This article is from the DVD Formats FAQ, by jtfrog@usa.net (Jim Taylor) with numerous contributions by others.
Most scratches will cause minor channel data errors that are easily
corrected. That is, data is stored on DVDs using powerful error correction
techniques that can recover from scratches as big as 6 millimeters with no
loss of data. A common misperception is that a scratch will be worse on a
DVD than on a CD because of higher storage density and because video is
heavily compressed. DVD data density (say that fast ten times!) is
physically four times that of CD-ROM, so it's true that a scratch will
affect more data. But DVD error correction is at least ten times better
than CD-ROM error correction and more than makes up for the density
increase. It's also important to realize that MPEG-2 and Dolby Digital
compression are partly based on removal or reduction of imperceptible
information, so decompression doesn't expand the data as much as might be
assumed. Major scratches may cause uncorrectable errors that will produce
an I/O error on a computer or show up as a momentary glitch in DVD-Video
picture. Paradoxically, sometimes the smallest scratches can cause the
worst errors (because of the particular orientation and refraction of the
scratch). There are many schemes for concealing errors in MPEG video, which
may be used in future players (see section D.12 of
<http://icib.igd.fhg.de/icib/it/iso/cd_13818-2/read1.html>).
See 1.39 for information on care and cleaning of DVDs.
The DVD computer advisory group specifically requested no mandatory caddies
or other protective carriers. Consider that laserdiscs, music CDs, and
CD-ROMs are likewise subject to scratches, but many video stores and
libraries rent them. Major chains such as Blockbuster and West Coast
Entertainment rent DVDs in many locations. So far most reports of rental
disc performance are positive. A nice list of DVD rental outlets is at
<http://home.earthlink.net/~tlfordham/rental.html>.
 
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