Information Theory: Difference between revisions
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{{BlueBox|TEXT=From the earliest beginnings of message transmission as an engineering discipline, it has been the endeavour of many engineers and mathematicians to find a quantitative measure for the | {{BlueBox|TEXT=From the earliest beginnings of message transmission as an engineering discipline, it has been the endeavour of many engineers and mathematicians to find a quantitative measure for the | ||
*contained $\rm information$ $($quite generally: | *contained $\rm information$ $($quite generally: »the knowledge about something«$)$ | ||
*in a $\rm message$ $($here we mean | *in a $\rm message$ $($here we mean »a collection of symbols and/or states»$)$. | ||
The $($abstract$)$ information is communicated by the $($concrete$)$ message and can be conceived as the interpretation of a message. | The $($abstract$)$ information is communicated by the $($concrete$)$ message and can be conceived as the interpretation of a message. | ||
[https://en.wikipedia.org/wiki/Claude_Shannon '''Claude Elwood Shannon'''] succeeded in 1948, in establishing a consistent theory about the information content of messages, which was revolutionary in its time and created a new, still highly topical field of science: »'''Shannon's information theory«''' named after him. | [https://en.wikipedia.org/wiki/Claude_Shannon '''Claude Elwood Shannon'''] succeeded in 1948, in establishing a consistent theory about the information content of messages, which was revolutionary in its time and created a new, still highly topical field of science: »'''Shannon's information theory«''' named after him. | ||
This is what the fourth book in the $\rm | This is what the fourth book in the $\rm LNTwww$ series deals with, in particular: | ||
# Entropy of discrete-value sources with and | # Entropy of discrete-value sources with and without memory, as well as natural message sources: Definition, meaning and computational possibilities. | ||
# Source coding and data compression, especially the | # Source coding and data compression, especially the »Lempel–Ziv–Welch method« and »Huffman's entropy encoding«. | ||
# Various entropies of two-dimensional discrete-value random quantities. Mutual information and channel capacity. Application to digital signal transmission. | # Various entropies of two-dimensional discrete-value random quantities. Mutual information and channel capacity. Application to digital signal transmission. | ||
# Discrete-value information theory. Differential entropy. AWGN channel capacity with continuous-valued as well as discrete-valued input. | # Discrete-value information theory. Differential entropy. AWGN channel capacity with continuous-valued as well as discrete-valued input. | ||
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In addition to these theory pages, we also offer exercises and multimedia modules on this topic, which could help to clarify the teaching material: | In addition to these theory pages, we also offer exercises and multimedia modules on this topic, which could help to clarify the teaching material: | ||
$(1)$ [https://en.lntwww.de/Category:Information_Theory:_Exercises $\text{Exercises}$] | $(1)$ [https://en.lntwww.lnt.ei.tum.de/Category:Information_Theory:_Exercises $\text{Exercises}$] | ||
$(2)$ [[LNTwww:Learning_videos_to_"Information_Theory"|$\text{Learning videos}$]] | $(2)$ [[LNTwww:Learning_videos_to_"Information_Theory"|$\text{Learning videos}$]] | ||
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[[de:Informationstheorie]] | |||
Latest revision as of 14:27, 16 March 2026
Brief summary
From the earliest beginnings of message transmission as an engineering discipline, it has been the endeavour of many engineers and mathematicians to find a quantitative measure for the
- contained $\rm information$ $($quite generally: »the knowledge about something«$)$
- in a $\rm message$ $($here we mean »a collection of symbols and/or states»$)$.
The $($abstract$)$ information is communicated by the $($concrete$)$ message and can be conceived as the interpretation of a message.
Claude Elwood Shannon succeeded in 1948, in establishing a consistent theory about the information content of messages, which was revolutionary in its time and created a new, still highly topical field of science: »Shannon's information theory« named after him.
This is what the fourth book in the $\rm LNTwww$ series deals with, in particular:
- Entropy of discrete-value sources with and without memory, as well as natural message sources: Definition, meaning and computational possibilities.
- Source coding and data compression, especially the »Lempel–Ziv–Welch method« and »Huffman's entropy encoding«.
- Various entropies of two-dimensional discrete-value random quantities. Mutual information and channel capacity. Application to digital signal transmission.
- Discrete-value information theory. Differential entropy. AWGN channel capacity with continuous-valued as well as discrete-valued input.
⇒ First a »content overview« on the basis of the »four main chapters« with a total of »13 individual chapters« and »106 sections«:
Content
Exercises and multimedia
In addition to these theory pages, we also offer exercises and multimedia modules on this topic, which could help to clarify the teaching material:
$(1)$ $\text{Exercises}$
$(2)$ $\text{Learning videos}$
$(3)$ $\text{Applets}$
Further links
