Introduction to Information Theory

Course manual 2021/2022

Course content

This course will give an introduction to information theory – the mathematical theory of information. Ever since its inception, information theory has had a profound impact on society. It underpins important technological developments, from reliable memories to mobile phone standards, and its versatile mathematical toolbox has found use in computer science, machine learning, physics, and even pure mathematics.

Starting from probability theory, we will discuss how to mathematically model information sources and communication channels, how to optimally compress information, and how to design error-correcting codes that allow us to reliably communicate over noisy communication channels. We will also see how techniques used in information theory can be applied more generally to make predictions from noisy data.

Objectives

• mathematically model memoryless and Markov information sources using probability theory
• mathematically model memoryless information channels using probability theory
• compute basic properties of probability distributions, such as entropies and essential bit contents, using mathematical techniques such as Jensen’s inequality
• define typical sets and estimate their size and probability
• prove and apply Shannon’s source coding theorem
• prove and apply the Kraft inequality for uniquely decodable (UD) codes, its converse for prefix codes, and use it to bound the average length for optimal UD or prefix codes
• design optimal symbol codes using Huffman’s coding algorithm
• analyze and apply the Lempel-Ziv algorithm for stream coding
• analyze and apply arithmetic coding for different probabilistic models
• compute basic properties of joint probability distributions, such as conditional entropies and mutual informations
• prove and apply Shannon’s noisy channel coding theorem
• understand basic properties of block codes, such as their rate and various probabilities of error
• encode Reed-Solomon codes and decode them for erasure errors
• understand maximum likelihood approach to codeword and bitwise decoding
• design and apply message passing algorithms for encoding and inference problems
• independently read about a topic in information theory and present it to your peers

Teaching methods

• Lecture
• Self-study
• Exercise class
• Presentation/symposium

Learning activities

Attendance

Programme's requirements concerning attendance (OER-B):

• Each student is expected to actively participate in the course for which he/she is registered.
• If a student can not be present due to personal circumstances with a compulsory part of the programme, he / she must report this as quickly as possible in writing to the relevant lecturer and study advisor.
• It is not allowed to miss obligatory parts of the programme's component if there is no case of circumstances beyond one's control.
• In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are stated in advance in the course manual and on Canvas.
• In the first and second year, a student should be present in at least 80% of the seminars and tutor groups. Moreover, participation to midterm tests and obligatory homework is required. If the student does not comply with these obligations, the student is expelled from the resit of this course. In case of personal circumstances, as described in OER-A Article A-6.4, an other arrangement will be proposed in consultation with the study advisor.

Assessment

The final grade will be determined by the following calculation:

60% exam grade + 30% homework grade + 10% presentation grade

The same rule applies for the re-sit exam.

There will be one homework problem set per week (in total 6), posted on the course homepage by Monday. You must submit your completed homework (on Canvas) before Monday the week after. We will ask you to collaborate and submit in groups of 3-4 students. The solutions will be discussed in the Wednesday exercise class (among other things). Assignments will be accepted late only if you have extenuating circumstances (such as sickness or family emergency) and provided you confirm with the lecturer before the deadline. Your problem set with the lowest score will be ignored (this includes any problem set you did not submit).

Instead of having a midterm exam, we would like you to read about a topic in information theory and give a short presentation to your peers. You will present as a group of 3-4 students; everyone should speak for a few minutes. We will give you many suggestions for topics (on Canvas) but you are free to pick your own topic (but please confirm it with us).

Everything that we discussed in class and on the homework is in principle in scope for the exam. We recommend that you revisit the homework problems and the exercises as a preparation. You are allowed to bring one self-prepared “cheat sheet” to the exam (A4 paper, hand-written, you can use both sides).

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• dr. Michael Walter