# Unit information: Information Theory 3 in 2020/21

Unit name Information Theory 3 MATH34600 10 H/6 Teaching Block 1B (weeks 7 - 12) Dr. Jaggi Not open Year 2 Theoretical Physics OR MATH11300 Probability 1 (or MATH10013 Probability and Statistics) OR Level 2 Physics MATH11400 Statistics 1 is helpful, but not necessary None School of Mathematics Faculty of Science

## Description

Unit Aims

To give a rigorous and modern introduction into Shannon's theory of information, with emphasis on fundamental concepts and mathematical techniques.

Unit Description

Shannon's information theory underlies many aspects of modern life, including streaming an MP3 or movie, or taking and storing digital photos. It is one of the great intellectual achievements of the 20th century, which continues to inspire communications engineering and to generate challenging mathematical problems. Recently it has extended dramatically into physics as quantum information theory. The course is about the fundamental ideas of this theory: data compression and reliable communication over noisy channels.

It is a statistical theory, so notions of probability play a great role, and in particular laws of large numbers as well as the concept of entropy are fundamental, culminating in Shannon's coding theorems. The course aims at demonstrating information theoretical modelling, and the mathematical techniques required will be rigorously developed.

Relation to Other Units

It is a natural companion to the Quantum Information course offered in Mathematics (MATHM5610), and to a certain degree to Cryptography B (COMSM0007), offered in Computer Science, and Communications (EENG 22000), in Electrical Engineering. It may also be interesting to physicists having attended Statistical Physics (PHYS30300).

## Intended learning outcomes

This unit should enable students to:

• understand how information problems are modeled and solved;
• model and solve problems of information theory: data compression and channel coding;
• discuss basic concepts such as entropy, mutual information, relative entropy, capacity;
• use information theoretical methods to tackle information theoretical problems, in particular probabilistic method and information calculus.

Transferable skills:

Mathematical - Knowledge of basic information theory; probabilistic reasoning.

General skills - Modelling, problem solving and logical analysis Assimilation and use of complex and novel ideas

## Teaching details

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

## Assessment Details

80% Timed, open-book examination 20% Group projects

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Recommended

• Robert Ash, Information Theory, Dover Publications, 1990
• T. M. Cover, Joy Thomas, Elements of Information Theory, Wiley, 1991
• David MacKay, Information Theory, Inference and Learning Algorithms, Cambridge University Press, 2003

Further

• Imre Csiszár, János Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems, Cambridge University Press, 2011
• Claude Elwood Shannon, Warren Weaver, The Mathematical Theory of Communication, University of Illinos Press, 1963
• Geoffrey Grimmett, Probability: An Introduction, Oxford University Press, 2014
• Noga Alon, Joel Spencer, The Probabilistic Method, John Wiley, 2008