General: Information Theory and Coding
Course schedule
Type | Day | Hours | Room | |||
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Lecture | Tuesday | 13h15 – 15h00 | CO 1 | |||
Lecture | Friday | 13h15 – 15h00 | CM 3 | |||
Exercises | Tuesday | 15h15 – 16h00 | CO 1 | |||
Exercises | Friday | 15h15 – 16h00 | CM 3 |
Course Mechanics
Weekly Assignments | ||||
Midterm Exam: | 50% | (Tentative Date: Friday, November 9.) | ||
Final Exam: | 50% |
More Information:
Homework Assignments: Information Theory and Coding
Homework 1 Solutions to Homework 1
Homework 2 Solutions to Homework 2
Homework 3 Solutions to Homework 3
Homework 4 Solutions to Homework 4
Homework 5 Solutions to Homework 5
Homework 6 Solutions to Homework 6
Midterm Midterm Solutions
Homework 7 Solutions to Homework 7
Homework 8 Solutions to Homework 8
Homework 9 Solutions to Homework 9
Homework 10 Solutions to Homework 10
Homework 11 Solutions to Homework 11
Midterm 2005-2006 Solutions
Midterm 2002-2003 Solutions
Midterm 2001-2002 Solutions
Midterm 2000-2001 Solutions
Histogram for the Midterm Exam
0 – 9: + + + + +
10 – 19: + + + + + + + + +
20 – 29: + + + + + + + + + + + + + + + + +
30 – 39: + + + + + + + + + + + +
40 – 49: + + + + + + + + + + + + + + + + + + +
50 – 59: + + + + + + + + + + + +
60 – 69: + + + + + + + +
70 – 79: + + + + + + + + +
80 – 89: + + + + + +
90 – 99: + + + +
100 – 109: + +
Coverage and Lecture notes: Information Theory and Coding
Cover & Thomas Chapters and Sections are provided. They do not encompass everything taught in the class.
Friday, | Sep | 21 | Source Coding: singular, uniquely decodable, prefix-free codes. Kraft’s inequality and its converse for prefix-free codes, entropy and average codeword length. Cover & Thomas: Ch. 5, Sections 5.1,5.2,5.3,5.4,5.5 |
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Tuesday, | Sep | 25 | Source Coding: Huffman’s procedure for optimal coding, properties of optimal codes, proof of Huffman’s procedure, kraft’s inequality for uniquely decodable codes. Cover & Thomas: Ch. 5, Sections 5.5,5.6,5.8 |
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Friday, | Sep | 28 | Source Coding: entropy of a source, properties of entropy, chain rule of entropy, mutual information. Cover & Thomas: Ch. 2, Sections 2.1,2.2,2.3,2.4,2.5 |
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Tuesday, | Oct | 2 | Source Coding: binary entropy, upper bound on entropy, properties of mutual information, distance between distributions and its relation to mutual information, convex sets and functions. Cover & Thomas: Ch. 2, Sections 2.6 |
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Friday, | Oct | 5 | Source Coding: concavity of entropy, chain rule of mutual information, conditional entropy and mutual information, chain rule for conditional entropy and mutual information. Cover & Thomas: Ch. 2, Same sections as above |
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Tuesday, | Oct | 9 | Source Coding: conditional mutual information, chain rule for conditional mutual information, stationary processes, entropy rate for stationary processes, markov chains, entropy rate for markov chains. Cover & Thomas: Ch. 4, Sections 4.1,4.2 |
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Friday, | Oct | 12 | Source Coding: weak and strong laws of large numbers, asymptotic equipartition property (AEP), typical sequences, properties of typical sequences, source coding via AEP, definition of a dictionary . Cover & Thomas: Ch. 3, Sections 3.1,3.2 |
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Tuesday, | Oct | 16 | Review of Probability Theory |
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Friday, | Oct | 19 | ||||
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Tuesday, | Oct | 23 | Source coding: Tunstall coding notes |
Friday, | Oct | 26 | ||||
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Tuesday, | Oct | 30 | Source coding: Lempel-Ziv |
Friday, | Nov | 2 | Source Coding: performance of Lemple-Ziv algorithm. Channel Coding: efficient/reliable communication, definition of channel, discrete memoryless without feedback channels . Cover & Thomas: Ch. 8, Sections 8.1, 8.5 |
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Tuesday, | Nov | 6 | Channel Coding: capacity of binary symmetric channel, capacity of binary erasure channel, Fano’s inequality. Cover & Thomas: Ch. 8, Sections 8.1,8.2, 8.3, 8.9 |
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Tuesday, | Nov | 13 | Channel Coding: data processing theorem, Shannon’s channel coding theorem – converse using fano’s inequality, block codes, rate of code . Cover & Thomas: Ch. 8, Sections 8.4, 8.5, 8.7 (for proof of achievability please refer to Professor’s notes below), 8.9 |
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Friday, | Nov | 16 | Channel Coding: typicality, Shannon’s channel coding theorem – achievability using random codes . Cover & Thomas: Ch. 8, Sections 8.6 Notes on Capacity with Constraints |
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Tuesday, | Nov | 20 | Channel Coding: continuation of Shannon’s channel coding theorem |
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Friday, | Nov | 23 | Channel Coding: maximization of mutual information by Kuhn-Tucker conditions |
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Tuesday, | Nov | 27 | Channel Coding: continuous random variables – differential entropy, mutual information, gaussian random variables, properties of differential entropy . Cover & Thomas: Ch. 9, Sections 9.1, 9.2, 9.3, 9.4, 9.5, 9.6 |
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Friday, | Nov | 30 | Channel Coding: capacity of continuous alphabet channel with input constraints, Shannon’s channel coding theorem, additive white gaussian noise channel and its capacity Cover & Thomas: Ch. 10, Sections 10.1, 10.2 |
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Tuesday, | Dec | 4 | ||||
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Friday, | Dec | 7 | Channel coding: differential versus discrete entropy, parallel gaussian channels, water filling solution, wide sense stationary processes, auto-correlation function and power spectral density, capacity of band-limited channels . Cover & Thomas: Ch. 10, Sections 10.3, 10.4 |
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Tuesday, | Dec | 11 | Channel Coding: binary block codes, hamming distance, minimum distance of a code, dimension of a code, sphere-packing bound on the number of codewords, Gilbert-Varshamov bound on the number of codewords Notes on Coding |
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Friday, | Dec | 14 | Channel Coding: binary linear block codes, hamming distance, weight of a codeword, minimum distance of a linear code, (7,4,3) hamming code and general hamming codes |
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Tuesday, | Dec | 18 | Channel Coding: error correction and detection using hamming codes, Reed-Solomon (RS) codes, construction of RS codes, dimension and minimum distance of RS codes |
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Friday, | Dec | 21 | Quantization/Lossy compression: rate distortion theory, Shannon’s theorem on rate distortion, rate distortion function of gaussian sources . Cover & Thomas: Ch. 13, Sections 13.1, 13.2, 13.3, 13.4, |
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Recommended Reading: Information Theory and Coding
Textbook: T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley, 2006.
Reference Material:
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R. G. Gallager, Information Theory and Reliable Communication, Wiley, 1968.
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C. E. Shannon, The Mathematical Theory of Communication , U. of Illinois Press, 1963.
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J. M. Wozencraft and I. M. Jacobs, Principles of Communication Engineering, Wiley 1965 (also, Waveland, 1990).