Information Theory

Since the early beginnings of communications as an engineering discipline, many engineers and mathematicians have sought to find a quantitative measure of

• the $\rm Information$  (in general: "the knowledge of something") contained in a  $\rm message$  (here we understand "a collection of symbols and/or states").

The (abstract) information is communicated by the (concrete) message and can be seen as an interpretation of a message.

Claude Elwood Shannon  succeeded in 1948 in establishing a consistent theory of the information content of messages, which was revolutionary in its time and created a new, still highly topical field of science:  the theory named after him  $\text{Shannon's Information Theory}$.

The course material corresponds to a  $\text{lecture with two semester hours per week (SWS) and one SWS exercise}$.

Here is a table of contents based on the  $\text{four main chapters}$  with a total of  $\text{13 individual chapters}$.

Contents

Entropy of Discrete Sources

• Discrete Memoryless Sources
• Discrete Sources with Memory
• Natural Discrete Sources

Source Coding - Data Compression

• General Description
• Compression According to Lempel, Ziv and Welch
• Entropy Coding According to Huffman
• Further Source Coding Methods

Mutual Information Between Two Discrete Random Variables

• Some Preliminary Remarks on Two-Dimensional Random Variables
• Different Entropy Measures of Two-Dimensional Random Variables
• Application to Digital Signal Transmission

Information Theory for Continuous Random Variables

• Differential Entropy
• AWGN Channel Capacity for Continuous Input
• AWGN Channel Capacity for Discrete Input

In addition to these theory pages, we also offer Exercises and multimedia modules that could help to clarify the teaching material:

• $\text{Exercises}$
• $\text{Learning videos}$
• $\text{redesigned applets}$, based on HTML5, also executable on smartphones
• $\text{former Applets}$, based on SWF, executable only under WINDOWS with Adobe Flash Player.

$\text{More links:}$

$(1)$    $\text{Recommended literature for the book}$

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