Channel Coding

Channel coding  (also known as error-control coding)  includes both

• Error detection methods,

• and forward error correction  $\rm (FEC)$,  which often make digital signal transmission possible with a bad channel  $($low SNR$)$  and lead to very low error rates with a sufficiently good channel  $($high SNR$)$.

Linear block codes, Reed-Solomon codes and convolutional and turbo codes as well as their  $($possibly iterative$)$  decoding are described.

The subject matter corresponds to a  $\text{lecture with three semester hours per week (sh/w) and two additional  sh/w  exercises}$.

Here is a table of contents based on the  $\text{four main chapters}$  with a total of  $\text{22 individual chapters}$.

Contents

Binary Block Codes for Channel Coding

• Objective of Channel Coding
• Channel Models and Decision Structures
• Examples of Binary Block Codes
• General Description of Linear Block Codes
• Decoding of Linear Block Codes
• Limits for Block Error Probability
• Information Theoretical Limits of Channel Coding

Reed–Solomon–Codes and Their Decoding

• Some Basics of Algebra
• Extension Field
• Definition and Properties of Reed-Solomon Codes
• Reed-Solomon Decoding for the Erasure Channel
• Error Correction According to Reed-Solomon Coding
• Error Probability and Application Areas

Convolutional Codes and Their Decoding

• Basics of Convolutional Coding
• Algebraic and Polynomial Description
• Code Description with State and Trellis Diagram
• Decoding of Convolutional Codes
• Distance Characteristics and Error Probability Bounds

Iterative Decoding Methods

• Soft-in Soft-Out Decoder
• The Basics of Product Codes
• The Basics of Turbo Codes
• The Basics of Low-Density Parity Check Codes

In addition to these theory pages, we also offer tasks and multimedia modules that could help to clarify the topic:

• $\text{Exercises}$

• $\text{Learning videos}$

• $\text{Applets}$

$\text{Recommended Literature:}$

• Böcherer, G.: Channel Coding. Vorlesungsmanuskript. Lehrstuhl Für Nachrichtentechnkik, TU München, 2015
• Bossert, M.: Channel Coding for Telecommunications. Chichester: Wiley, 2000. ISBN 978-0-471-98277-7
• Bossert, M.: Kanalcodierung. Stuttgart: Vieweg+Teubner Verlag, 2014. ISBN 978-3-322-90917-6
• Cover, T. M.; Thomas, J. A.: Elements of Information Theory. 2. Aufl. Hoboken, N.J: Wiley-Interscience, 2006. ISBN 978-0-47124-195-9
• Friedrichs, B.: Kanalcodierung. Grundlagen und Anwendungen in modernen Kommunikationssystemen. Berlin u.a.: Springer, 1996. ISBN 3-540-58232-0
• Gallager, R. G.: Information Theory and Reliable Communication. New York NY u.a.: Wiley, 1968. ISBN 0-471-29048-3
• Hindelang, T.: Source-Controlled Channel Decoding and Decoding for Mobile Communications. Dissertation. Lehrstuhl für Nachrichtentechnik.
  München: VDI Fortschritt-Berichte, Reihe 10, Nr. 695, 2002
• Huber, J.: Codierung für gedächtnisbehaftete Kanäle. Dissertation – Universität der Bundeswehr München, 1982
• Johannesson, R.; Zigangirov, K. S.: Fundamentals of Convolutional Coding. New York: IEEE Press, 1999. ISBN 978-0-470-27683-9
• Klimant, H.; Piotraschke, R.; Schönfeld, D.: Informations- und Kodierungstheorie. 2. Aufl. Wiesbaden (u.a.): Vieweg+Teubner Verlag, 2003. ISBN 978-3-51923-003-8
• Kötter, R.; Mayer, T.; Tüchler, M.; Schreckenbach, F.; Brauchle, J.: Channel Coding. Vorlesungsmanuskript. Lehrstuhl für Nachrichtentechnik, TU München, 2008
• Lidl, R.; Niederreiter, H.: Finite Fields. Encyclopedia of Mathematics and its Application. 2nd ed. Cambridge: University Press, 1997 NEU
• Liva, G.: Channel Coding. Vorlesungsmanuskript. Lehrstuhl Für Nachrichtentechnik, TU München und DLR Oberpfaffenhofen, 2010
• Ryan, W.; Lin, S.: Channel Codes. Classical and modern. Cambridge: Cambridge University Press, 2009. ISBN 978-0-52184-868-8
• Schönfeld, D.; Klimant, H.; Piotraschke, R.: Informations- und Kodierungstheorie. 4. Aufl. Wiesbaden: Vieweg+Teubner Verlag, 2012. ISBN 978-3-83480-647-5
• Schneider-Obermann, H.; Mildenberger, O.: Kanalcodierung. Theorie und Praxis fehlerkorrigierender Codes. Wiesbaden: Vieweg+Teubner Verlag, 1998.
  ISBN 978-3-528-03101-5
• Schulz, R.-H.: Codierungstheorie. Eine Einführung. 2. Aufl. Wiesbaden: Vieweg+Teubner Verlag, 2003. ISBN 978-3-322-80328-3
• Shannon, C. E.; Weaver, W.: The Mathematical Theory of Communication. Urbana: Univ. of Illinois Press, 1998. ISBN 978-0-25272-548-7
• Tröndle, K.: Codier-und Decodiermethoden zur Fehlerkorrektur. Habilitationsschrift. München: TU München, 1974
• Wachter-Zeh, A.: Channel Coding. Vorlesungsmanuskript. Professur für Coding for Communications and Data Storage, TU München, 2017

Neue Einträge:

• Roth, R.M.: Introduction to Coding Theory. Cambridge Univ. Press, 2006

• Justesen, J.; Høholdt; T.: A Course in Error-Correcting Codes. European Mathematical Society, Jan. 2004. [2]

• Blahut, R.E.: Algebraic Codes for Data Transmission, 1st edition. Cambridge Univ. Press, 2003

• Johannesson, R.;Zigangirov, K.S. Fundamentals of Convolutional Coding, Chichester: Wiley, 1999

• Lint, J.H. van. Introduction to Coding Theory, 3rd edition. Springer, 1998

Main literature: • R. M. Roth, Introduction to Coding Theory, Cambridge Univ. Press, 2006 [1]

• M. Bossert, Kanalcodierung, 3rd ed. Oldenburg, 2013 [3]. (M. Bossert, Channel Coding for Telecommunications, Wiley, 1999 [4]) Further literature: • R. E. Blahut, Algebraic Codes for Data Transmission, 1st ed. Cambridge Univ. Press, 2003 [5] • R. Johannesson and K. S. Zigangirov, Fundamentals of Convolutional Coding, Wiley, 1999 [6]

References for

$\text{Notes on the authors and the materials used as a basis for the preparation of the book}$.