Originally posted by AK-47
What you say is only correct if you transform digital audio to analog, and then back again to digital. Every time you go through this process quality will be lost. It is, however, very possible to transform a compressed digital audio file into another form of a compressed digital audio file without losing any quality, what so ever, as long as the software is specific enough.
As long as the codec is the same, and you are only changing the wrapper (say, from a QuickTime wrapper over MP4 to an AVI wrapper over MP4), this is true. But that's not going through a decode/code cycle, it is just repackaging the bits.
I am not sure what you mean by transforming the digital audio to analog. While a true D/A + A/D conversion cycle would obviously cause signal degradation (that is patently obvious, right?), I don't think anyone here is suggesting such. Going from MP3 -> WAV (PCM encoding, which is not analog) -> MP3 is known to cause signal degradation.
You can see this visually as well. Take a JPEG image, convert it to TIFF. Convert back to JPEG (same quality setting). Do a file diff: are the original and recoded JPEG files bit-for-bit identical? No, they are not. Some information has been lost (by definition, if the round-tripped file is not bit-identical with the original in the same compression format). Look at them: do they look pretty similar? Of course they do. Repeat the process ten times, however, and you'll likely start noticing differences. Repeat it a hundred times and you'll definitely see differences (I'm not sure if OS X has the JPG-tiff command-line conversion tools or not, but you should be able to download them and build them for OS X fairly quickly, or just go to a Linux box ... writing a script to do 100 round-trip conversions would be an extremely simple matter).
Understand two terms:
Lossless: a decoding/encoding round trip of encoded data will not result in loss of data. Encoding of unencoded data may result in a loss of data due to the format's limitations; re-encodings are guaranteed to retain all data. This is the type of encoding most commonly desired for editing applications.
Lossy: a decoding/encoding round trip of encoded data will result in loss of some data. Editing applications generally avoid such formats as each edit/save cycle will lose more data.
JPEG is lossy. It loses information on compression, and it loses information on a round-trip JPEG-to-JPEG recompression. MP3 is very similar in its lossy-ness.
PCM is not lossy. Going from non-PCM to PCM will lose information that the format can not handle, but a round-trip PCM-to-PCM recompression does not lose additional information.
Going back to earlier, someone was comparing GIF to MP3, which is a very bad comparison as, again, by definition, GIF is not lossy. Yes, going from a 32-bit TIFF to 8-bit-palletted GIF is obviously going to lose data (see the definitions above). But GIF-to-GIF recompression will not lose any additional information.
Basically, if you could take an existing MP3 file, convert it to any other encoding (ie, not the MP3 codec, not just change the wrapper) then re-encode it as MP3, and end up with a bit-for-bit identical file as that which with you started, then MP3 would not be a lossy format. It would be lossless compression. That, my friend, would be a really neat trick, and would be a tremendous surprise to the MPE Group that developed the MP3 standard.