Information Theory & Coding
Instructor | Emre Telatar |
Office | INR 117 |
Phone | +41 21 69 37693 |
emre.telatar@epfl.ch | |
Office Hours | By appointment |
Teaching Assistant | Mani Bastani Parizi |
Phone | +41 21 69 31359 |
Office | INR032 |
mani.bastaniparizi@epfl.ch | |
Office Hours | By appointment |
Teaching Assistant | Rafah El-Khatib |
Phone | +41 21 69 31361 |
Office | INR 032 |
rafah.el-khatib@epfl.ch | |
Office Hours | By appointment |
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 |
See the course information.
Special Announcements
Midterm Exam
Your midterm exam will take place on Tuesday October 27, at 13:15 in rooms ELA2, DIA003, and CO120.
- Please find your room and seat before the exam according to the following seating plan:
- This is a closed book exam but you are allowed to have one A4 page of notes (double-sided) with you.
Here is some statistics about midterm grades:
Average | Standard Deviation | |
---|---|---|
P1 | 6.39 | 3.72 |
P2 | 9.51 | 4.45 |
P3 | 5.09 | 4.09 |
Total | 21 | 9.18 |
You can also find a histogram of the grades here.
Final Exam
Your final exam will take place on Monday, January 11, 2016, at 8:15 in rooms INM200 and INM202.
- Please be there well in advance to find your room and seat.
- This is a closed book exam, but you are allowed to bring two A4 pages of notes (double-sided) with you.
Detailed Schedule
Date | Topics Covered | Assignment | Solutions | Remarks | |
---|---|---|---|---|---|
Sep 14 | - Introduction to Source Coding - Non-singular codes - Uniquely decodable codes - Prefix-free codes - Kraft's inequality for prefix-free codes - Kraft's inequality for extensions of codes | ||||
Sep 15 | - Kraft's inequality for uniquely decodable codes - Reverse Kraft's inequality - Expected codeword length - Entropy as a lower-bound to the expected codeword length | hw1.pdf | sol1.pdf | ||
Sep 21 | Public Holiday | ||||
Sep 22 | - Existence of prefix-free codes with average length at most entropy + 1 - Entropy of multiple random variables - Properties of optimal codes - Huffman procedure | hw2.pdf | sol2.pdf | ||
Sep 28 | - Equivalence of prefix-free codes and strategy for guessing via binary questions - Interpretation of entropy as expected number of questions for guessing the random variable - Conditional Entropy and Mutual Information - Chain Rules for entropy and mutual information | ||||
Sep 29 | - Review of Markov Chains - Data Processing inequality - Entropy Rate - Entropy rate of Stationary Processes | hw3.pdf | sol3.pdf | ||
Oct 5 | - Coding Theorem for Stationary Sources - Fixed-to-Fixed Length Source Codes - Typicality | ||||
Oct 6 | - Properties of Typical Sets - Asymptotic Equipartition Property - Source Coding by AEP - Variable-to-Fixed Length Source Codes - Valid and Prefix-Free Dictionaries | hw4.pdf | sol4.pdf | ||
Oct 12 | - Relationship between word- and letter-entropies for valid, prefix-free dictionaries - Tunstall procedure - Analysis of Tunstall procedure | Notes on Tunstall Coding | |||
Oct 13 | - Universal Source Coding - Lempel–Ziv method - Analysis of Lempel–Ziv (finite state machine compressions, FSM compressibility of a sequence, LZ compressibility of a sequence) | hw5.pdf | sol5.pdf | ||
Oct 19 | - Information-Lossless FSM Compressors - Lower bound on the output length of an IL FSM Compressor | Notes on Lempel–Ziv Compression | |||
Oct 20 | - LZ Compressibility of sequences - Optimality of Lempel–Ziv - Communication Channels - Discrete Memoryless Channels | hw6.pdf | sol6.pdf | ||
Oct 26 | - Examples of Discrete Memoryless Channels (BSC and BEC) - Transmission with or without feedback - Channel Capacity - Fano's Inequality | ||||
Oct 27 | Midterm Exam | midterm.pdf | midsol.pdf | ||
Nov 2 | - Converse to the Channel Coding Theorem | ||||
Nov 3 | - Proof of the Channel Coding Theorem | hw7.pdf | sol7.pdf | ||
Nov 9 | - Capacity of BSC and BEC - Jensen's Inequality - Concavity of Mutual Information in Input Distribution - KKT Conditions | ||||
Nov 10 | - KKT Conditions (cont'd) - Application of KKT: Capacity of Z Channel - Continuous Alphabet: Differential Entropy | hw8.pdf | sol8.pdf | ||
Nov 16 | - Properties of differential entropy - Entropy-typical seqeuences - Quantization - Entropy of Gaussian distribution | ||||
Nov 17 | - Capacity under cost constraint - Capacity of AWGN - Converse to the channel coding theorem with cost constraint - Parallel Gaussian channels (water-filling) | hw9.pdf | sol9.pdf | ||
Nov 23 | - Proof of Channel Coding Theorem for general channels via Threshold Decoding | ||||
Nov 24 | - Channel Codes - Minimum Distance - Singleton Bound - Sphere-packing Bound - Gilbert–Varshamov Bound | hw10.pdf | sol10.pdf | ||
Nov 30 | - Linear Codes - Generator Matrix - Parity-check Matrix - Hamming Codes | ||||
Dec 1 | - Reed–Solomon Codes | hw11.pdf | sol11.pdf | ||
Dec 7 | - Polar Codes | ||||
Dec 8 | - Polar Codes | hw12.pdf | sol12.pdf | ||
Dec 14 | - Polar Codes | ||||
Dec 16 | - Rate–Distortion Theory | ||||
Jan 11 | Final Exam | final.pdf | finalsol.pdf |
Textbook
- 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.
- Notes on Tunstall Coding.
- Notes on Lempel-Ziv Algorithm
To Review Basic Probability Theory
- K. L. Chung, A Course in Probability Theory, Academic Press.
- W. Feller, An Introduction to Probability Theory and Its Applications, Wiley.
- G. Grimmett and D. Stirzaker, Probability and Random Processes, Oxford University Press.
- A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill.
- S. M. Ross, A First Course in Probability, Pearson Education.