Topics in Error Correcting Codes

Class Number: 20214921
Schedule: Thu . l6:00-18:00
Office Hours: Sun 14:00-16:00
Build 37 Office 303
Submission deadline: 01.08.2023

Outline

The study of Error Correcting Codes(ECC) revolves around the question of how one party can reliably transmit a message to another party when there is noise in the channel. Error correcting codes add some redundant bits, which allow correct decoding even in the case of corruptions caused by transfer over the channel. Coding theory originated with the 1948 publication of the paper “A mathematical theory of communication” by Claude Shannon. For the past half-century, coding theory has grown into a discipline intersecting mathematics and engineering with applications to almost every area of communication such as satellite and cellular telephone transmission, compact disc recording, and data storage.

This project aims to give the first experience with research in the area. The students will learn the independent reading of academic literature. The students will be given a subject in Error Correcting Codes and papers, and the goal will be to implement code or protocol and experiment with it. The best students can continue this project to comprehensive academic research.

General Information

There will be one-two lectures where the students will be introduced to the area, and will be told about the topics they can choose. Within four weeks after the beginning of the semester, the students are supposed to choose a paper, and to inform the teacher of their choice. The work can be done in pairs or triples. Part of project is learning working in the group. All students of the group must know what is going on in the project.
From that point on, every month each team should contact the teacher and set an appointment to evaluate the team's progress. These meetings will also be used for consulting the teacher concerning the problems that arose during the research. At the last meeting, the students will present their final project. This last meeting should occur before the end of the examination period of the autumn semester.
The grade will be composed of 70% evaluation of the final project and 30% evaluation of the group's progress throughout the semester.
All the correspondence between the students and the teacher should be conducted through email; phone calls should be used only for very urgent affairs or if the teacher failed to answer a student's email within a period of one week (hopefully, this won't happen).
Slides of the first lecture Slides

Report Guidelines

Projects reports should be written in English. The report should include names and i.d. numbers. The first part of the report should include problem definition, goals and solution to the problem. If applicable, please explain what are other possible solutions to this problem and compare them.
The second part should include experiments. I encourage you to run experiments in the range of parameters without promise that algorithms will work.
The last part of the report should include conclusions and ideas for improvement.  

Usefull links

Projects

In all of the projects bellow implement an algorithm. Think of experiments you can make and run them. Think on the future directions for research. Before implementing amost all projects it is highly recomended to make sure that you know what is finite fields(at least of prime order). You can look on "Finite fields" and "Modular arithmetic" sections in wikipedia.