M8170 Coding

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jan Paseka, CSc. (lecturer)
Guaranteed by
prof. RNDr. Jan Paseka, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Mathematical analysis I. and II., Linear algebra and geometry I. and II. , Fundamentals of mathematics, Algebra I, Probability and Statistics.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The basic goal of the course is the introduction of the student to establish the mathematical basics of coding theory. Some applications of coding theory are mentioned, specially in the area of data transmission. At the end of this course, students should be able to: understand rudiments of coding theory; explain basic notions and relations among them. The student will be able to use the acquired knowledge of coding techniques in solving specific problems from the area of data transmission.
Syllabus
  • Introduction. A very abstract summary. History. Outline of the course. Entropy. Uncertainty. Entropy and its properties. Information. Communication through channels. The discrete memoryless channel. Codes and decoding rules. The noisy coding theorem. Error-correcting codes. The coding problem - need for error correction. Linear codes. Binary Hamming codes. Cyclic codes. Reed--Muller codes. General sources. The entropy of a general source. Stationary sources. Markov sources. The structure of natural languages. English as a mathematical source. The entropy of English.
Literature
  • Roman, Steven, Coding and Information Theory, Graduate Texts in Mathematics, Springer Verlag, 1992
  • Hamming, R. W. Coding and information theory, Prentice-Hall, New-Jersey 1950
  • Welsh D., Codes and cryptography, Oxford, University Press, New York, 1988
  • Adámek, Jiří. Foundations of coding, John Wiley \& Sons, Inc. 1991
  • ADÁMEK, Jiří. Kódování. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1989, 191 s. URL info
Teaching methods
Lectures: theoretical explanation with practical examples Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks. Students will be asked to have an active participation at seminars or a written homework that will be lectured at some seminar. The theme will be chosen after the negotiation with the lecturer.
Assessment methods
Lecture with a seminar. Examination is oral with a written preparation. The success at the examination is based on providing an exposition with respect to a chosen chapter.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is taught: every week.
Teacher's information
http://www.math.muni.cz/~paseka
The course is also listed under the following terms Spring 2001, Spring 2003, Spring 2005, Spring 2007, Spring 2009, Spring 2011, Spring 2013, Spring 2015, Spring 2017, Spring 2019, Spring 2021, Spring 2023, Spring 2025.