Difference between revisions of "Information Theory"
From LNTwww
| (87 intermediate revisions by 7 users not shown) | |||
| Line 1: | Line 1: | ||
| − | == | + | ===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.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=== | ||
| + | |||
| + | {{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__ | ||
Latest revision as of 18:50, 31 December 2023
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
