ong>Projectong>: ong>Communicationong> on Noisy Channels
Methods for efficient coding and decoding are important in many
areas; just to mention deep space communication and reading from
defect CD-media. In this project, methods from several mathematical
areas like linear algebra, algebra and probability theory play together
as foundations for information theory and the theory of errorcorrecting
codes. The results aimed for are definitely non-trivial; they
can often be obtained as applications of very concrete mathematical
methods. For example, students will perform calculations on matrices
over finite fields; they have to use probabilistic methods dealing with
concrete information channels and codes.
ong>Projectong>s should cover material from both coding theory and information theory and they should seek
connections between both areas. To begin with, student groups investigate the foundations 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 calculations underpinning the implications of the theory in concrete 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 months of
the semester as well as
- a course on Coding and Information Theory given in parallel with the project; many of the notions
and results in this course use foundations from Linear Algebra, Algebra and Probability Theory.
- Regular consultation and support from the group’s supervisor, who gives feedback on the work
already done; at times, she or he comes up with suggestions for directions of further work.
We expect project reports to include topics from the following areas:
- The Noiseless Coding Theorem
- The Noisy Coding Theorem and its inverses
- Concrete constructions of error-correcting codes
- Decoding of error-correcting codes
Prerequisites: Linear Algebra and Algebra, Probability Theory, Coding and Information Theory (the latter
two are developed in parallel with the project)
Credits: 17 ETCS
Individual oral exam (combined with exam in the course “Coding and Information Theory)
Have a look at a recent project report – the result of
four months’ work of a group of 2nd year students
(unfortunately in Danish)