Project: Communication on Noisy Channels

**on****on** **Noisy** **Channels**

Methods for efficient coding and decoding are important in many

areas; just to menti**on** deep space communicati**on** and reading from

defect CD-media. In this project, methods from several mathematical

areas like linear algebra, algebra and probability theory play together

as foundati**on**s for informati**on** theory and the theory of errorcorrecting

codes. The results aimed for are definitely n**on**-trivial; they

can often be obtained as applicati**on**s of very c**on**crete mathematical

methods. For example, students will perform calculati**on**s **on** matrices

over finite fields; they have to use probabilistic methods dealing with

c**on**crete informati**on** channels and codes.

**on** theory and they should seek

c**on**necti**on**s between both areas. To begin with, student groups investigate the foundati**on**s of the theories.

Later **on**, every group decides **on** topics to look at and to describe in depth. The students collaborate **on**

several tasks like finding relevant, interesting and digestible literature, discussing the topics to be covered

and how to combine them in the report, writing draft papers **on** various chapters of the report in progress

and finally, performing calculati**on**s underpinning the implicati**on**s of the theory in c**on**crete examples.

Ample support is given:

- The students can make use of their experiences from courses in Linear Algebra and in

Algebra from previous semesters.

- Students are supposed to follow a course **on** Probability Theory that is held in the first m**on**ths of

the semester as well as

- a course **on** Coding and Informati**on** Theory given in parallel with the project; many of the noti**on**s

and results in this course use foundati**on**s from Linear Algebra, Algebra and Probability Theory.

- Regular c**on**sultati**on** and support from the group’s supervisor, who gives feedback **on** the work

already d**on**e; at times, she or he comes up with suggesti**on**s for directi**on**s of further work.

We expect project reports to include topics from the following areas:

- Entropy

- The Noiseless Coding Theorem

- The **Noisy** Coding Theorem and its inverses

- C**on**crete c**on**structi**on**s of error-correcting codes

- Decoding of error-correcting codes

Prerequisites: Linear Algebra and Algebra, Probability Theory, Coding and Informati**on** Theory (the latter

two are developed in parallel with the project)

Credits: 17 ETCS

Exam:

Individual oral exam (combined with exam in the course “Coding and Informati**on** Theory)

Have a look at a recent project report – the result of

four m**on**ths’ work of a group of 2nd year students

(unfortunately in Danish)