channel coding theorem for discrete memoryless channel
- AEP and typical sequences
- channel coding theorem
- continuous random variables and entropy
- channel coding theorem for the AWGN channel
We hope that a student who finishes the course will be able to understand
the basic principles underlying any communication or data storage
system.
Prerequisites
The following lectures/topics are recommended:
- Probability
- once more Probability
- Principles of Communication Engineering I and II (preferably)
- joy in math and engineering
Textbook
The course will be mainly be based on
- Thomas M. Cover and Joy A. Thomas: "Elements of Information Theory," second edition, Wiley, 2006.
You find here a link to an electronic version of the book.
Sometimes additional lecture notes will be distributed.
Further references and recommended readings:
- Robert G. Gallager: "Information Theory and Reliable Communication," Wiley, 1968.
- Raymond W. Yeung: "A First Course in Information Theory," Kluwer Academic Publishers, 2005.
- James L. Massey: "Applied Digital Information Theory I and II," lecture notes, Swiss Federal Institute of Technology (ETH), Zurich. (Link to electronic version)
Grading
Every week there will be an exercise consisting of a couple of
problems that needs to be solved at home. For the understanding of the
course and also as a preparation for the mid-term and final exam we
highly recommend to solve the exercises! Since the material of this
course is rather demanding by itself, we have decided not to further
challenge the students with additional tasks like, e.g., a
presentation of a paper. We hope that the saved time will instead be used
for solving the exercises and reading the textbook!
The grade will be an average of
- the homework (15%),
- the midterm exam (35%), and
- the final exam (50%).
The grade of the homework will not be based on the
correctness of the answers, but rather the effort the student shows in
trying to solve them. To pass the course there is the additional
condition that at least 10 exercises have to
be handed in.
This course is worth 3 credits.
Time Table
Date |
Topic |
Handouts |
Exercise (due on) |
Solutions |
Comments |
26 Feb. |
Introduction, measure of information, IT-inequality, entropy |
Syllabus (Version 2) |
Exercise 1 (5 Mar.) |
|
Problem 6 of Exercise 1 is canceled Chapter 2 |
28 Feb. |
No lecture |
|
|
|
|
5 Mar. |
Conditional entropy, relative entropy, mutual information, Jensen's inequality, data compression |
Handout 1 |
Exercise 2 (12 Mar.) |
|
Chapter 2 |
7 Mar. |
Rooted trees, leaf-counting/leaf-depth lemma, Kraft inequality |
Handout 2 |
|
Solutions 1 |
Handout 2 |
12 Mar. |
Path length lemma, leaf-entropy theorem, coding theorem for a single RV, Shannon-Fano codes, types of codes, McMillan |
|
Exercise 3 (19 Mar.) |
|
Handout 2, Chapter 5 |
14 Mar. |
Huffman Codes, coding of an information source |
Handout 3 |
|
Solutions 2 |
Handout 2, Chapter 5 |
19 Mar. |
Coding of an information source, block-to-variable-length coding, variable-length-to-block coding, Tunstall coding |
Handout 4 |
Exercise 4 (26 Mar.) |
|
Handout 4 |
21 Mar. |
Stochastic processes, stationarity, Markov processes, entropy rate |
|
|
Solutions 3 |
Chapter 4 |
26 Mar. |
Entropy rate, Cesaro mean, coding of sources with memory |
Handout 5 |
Exercise 5 (2 Apr.) |
|
Chapter 4, Handout 5 |
28 Mar. |
Elias-Willems universal coding scheme |
|
|
Solutions 4 |
Handout 5 |
2 Apr. |
AEP, typical sets, transmission over a noisy channel |
|
Exercise 6 (9 Apr.) |
|
Chapter 3 |
4 Apr. |
No lecture |
|
|
----- |
|
9 Apr. |
discrete memoryless channel DMC, information capacity |
|
Exercise 7 (18 Apr.) |
Solutions 5 |
Chapter 7 |
11 Apr. |
Coding for a DMC, Fano's lemma, data processing inequality, converse of coding theorem for a DMC |
|
|
Solutions 6 |
Chapter 7 |
16 Apr. |
No lecture |
|
----- |
|
|
18 Apr. |
Jointly typical sequences, coding theorem for a DMC |
|
Exercise 8 (30 Apr.) |
Solutions 7 |
Chapter 7 |
23 Apr. |
Coding Theorem for a DMC, convex optimization |
|
----- |
|
Chapter 7, R. Gallager's book |
25 Apr. |
Midterm Exam |
|
|
----- |
ATTENTION: This is a 3 hours exam: 15:40-18:30 |
30 Apr. |
Finding channel capacity: convex optimization, Kuhn-Tucker conditions |
|
Exercise 9 (7 May) |
|
R. Gallager's book |
2 May |
Kuhn-Tucker conditions, joint source channel coding theorem |
|
|
Solutions 8 |
R. Gallager's book, Chapter 7.13 |
7 May |
Joint source channel coding theorem, differential entropy |
|
Exercise 10 (14 May) |
|
Chapter 7.13, Chapter 8 |
9 May |
differential entropy, continuous-alphabet AEP |
|
|
Solutions 9 |
Chapter 8 |
14 May |
Additive Gaussian noise channel |
|
Exercise 11 (21 May) |
|
Chapter 9 |
16 May |
Sampling Theorem |
|
|
Solutions 10 |
Chapter 9 |
21 May |
Bandlimited Gaussian channel, parallel Gaussian channels |
|
Exercise 12 (28 May) |
|
Chapter 9 |
23 May |
Parallel Gaussian channels with colored noise |
|
|
Solutions 11 |
Chapter 9 |
28 May |
Convolutional codes |
Handout 6 |
Exercise 13 (4 June) |
|
Handout 6 |
30 May |
Quality of convolutional codes: signalflowgraphs |
|
|
Solutions 12 |
Handout 6 |
4 June |
Quality of convolutional codes: signalflowgraphs, Bhattacharyya bound |
|
Exercise 14 (11 June) |
|
Handout 6 |
6 June |
Quality of convolutional codes |
|
|
Solutions 13 |
Handout 6 |
11 June |
Exercises, questions |
|
Exercise 15 (13 June) |
|
Note: the due date of Exercise 14 has been moved to 13 June |
13 June |
Discussion Exercises 14 and 15, questions, general information about final exam |
|
|
Solutions 14, Solutions 15 |
|
18 June |
No lecture |
|
----- |
|
Class evaluation online until June 29! |
20 June |
Final Exam |
|
|
|
ATTENTION: This is a 3 hours exam: 15:40-18:30 |
25 June |
Discussion of final exam |
|
----- |
|
|
27 June |
No lecture |
|
|
----- |
|
Special Remarks
The lecture will be held in English.
-||- _|_ _|_ / __|__ Stefan M. Moser
[-] --__|__ /__\ /__ Senior Scientist, ETH Zurich, Switzerland
_|_ -- --|- _ / / Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan
/ \ [] \| |_| / \/ Web: https://moser-isi.ethz.ch/
Last modified: Thu Feb 19 08:17:30 UTC+8 2009
|