SubjectsSubjects(version: 806)
Course, academic year 2017/2018
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Automata and Convolutional Codes - NMMB401
Czech title: Automaty a konvoluční kódy
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:3/1 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information: http://www.karlin.mff.cuni.cz/~holub/konvoluce.html
Guarantor: Mgr. et Mgr. Jan Žemlička, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinné
M Mgr. MSTR
M Mgr. MSTR > Povinně volitelné
Classification: Mathematics > Algebra
Incompatibility : NMIB401
Interchangeability : NMIB401
Annotation -
Last update: T_KA (14.05.2013)

Course is an introduction into convolutional codes. Description of encoders is facilitated by an overview of finite automata. The algebraic structure of convolutional codes is explored, as well as its performance and basic decoding methods.
Literature -
Last update: T_KA (14.05.2013)

Rolf Johannesson, Kamil Sh. Zigangirov, Fundamentals of Convolutional Coding, Wiley-IEEE Press, 1998

T. Richardson, R. Urbanke, Modern Coding Theory, Cambridge University Press 2008

Syllabus -
Last update: T_KA (14.05.2013)

1. Basic properties of finite automata

  • finite automata, regular expressions, Kleene's theorem

2. Convolutional codes and their algebraic structure

  • representation by transition diagram and trellis, properties of

generating matrices and their realization, minimal encoders

3. Performance

  • free distance of the code, error-probability bounds

4. Decoding

  • Viterbi algorithm, sequential decoding, iterative decoding.

 
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