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I think there's more you could add to this FAQ. I have used two disc scratch removal products. One is a handheld repairer. You crank the handle, and a felt band rubs across the disc as it turns. The disc must be wetted first to reduce friction.
Another type is a Philips motorized repairer. It has 3 discs, from rough, to polishing, to cleaning. You use them in order.
I practice though, I just use the rough disc and it works with one 2minute session.
Another tidbit I could add. Why do they always say to clean discs from the center outwards? Well for CD's I can say for sure, it's how the error correction is layed out on the disc.
I can explain it very simply as follows: if you store data, add an extra digit which is 1 if there's an even number of 1's in the data. So 1111 adds 1, 1110 adds 0. Then if there's ever the wrong number of 1's, you know there's a problem. Great, this is called parity and detects an error. Now arrange the data in a two dimensional table. Add the parity for each row and column. Now, not only can you detect the error, but you can pinpoint the exact point at which it ocurred. To fix the error, just flip the bit.
Good data:
11 1
01 0
--
0 1
Bad bit:
01 1
01 0
--
0 1
You can see that row 1 and column 1 have the wrong parity, thus bit (1,1) should be flipped.
Yep, that's basically how error correction works. You can read more about Hamming codes. There are other codes and it's pretty cool how they work. The one on CD's is called Reed Solomon code. There are codes to detect insertions and deletions, bits flipping in just one direction, and other variations. Satellite transmissions and cell phones use other types. You can read about Turbo Codes which are close to theoretically ideal (best protection per extra data), but also fast to decode.
Anyhow, the error correcting codes are stored circumfrentially, so scratches from the hub radially only affect several bits, which is easily correctable. I believe up to 1mm scratch is correctable, I'd have to look it up.
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