Information Theory: Difference between revisions
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===Brief summary=== | |||
{{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: »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. | |||
[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 $\rm LNTwww$ 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=== | |||
{{Collapsible-Kopf}} | {{Collapsible-Kopf}} | ||
{{Collapse1| header= | {{Collapse1| header=Entropy of Discrete Sources | ||
| submenu= | | submenu= | ||
*[[/ | *[[/Discrete Memoryless Sources/]] | ||
*[[/ | *[[/Discrete Sources with Memory/]] | ||
*[[/ | *[[/Natural Discrete Sources/]] | ||
}} | }} | ||
{{Collapse2 | header= | {{Collapse2 | header=Source Coding - Data Compression | ||
|submenu= | |submenu= | ||
*[[/ | *[[/General Description/]] | ||
*[[/ | *[[/Compression According to Lempel, Ziv and Welch/]] | ||
*[[/ | *[[/Entropy Coding According to Huffman/]] | ||
*[[/ | *[[/Further Source Coding Methods/]] | ||
}} | }} | ||
{{Collapse3 | header=Information | {{Collapse3 | header=Mutual Information Between Two Discrete Random Variables | ||
|submenu= | |submenu= | ||
*[[/ | *[[/Some Preliminary Remarks on Two-Dimensional Random Variables/]] | ||
*[[/ | *[[/Different Entropy Measures of Two-Dimensional Random Variables/]] | ||
*[[/ | *[[/Application to Digital Signal Transmission/]] | ||
}} | }} | ||
{{Collapse4 | header= | {{Collapse4 | header=Information Theory for Continuous Random Variables | ||
|submenu= | |submenu= | ||
*[[/ | *[[/Differential Entropy/]] | ||
*[[/ | *[[/AWGN Channel Capacity for Continuous-Valued Input/]] | ||
*[[/ | *[[/AWGN Channel Capacity for Discrete-Valued Input/]] | ||
}} | }} | ||
{{Collapsible-Fuß}} | {{Collapsible-Fuß}} | ||
===Exercises and multimedia=== | |||
{{BlaueBox|TEXT= | |||
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.lnt.ei.tum.de/Category:Information_Theory:_Exercises $\text{Exercises}$] | |||
$(2)$ [[LNTwww:Learning_videos_to_"Information_Theory"|$\text{Learning videos}$]] | |||
$(3)$ [[LNTwww:Applets_to_"Information_Theory"|$\text{Applets}$]] }} | |||
===Further links=== | |||
$\text{ | {{BlaueBox|TEXT= | ||
$(4)$ [[LNTwww:Bibliography_to_"Information_Theory"|$\text{Bibliography}$]] | |||
$(5)$ [[LNTwww:Imprint_for_the_book_"Information_Theory"|$\text{Impressum}$]]}} | |||
<br><br> | |||
__NOTOC__ | __NOTOC__ | ||
__NOEDITSECTION__ | __NOEDITSECTION__ | ||
[[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
