Difference between revisions of "Channel Coding"
From LNTwww
| (31 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| + | ===Brief summary=== | ||
| − | Channel | + | {{BlueBox|TEXT=»'''Channel Coding'''« $($or »Error-Control Coding«$)$ includes both, »Error Detection« as well as »Forward Error Correction« |
| − | + | *which first enables digital signal transmission when the channel is bad $($small SNR$)$ | |
| − | * | ||
| + | *and leads to very small error rates when the channel is good enough $($large SNR$)$. | ||
| − | |||
| + | Here are some keywords from the book content: | ||
| + | |||
| + | # Binary linear block codes: Generator matrix, parity-heck matrix and decoding. Examples: Single parity-check codes, repetition codes, Hamming codes. | ||
| + | # Error probability bounds: Minimum distance, Union bound, Shannon bound. Channel coding theorem and channel capacity: error rate vs. code rate. | ||
| + | # Reed-Solomon codes: Algebra fundamentals, Extension fields, code parameters, encoding– and decoding principle, Singleton bound, applications. | ||
| + | # Convolutional codes: Algebraic and polynomial description, state and trellis diagram, decoding using Viterbi and BCJR algorithm. | ||
| + | # Iterative decoding methods: Soft-in soft-out decoders, product codes, turbo codes and low-density parity-check $($LDPC$)$ codes. | ||
| − | |||
| − | + | <u>Notes:</u> | |
| + | |||
| + | *Knowledge of »[[Theory_of_Stochastic_Signals]]« and the »[[Information theory]]« is helpful, but not essential for understanding channel coding. | ||
| + | |||
| + | *Their mathematics is fundamentally different from that in other disciplines. However, analogies can often be seen, e.g., to [[Signal_Representation/The_Convolution_Theorem_and_Operation|»conventional convolution«]]. | ||
| + | |||
| + | * An encoding type with a different goal is the [[Information_Theory/General_Description|»Source coding«]] $($"Data compression"$)$. Here, redundancy is not added, but reduced. | ||
| + | |||
| + | * Another type of coding is [[Digital_Signal_Transmission/Basics_of_Coded_Transmission#Source_coding_.E2.80.93_Channel_coding_.E2.80.93_Line_coding|»Line Coding«]] with the aim, to adapt the transmitted signal spectrally to the transmission channel in the best possible way. | ||
| + | |||
| + | |||
| + | ⇒ Here first a »'''contents overview'''« based on the »'''four main chapters'''« with a total of »'''22 individual chapters'''« and »'''175 sections'''«.}} | ||
| + | |||
===Contents=== | ===Contents=== | ||
| Line 30: | Line 48: | ||
*[[/Reed-Solomon Decoding for the Erasure Channel/]] | *[[/Reed-Solomon Decoding for the Erasure Channel/]] | ||
*[[/Error Correction According to Reed-Solomon Coding/]] | *[[/Error Correction According to Reed-Solomon Coding/]] | ||
| − | *[[/Error Probability and Areas | + | *[[/Error Probability and Application Areas/]] |
}} | }} | ||
{{Collapse3 | header=Convolutional Codes and Their Decoding | {{Collapse3 | header=Convolutional Codes and Their Decoding | ||
| Line 38: | Line 56: | ||
*[[/Code Description with State and Trellis Diagram/]] | *[[/Code Description with State and Trellis Diagram/]] | ||
*[[/Decoding of Convolutional Codes/]] | *[[/Decoding of Convolutional Codes/]] | ||
| − | *[[/Distance Characteristics and Error Probability | + | *[[/Distance Characteristics and Error Probability Bounds/]] |
}} | }} | ||
{{Collapse4 | header=Iterative Decoding Methods | {{Collapse4 | header=Iterative Decoding Methods | ||
| Line 48: | Line 66: | ||
}} | }} | ||
{{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:Channel_Coding:_Exercises $\text{Exercises}$] | |
| − | |||
| − | |||
| − | |||
| − | |||
| + | $(2)$ [[LNTwww:Learning_Videos_to_"Channel_Coding"|$\text{Learning videos}$]] | ||
| − | $\text{ | + | $(3)$ [[LNTwww:Applets_to_"Channel_Coding"|$\text{Applets}$]] }} |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| + | ===Further links=== | ||
| + | {{BlaueBox|TEXT= | ||
| + | $(4)$ [[LNTwww:Bibliography_to_"Channel_Coding"|$\text{Bibliography}$]] | ||
| − | [[LNTwww: | + | $(5)$ [[LNTwww:Imprint_for_the_book_"Channel_Coding"|$\text{Impressum}$]]}} |
| + | <br><br> | ||
{{Display}} | {{Display}} | ||
Latest revision as of 18:17, 26 March 2023
Brief summary
»Channel Coding« $($or »Error-Control Coding«$)$ includes both, »Error Detection« as well as »Forward Error Correction«
- which first enables digital signal transmission when the channel is bad $($small SNR$)$
- and leads to very small error rates when the channel is good enough $($large SNR$)$.
Here are some keywords from the book content:
- Binary linear block codes: Generator matrix, parity-heck matrix and decoding. Examples: Single parity-check codes, repetition codes, Hamming codes.
- Error probability bounds: Minimum distance, Union bound, Shannon bound. Channel coding theorem and channel capacity: error rate vs. code rate.
- Reed-Solomon codes: Algebra fundamentals, Extension fields, code parameters, encoding– and decoding principle, Singleton bound, applications.
- Convolutional codes: Algebraic and polynomial description, state and trellis diagram, decoding using Viterbi and BCJR algorithm.
- Iterative decoding methods: Soft-in soft-out decoders, product codes, turbo codes and low-density parity-check $($LDPC$)$ codes.
Notes:
- Knowledge of »Theory of Stochastic Signals« and the »Information theory« is helpful, but not essential for understanding channel coding.
- Their mathematics is fundamentally different from that in other disciplines. However, analogies can often be seen, e.g., to »conventional convolution«.
- An encoding type with a different goal is the »Source coding« $($"Data compression"$)$. Here, redundancy is not added, but reduced.
- Another type of coding is »Line Coding« with the aim, to adapt the transmitted signal spectrally to the transmission channel in the best possible way.
⇒ Here first a »contents overview« based on the »four main chapters« with a total of »22 individual chapters« and »175 sections«.
Contents
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
