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Valid for year : 2011
 
TSDT16 Error Correcting Codes, 6 ECTS credits.
/Felrättande koder/

For:   CS   D   I   Ii   IT   MMAT   SY   Y  

 

Prel. scheduled hours: 48
Rec. self-study hours: 112

  Area of Education: Technology

Main field of studies: Electrical Engineering

  Advancement level (G1, G2, A): A

Aim:
This course is intended to provide some basic knowledge in the field of algebraic coding theory. After completed course the student should be able to
  • define correctly and explain about the following notions: Hamming distance, linear error correcting code, cyclic code, cyclotomic coset, finite field.
  • define correctly and state the fundamental parameters for the following classes of codes: Hamming, Reed-Solomon, Golay, BCH, LDPC.
  • carry out decoding of an RS code or a BCH code according to Petersons, Berlekamps and Euclides algorithms.
  • fairly well handle necessary mathematical tools: groups, rings, fields, linear spaces.
  • draw encoding and decoding circuits for cyclic codes.
  • apply the Viterbi decoding algorithm.


Prerequisites: (valid for students admitted to programmes within which the course is offered)
A course in Linear algebra. Basic courses in Discrete mathematics, Abstract algebra and Telecommunications are desired but not required. All theory needed will be derived within the course.

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
Organisation:
Teaching is organized in lectures and exercises.

Course contents:
The lectures and the exercises treat parts of the following areas within algebraic coding theory.
  • Algebraic structures: groups, rings, finite fields.
  • General notions: polynomials, linear codes, cyclic codes, Hamming distance, decoding region, cyclotomic cosets.
  • Bounds: Hamming, Singleton.
  • Particular error correcting code constructions: Hamming, Golay, Reed-Solomon, BCH, LDPC.
  • Encoding and decoding circuits for cyclic codes.
  • Decoding of block codes: basic equations, syndrome decoding, the Euclidean algorithm, Peterson's and Berlekamp's algorithms, "error-trapping" decoding.
  • Convolutional and "turbo" codes.
  • Decoding of convolutional codes: the Viterbi and BCJR algorithms.


Course literature:
Shu Lin and Daniel J. Costello, Jr., Error Control Coding, Pearson / Prentice Hall 2004, second edition, ISBN 0-13-017973-6 (0-13-042672-5)

Examination:
Written examination (oral in case of few attendants)
 6 ECTS
 


Course language is English.
Department offering the course: ISY.
Director of Studies: Lasse Alfredsson
Examiner: Danyo Danev
Link to the course homepage at the department


Course Syllabus in Swedish

Linköping Institute of Technology
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Contact: TFK , val@tfk.liu.se
Last updated: 02/06/2016