Instructor | Emre Telatar |
Office | INR 117 |
Phone | +41 21 69 37693 |
[email protected] | |
Office Hours | By appointment |
Teaching Assistant | Elie Najm |
Phone | +41 21 69 37535 |
Office | INR141 |
[email protected] | |
Office Hours | By appointment |
Teaching Assistant | Aleksei Triastcyn |
Phone | +41 21 69 36674 |
Office | INR 238 |
[email protected] | |
Office Hours | By appointment |
Teaching Assistant | Pierre Quinton |
[email protected] |
Lectures | Monday | 13:00 – 15:00 (Room: ELA 1) |
Tuesday | 13:00 – 15:00 (Room: ELA 2) | |
Exercises | Tuesday | 15:00 – 17:00 (Room: ELA 2) |
Language: | English | |
Credits : | 7 ECTS |
Course Information
See the course information.
Special Announcements
Midterm Exam
- Your midterm exam will take place on Tuesday October 31st, at 13:15 in BCH 2201.
- You are allowed to bring a two-sided A4 handwritten cheat sheet.
- The material covered is up to and including Homework 6.
Graded Homework
- The graded homework is out on Tuesday, November 21st and is due on Monday, December 4th at 13:15.
- You are allowed to collaborate among yourselves but you have to write your own solution and indicate who you collaborated with.
Final Exam
- Your final exam will take place on Tuesday January 23rd, at 08:15 in CM 1105 and CM 1106.
- You are allowed to bring 2 two-sided A4 handwritten cheat sheets (2 sheets, 4 pages).
- The exam covers all the material seen in class during the semester.
Detailed Schedule
Date | Topics Covered | Assignment | Solutions | Remarks | ||||
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Sep 18 | Public Holiday | |||||||
Sep 19 |
– Introduction to Source Coding |
hw1.pdf | sol1.pdf | |||||
Sep 25 |
– Kraft’s inequality for uniquely decodable codes |
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Sep 26 |
– Existence of prefix-free codes with expected length at most entropy + 1 |
hw2.pdf | sol2.pdf | |||||
Oct 02 | – Entropy of multiple random variables – Source coding by describing words of n letters – Conditional entropy and mutual information – Chain Rules for entropy and mutual information |
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Oct 03 | – Short reminder for Markov Chains – Minimal and maximal values of H(U) – Data Processing inequality – Entropy Rate – Entropy rate of Stationary Processes |
hw3.pdf | sol3.pdf | |||||
Oct 09 | – Coding Theorem for Stationary Sources – Fixed-to-Fixed Length Source Codes – Typicality |
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Oct 10 | – Properties of Typical Sets – Asymptotic Equipartition Property – Source Coding via Typicality – Universal coding example for iid binary sources |
hw4.pdf | sol4.pdf | |||||
Oct 16 | – Finite state machine (FSM) compressors – invertible machines, information lossless (IL) machines – lower bound to the output length for IL FSMs |
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Oct 17 | – Lempel-Ziv data compression algorithm – analysis and competitive optimality of Lempel-Ziv with respect to FSMs. – asymptotic optimality of Lempel-Ziv |
hw5.pdf | sol5.pdf | Notes on Lempel-Ziv | ||||
Oct 23 | – Communication channels – memoryless/stationary channels, communication without feedback – C(W) = max I(X;Y), examples with binary erasure channel and binary symmetric channels |
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Oct 24 |
– Fano’s inequality |
hw6.pdf | sol6.pdf | |||||
Oct 30 |
– computation of C(W), KKT conditions |
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Oct 31 | Midterm | midterm.pdf | midsol.pdf | |||||
Nov 06 | – channel coding theorem – proofs by random constructions |
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Nov 07 | – proof of the channel coding theorem via random codes and typicality decoder | hw7.pdf | sol7.pdf | |||||
Nov 13 | – revisit the random coding method for the BEC – differential entropy and its properties |
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Nov 14 | – Properties of differential entropy – Entropy-typical seqeuences – Quantization – Entropy of Gaussian distribution |
hw8.pdf | sol8.pdf | |||||
Nov 20 | – Capacity under cost constraint – Capacity of AWGN – Converse to the channel coding theorem with cost constraint |
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Nov 21 |
– Parallel Gaussian channels (water-filling) |
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Nov 27 | – Sphere-packing bound – Gilbert bound – Singleton bound – Linear codes – Generator and parity check matrices |
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Nov 28 | – Reed-solomon codes – Polar codes |
hw10.pdf | sol10.pdf | |||||
Dec 04 | – Polar codes | Coding Notes | ||||||
Dec 05 | – Polar codes | hw11.pdf | sol11.pdf | |||||
Dec 11 | – Rate distortion | |||||||
Dec 12 | – Rate distortion | hw12.pdf | sol12.pdf | |||||
Dec 18 | – Multi-access channel | |||||||
Dec 19 | – Multi-access channel | hw13.pdf | sol13.pdf | |||||
Jan 23 | final.pdf | finalsol.pdf |
Textbook
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T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley 2006.
Additional Reading Material
-
C. E. Shannon, A Mathematical Theory of Communications, Bell System Technical Journal, 1948.
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Notes on Tunstall Coding.
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Notes on Lempel-Ziv Algorithm
To Review Basic Probability Theory
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K. L. Chung, A Course in Probability Theory, Academic Press.
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W. Feller, An Introduction to Probability Theory and Its Applications, Wiley.
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G. Grimmett and D. Stirzaker, Probability and Random Processes, Oxford University Press.
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A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill.
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S. M. Ross, A First Course in Probability, Pearson Education.