Philip,
You stated that "Information is the basic material of reality, but the processing of information raises paradoxes...", but the paradoxes only arise, when an inappropriate conception of information is being employed.
Your statement that "because he produced some theory on the quantity of information in random variables" indicates that you have yet to comprehend the significance of his theory; he has proven that there is a finite, often small, amount of information, that can ever be measured, with certainty, from any set of physical measurements whatsoever. That means that any entity manifesting just one such bit of information, can never be measured in any manner, capable of producing two uncorrelated measurements, even when the measurements might otherwise have been independent, orthogonal variables.
This has direct relevance to the validity of Bell's theorem - it is only valid for entities that manifest more than one bit of information. In other words, classical, deterministic entities that manifest only one bit, will behave just like quantum entities. You do not have to understand Shannon's paper to prove that. You can simply run the short code (available on this website) that will produce such objects and perform a Bell test on them, right in front of your very eyes. You can do it on your own computer, in your own home, within an hour, then ponder why it works (and violates the 1987 Garg/Mermin claim that no classical system, can ever reproduce Bell's correlations, with a single detector efficiency above 83%) for as long as you like. And if you feel up to it, you can completely rewrite the code, to convince yourself that it really does work, as Colin Walker did (replied on Sep. 12, 2016)
Stefen,
"How can you know that what Shannon wrote (for example on page 44) isn't also merely meaningless noise?"
Because, I have personally designed and constructed real systems, that do exactly the types of things he is describing. So have legions of other communications engineers. Almost all the modern, wireless communications devices you use, are based on these concepts; so they are not just "idle talk", as quantum information theory is.
"(when one logically deciphers your lines of reasoning)" try logically deciphering the code noted above, after your own, inanimate, classical computer violates Bell's theorem right in front of you - no "quantum computer" required. Then, you too will know.
Rob McEachern