Here is a useful chart from the paper:Since you have the AES paper Amir perhaps you could fill in the details.
Normally the PCM encoding is a rectangle of bits in one direction and sampling rate in the other. The thesis from Meridian is that such encoding is wasteful. That by examining the source content, we can allocate just the number of bits and spectrum to track the content as opposed to random noise. You see an example of that and where the 10:1 compression number came from.
We see that the spectrum doesn't go much past 48 Khz, and that the amplitude of the useful data is dropping exponentially (the graph is a log so exponents show up as lines). As the amplitude drops we can reduce the number of bits we use to allocate to the signal as its dynamic range requires. Close to 48 Khz for example the difference between the signal and its noise floor is less than 10 db so 3 bits or so would be sufficient to represent it. Allocating 24 bits would hence be wasteful.
Of course different tracks will have different noise floors and peaks and hence the reason they require encoding of the content.