Channel Coding

Announcements

In the winter semester 2022/23 this lecture will be organized via Moodle. Registration is open now.

Linear block-codes

  • Generator and parity-check matrix
  • Cosets
  • Principles of decoding
  • Hamming codes
  • Bounds for code parameters (Hamming-, Singleton-, Gilbert-Varshamov-Bounds)
  • Trellis representation of block-codes
  • Plotkin construction, Reed-Muller (RM) codes (relationship to binary PN- and Walsh-Hadamard sequences)
  • APP and ML decoding (sequence and symbol based)

Algebraic coding

  • Prime fields, primitive elements, component- and exponent representation
  • Reed-Solomon (RS) codes as cyclic codes with generator- and check-polynomials
  • Algebraic error and erasure correction with the Euclidean algorithm
  • BCH codes (as subfield subcodes of RS codes)
  • The perfect Golay-code as non-primitive BCH-code
  • Decoding of algebraic codes (key equation, Euclidean- and Berlekamp-Massey algorithm)

Convolutional codes

  • Algebraic properties
  • State Diagram
  • Trellis representation
  • Error correction capabilities of convolutional codes
  • Viterbi- and BCJR algorithm (flow in graphs)

Further coding and decoding techniques

  • LDPC codes
  • Permutations-, Majority- and Information-Set decoding
  • Dorsch algorithm (ordered statistics decoding)
  • Parallel (Turbo)- and serial concatenated codes and their iterative decoding

Introduction to generalized code concatenation and coded modulation

Introductory Lecture

Lab 1 ( Unique Decoding of Reed–Solomon Codes with the Extended Euclidean Algorithm  | Templates )

Lab 2 ( Decoding of Convolutional Codes using the Viterbi Algorithm | Template )

Relevant chapters


Handout 1 (relevant topics)

Handout 2 (further topics)

  • Main book of the course (German/English)
    • Bossert M., Kanalcodierung, 3. Auflage, Oldenbourg, 2013
    • Bossert M., Channel Coding for Telecommunications, John Wiley & Sons, 1999
    • Johannesson, Zigangirov: Fundamentals of Convolutional Coding , IEEE Press
    • Lin, Costello: Error Control Coding, 2nd Edition, Prentice Hall, 2004
  • Further reading Coding Theory
    • Blahut R. E., Algebraic Codes for Data Transmission, Cambridge University Press, 2003
    • Roth R., Introduction to Coding Theory, Cambridge University Press, 2006
    • Justesen J. and Hoeholdt, T., A Course In Error Correcting Codes, EMS Publishing House, 2004
    • MacWilliams F. J. and Sloane N. J. A., The Theory of Error-Correcting Codes, Elsevier, 1977
  • Further reading Finite Fields/Algebra
    • McEliece R. J., Finite Fields for Computer Scientists and Engineers, Kluwer, 1987
    • Lidl R. and Niederreiter H., Introduction to Finite Fields and their Applications, Cambridge, 2002
    • Menezes A. and Blake I. F., Applications of Finite Fields, Kluwer, 1993
    • Lipson J. D., Elements of Algebra and Algebraic Computing, Addison-Wesley, 1981
  • Further reading Stochastics and Probability
    • Gubner J. A., Probability and Random Processes for Electrical and Computer Engineers, Cambridge, 2006

Additionally, the "Semesterapparat" to this Lecture may be of interest.

Winter Term 2022/23

Lecture

Exercise

Thursday 1pm - 4pm in room 45 / H 45.1

Monday 10am-12pm in room 45 / H 45.2

 
Language

English

Requirements

Bachelor

Exams

Oral exam