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Information Theory
Spring 2006


News

  • Final Grade: The results from the final exam and the final grade can now be collected at Joe's office. In case you are to able to go there in person, you may write an email to me or to Joe.
  • Final Exam: The final exam will take place on
    • Wednesday, June 21, 15:40-18:35 (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
  • Class Evaluation: There will be a class evaluation online available between June 12-June 23. I would very much like to encourage all students to participate! Thanks!
  • Mid-Term Exam: The mid-term exam will take place on
    • Wednesday, April 26, 15:40-18:35 (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 up to definition of information capacity, strongly and weakly symmetric DMCs (lecture of April 10)

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:

  • Joe Chen
    e-mail: <joechen.cm88g at nctu.edu.tw>
Time: Monday, 15:40-16:30
Room: Engineering Building IV, Room 811 (ED811)
Phone: 03-571 21 21 ext. 54571

Time and Place

The course is scheduled for 3 hours per week:

  • Monday, 16:40-17:30, Engineering Building IV, Room 303 (ED303)
  • Wednesday, 15:40-17:30, Engineering Building IV, Room 303 (ED303)

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," Wiley, 1991.

You find here a link to an electronic version of the book.

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
20 Feb. Introduction, measure of information Syllabus Exercise 1 (27 Feb.)   Chapter 2
22 Feb. Entropy, mutual information, relative entropy, IT-inequality, Jensen's inequality Handout 1     Chapter 2
27 Feb. Data compression: efficient coding of a single random variable: leaf-counting, leaf-depths, Kraft's inequality   Exercise 2 (6 Mar.)   Chapter 5, Handout 3
1 Mar. Kraft's inequality, path-length lemma, leaf-entropy theorem, converse of coding theorem for single RV, McMillan's theorem Handout 2,
Handout 3
  Solutions 1 Handout 2 and 3,
Chapter 5
6 Mar. McMillan's theorem, Huffman codes   Exercise 3 (13 Mar.)   Handout 3, Chapter 5
8 Mar. Huffman codes, block-to-variable-length coding of a DMS, variable-length-to-block coding of a DMS, general converse Handout 4   Solutions 2 Handout 3 and 4,
Chapter 5
13 Mar. Variable-length-to-block coding of a DMS: Tunstall, stationary stochastic processes   Exercise 4 (20 Mar.)   Handout 4, Chapter 4
15 Mar. Time-invariant Markov processes, entropy rates, entropy rates of stationary processes     Solutions 3 Chapter 4
20 Mar. Coding of sources with memory: coding theorem, universal source compression (Elias-Willems coding) Handout 5 Exercise 5 (27 Mar.)   Handout 5
22 Mar. Elias-Willems coding, Asymptotic Equipartition Property (AEP)     Solutions 4 Handout 5, Chapter 3
27 Mar. Typical sets, data compression using typical sets, high-probability sets   Exercise 6 (10 Apr.)   Chapter 3
BEWARE: Over the weekend (24-26 Mar.) a faulty version of Exercise 6 was online. If you have downloaded it, please delete it and download it once again!
29 Mar. Transmission over a noisy digital channel, DMC, information capacity, stronly symmetric DMCs     Solutions 5 Chapter 8
3 Apr. No lecture   -----    
5 Apr. No lecture     -----  
10 Apr. Weakly symmetric DMCs   Exercise 7 (17 Apr.)   Chapter 8
12 Apr. Definition of a channel code, operational capacity, Fano's lemma, data processing inequality, converse to the Channel Coding Theorem     Solutions 6 Chapter 8
17 Apr. Jointly typical sequences   Exercise 8 (1 May)   Chapter 8
19 Apr. Channel coding theorem     Solutions 7 Chapter 8
24 Apr. Finding channel capacity: convex optimization, Kuhn-Tucker conditions   -----   R. Gallager's book
26 Apr. Midterm Exam (3 hours)     ----- ATTENTION: This is a 3 hours exam: 15:40-18:35
1 May Discussion of Exam   Exercise 9 (8 May) Solutions Midterm
Exam
 
3 May Kuhn-Tucker conditions     Solutions 8 R. Gallager's book
8 May Joint source channel coding theorem   Exercise 10 (15 May)   Chapter 8
10 May Differential entropy     Solutions 9 Chapter 9
15 May Differential entropy, Gaussian channel   Exercise 11 (22 May)   Chapter 9, 10
17 May Gaussian channel     Solutions 10 Chapter 10
22 May Sampling theorem   Exercise 12 (29 May)   Chapter 10
24 May Band-limited Gaussian channels, parallel Gaussian channels     Solutions 11 Chapter 10
29 May Convolutional codes Handout 6 Exercise 13 (5 June)   Handout 6
31 May No lecture     -----  
5 June Signal flowgraph, transmission gain   Exercise 14 (12 June) Solutions 12 Handout 6
7 June Bhattacharyya bound, signal flowgraph bound on bit error probability     Solutions 13 Handout 6
12 June Bit error probability of convolutional encoders, signal flowgraphs   Exercise 15 (14 June)   Handout 6
Class evaluation online until June 23
14 June Repetition, exercises, questions     Solutions 14,
Solutions 15
 
19 June Time for questions...   -----    
21 June Final Exam (3 hours)       ATTENTION: This is a 3 hours exam: 15:40-18:35

Special Remarks

The lecture will be held in English.


-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Researcher & Lecturer, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adj. Professor, National Chiao Tung University (NCTU), Taiwan
/ \     []  \|    |_|   / \/    Web: http://moser-isi.ethz.ch/


Last modified: Thu Feb 19 08:16:46 UTC+8 2009