In the winter semester 2022/23 this lecture will be organized via Moodle. Registration is open now.
Channel Coding
Announcements
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
- 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 Thursday 10am-12pm in room 45 / H 45.2 |
Contact
Lecturer:
Prof. Dr.-Ing. Martin Bossert
Supervisor:
M.Sc. Cornelia Ott
Language
English
Requirements
Bachelor
Exams
Oral exam
Further Information
Hours per Week: 3V + 2Ü + 1P
8 ECTS Credits
LSF - ENGJ 70426