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:

• $\text{Exercises}$

• $\text{Learning videos}$

• $\text{Applets}$

$\text{Further links:}$

$(1)$    $\text{Bibliography for the book}$

$(2)$    $\text{General notes about the book}$   (authors,  other participants,  materials as a starting point for the book,  list of sources)

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