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There probably are CRCs run during the decoding process, but CRCs only tell you "yes this is correct" or "no, something went wrong."

There are additional protection schemes that can detect and correct bit errors. Those are probably also run during the decoding process. The problem is that you can only detect so many wrong bits in a given word, and beyond that no correction can be made. That is probably why the damaged disc half works.

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Yes it depends on the way you handle the response of the CRC, you could say "give me the data I don't care" or "please try to read it again it's wrong".

In my opinion that is just the proof that it's not as simple as "it just works or not" but rather : depending on muptiple factors such as error correction and the way your algorithm works on the receiver it may "half work" no matter what kind of cable you plug in.

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