Information Theory II
Spring 2021
⇒ to time table and download of class material
Aim
This course builds on Information Theory I. It introduces additional topics in single-user communication, connections between Information Theory and Statistics, and Network Information Theory.
The course has two objectives: to introduce the students to the key information theoretic results that underlie the design of communication systems and to equip the students with the tools that are needed to conduct research in Information Theory.
Contents
- Differential entropy, including maximum entropy principle
- AEP for continuous RVs
- The Gaussian channel
- The multiple-access channel (MAC)
- The broadcast channel (BC)
- Channels with states
- Method of types, Sanov's theorem, Stein's lemma
- Soft covering and wiretap channel
- Guessing and Rényi entropy
Prerequisites
- Undergraduate studies
- Solid foundation in probability and calculus
- Pleasure with mathematics
- Information Theory I
Instructors
| Prof. Amos Lapidoth | Prof. Stefan M. Moser | |
| Office: | ETF E107 | ETF E104 |
| Phone: | 044 632 51 92 | 044 632 36 24 |
| E-mail: |  |
 |
Teaching Assistant
Robert Graczyk
Office: ETF E104
Phone: 044 632 28 99
E-mail: 
Time and Place
- Lecture/Exercise: Thursday, 14:15–18:00, Zoom
Textbook
We use the book by Thomas M. Cover and Joy A. Thomas:
T.M. Cover, J.A. Thomas, Elements of Information Theory,
2nd Edition, John Wiley & Sons, Inc., New York, NY, USA.
(Here is a link to an
electronic copy of it.)
Supplementary Notes
Stefan M. Moser: Information Theory (Lecture Notes), 6th edition, Signal and Information Processing Laboratory, ETH Zürich, Switzerland, and Institute of Communications Engineering, National Chiao Tung University (NCTU), Hsinchu, Taiwan, 2018.
Stefan M. Moser: Advanced Topics in Information Theory (Lecture Notes), 4th edition, Signal and Information Processing Laboratory, ETH Zürich, Switzerland, and Institute of Communications Engineering, National Chiao Tung University (NCTU), Hsinchu, Taiwan, 2019.
A. El Gamal, Y.-H. Kim, Network Information Theory, Cambridge University Press
G. Kramer, Topics in Multi-User Information Theory, available here.
Exercises
Printed copies of the exercises will be handed out in class. See time table below.
Examination
Oral exam (30 min.).
Testat requirements
None.
Special Remarks
The lecture is held in English.
Time Table
| W | Date | Topic | Handouts | Exercise | Solutions | Lecturer |
| 1 | 25 Feb. | Differential entropy, relative entropy and mutual information for continuous RVs, max-entropy principle (IT: 16.1–5, 3.4; CT: 8.1, 8.3–6, 12.1) | Infos Contents | — | — | Stefan M. Moser |
| 2 | 4 Mar. | AEP for continuous RVs, typical sets, volume, properties, jointly typical sets, Gaussian channel (IT: 20.13, 17; CT: 8.2, 9.1–2) | Exercise 1 | Solutions 1 | Stefan M. Moser | |
| 3 | 11 Mar. | Gaussian channel: coding theorem (intuition, achievability, and converse), joint source and channel coding (IT: 17, 15; ATIT: 10.8; CT: 9.1-2) | Exercise 2 | Solutions 2 | Stefan M. Moser | |
| 4 | 18 Mar. | Multiple-Access Channel: channel model; rate region, time sharing, convex hull; coding-theorem: achievability (ATIT: 15; CT: 15.3) | Exercise 3 | Solutions 3 | Amos Lapidoth | |
| 5 | 25 Mar. | Multiple-Access Channel: q-pentagons, Q-region, equivalence to time-sharing (no redundant pentagon constraints, Caratheodory); coding-theorem: converse (ATIT: 15; CT: 15.3) | Handout 1 | Exercise 4 | Solutions 4 | Amos Lapidoth |
| 6 | 1 Apr. | Broadcast channel: setup, degraded BC, achievability by superposition coding, converse, Gaussian BC (ATIT: 18; CT: 15.6) | Exercise 5 | Solutions 5 | Stefan M. Moser | |
| — | 8 Apr. | holidays | — | — | ||
| 7 | 15 Apr. | Channels with States: introduction, examples; Gel'fand-Pinsker problem: achievability (ATIT: 17, 4.3 [Markov Lemma]) | Exercise 6 | Solutions 6 | Stefan M. Moser | |
| 8 | 22 Apr. | Gel'fand-Pinsker problem: converse; examples: Writing on Dirty Paper, Channels that Sometimes Get Stuck (ATIT: 17) | Exercise 7 | Solutions 7 | Stefan M. Moser | |
| 9 | 29 Apr. | Method of types: introduction, number and size of type classes, probability of observing a type; large deviation theory: universal source coding, Sanov's theorem (CT: 11; ATIT: 2,3) | Handout 2 | Exercise 8 | Solutions 8 | Amos Lapidoth |
| 10 | 6 May | Minimizing relative entropy subject to equality constraints; Stein's Lemma; Chernoff Information (CT: 11; ATIT: 3,5) | Handout 3 | Exercise 9 | Solutions 9 | Amos Lapidoth |
| — | 13 May | holiday | — | — | ||
| 11 | 20 May | Soft covering: proof of direct part | Handout 4 | Exercise 10 | Solutions 10 | Amos Lapidoth |
| 12 | 27 May | Wiretap channel | Handout 5 | Exercise 11 | Solutions 11 | Amos Lapidoth |
| 13 | 3 Jun. | Guessing and Rényi entropy | Exercise 12 | Solutions 12 | Robert Graczyk |
-||- _|_ _|_ / __|__ Stefan M. Moser 
[-] --__|__ /__\ /__ Senior Researcher & Lecturer, ETH Zurich, Switzerland
_|_ -- --|- _ / / Adj. Professor, National Yang Ming Chiao Tung University (NCTU), Taiwan
/ \ [] \| |_| / \/ Web: https://moser-isi.ethz.ch/
Last modified: Thu Jul 14 05:49:16 CEST 2022