PAM nonlinear amplitude compression in lower eyes
I needed some help to understand why at Rx, we observe different effective SNRs in individual eyes for higher level PAM signalling.


The eye shown isn't typical. It's an exaggerated example to make the point that one of the distortions possible in a PAM signal is unequal eye openings. This could result in the upper eye being smaller, the middle eye being smaller, or the lower eye being smaller. The example from the app note just happens to show the third of these possibilities.


  How valid is it to tell that we have lesser SNR for lower transitions.


In the example, the effective SNR is lower for the lower eye. To decode a PAM signal, you essentially use 3 comparators, one for each eye (possibly there are other schemes, but they won't avoid the essential problem). The low comparator needs to reliably determine whether some of the symbols are either 0's or other values (1's, 2's, and 3's). It's decision threshold will be placed in the middle of the lower eye.

Therefore, if the system noise causes a voltage error greater than half the amplitude of the lower eye, this comparator can produce an erroneous result. 

So, the effective SNR for this comparator is the lower eye amplitude divided by the system noise. Since the lower eye amplitude is smaller than the other eyes' amplitudes, the effective SNR is lower for this eye than for the others.