Information Theory, Shannon second theorem, bridge between channel coding and Coding Theory

 

I started to learn the encoding theory, but the more I learned it, the more I went into the fire. Why does coding solve the channel error? Redundant, yes, but there is always a lack of quantitative analysis and strict proof, getting dizzy and reluctant to look at the logic of different channel coding.

Then I started to learn from information theory and gradually gained a quantitative understanding of the simple channel (DMC). Then I finally clarified the clues more or less.

Information Theory-> Shannon second theorem-> maximum likelihood decoding-> Hamming minimum code margin-> channel coding theory based on linear algebra, finite fields, and elementary number theory.

However, none of the above clues are equivalent. For example, the maximum likelihood decoding and the minimum link between Chinese characters are equivalent in the case of DMC. Otherwise, they are not equivalent.

And...

In short, why do we limit the study of the encoding theory to ignore the channel model? Is coding completely unrelated to specific channel features?

What's more, what is the current complex channel model? Why didn't I see relevant monographs and documents?

In actual communication applications, how do we model, evaluate, and analyze the channel model?

How can we demonstrate that encoding has such powerful capabilities on any channel?

How do we simulate a channel?

For a lot of reasons, please answer them slowly...