I have to disapoint you by saying that to me the purpose of this
discussion was two-fold.
No problem, I just wanted to be sure what we were talking about.
I completely agree on the information loss when truncation is happeing,
I just do not see how adding noise fixes that. I said that it
does not fix anything, simply changes one distortion for another which
is more pleasant to us, humans. This created a wave of discagreement
with comments that there is a fundamental theoretical need for that
noise.
I'm not sure I'm following you here. Obviously by truncating you're going to reduce the signal's quality, that can't be "fixed". But by using dithering, that quality reduction is much less perceptible to human ears, which is the only thing that matters as far as I can see, since the only purpose of audio is to be listened to by humans (OK, perhaps with a few extremely rare exceptions).
But for audio applications when each
sample is transmitted only once, I simply do not see how the quality
(or more information) is beeing transmitted.
Certainly by using dithering you're not transmitting more information. I guess whether the "quality" is better or not depends on your definition of quality, but I think that for any reasonable definition you would have to say that dithering does increase quality.
Say, for example, that you encrypt an audio file with a certain key, then you send it to a receiver who doesn't know the key. The audio file still has the same amount of information (since it can be recovered by using your key), but for the receiver its quality is nil, since playing it will only yield noise.
So, I can only see the trade-off of distortions which is perfectly valid, but has no
theoretical grounds, in my opinion.
Again, I have no idea of what you mean by theoretical grounds here.
The solution to the 16bit prolem (questions 1 and 2) is to use some
sort of basis-set, other whan the comb in the time-domain to provide
higher quality with the same data rate. This is known as mpeg and all other compression
methods.
As you might know, mp3 also has a psychoacoustic basis. In fact, you could say that the only reason why mp3 is capable of relying audio with higher quality than raw s16 at the same bitrate is because it is based on a much more elaborate psychoacoustic model.
An audio file with N 16 bit samples can represent exactly the same number of audio signals whether it's encoded using raw s16 or CBR mp3 (namely, 2^(16 * N) signals). However, they are not the same signals, and mp3 has been designed so that the signals that can be represented using it sound much closer to the original audio to human ears. So, mp3 has the same exact purpose as dithering: allowing better quality in the same number of bits.