BER stands for Bit Error Rate. It is the main indicator of the quality of a link.
BER = (errors received) / (bit received)
Example: If the data rate is 1 Gbit/s, then it would mean 10exp9 bits are received in 1 second. If 0 errors are observed after 1second of measurement, then BER = 10exp-9. Instruments typically show both errors and BER.
What is acceptable BER value?
Most standards (e.g., Ethernet) ask for BER < 10exp-12. Some pretend better BER, typically < 10exp-15. Reference Clock Jitter and Supply noise are statistical; Pkpk values are extrapolated from Sigma.
Formulas typically assume p=1/(10exp-12) to be out. So, the pkpk jitter value is statistical and NOT absolute! Sooner or later they will exceed the pkpk values. Consequently, errors might appear.
BER measurement time:
Assume 1 Gbit/s of data rate. No. of bits transmitted in 1 second = 10exp-9. In 10 seconds, 10exp-10 bits will be transmitted. It takes almost two weeks to test 1 Gbit/s for 10exp-15.
Relationship between Eye and BER
The smaller the eye, the worse the BER, but consider BER = 10exp-12. 1 error every 1000 Billions bits! The eye may be very good! It will likely be the same as a 10exp-15 or better link. The oscilloscope does not tell the whole story.
Example: 10 Gbit/s
Bit is 100 ps wide. This rate needs pkpk TX Jitter in the order of 20 ps worst case. Do not expect anything to work if Refclk jitter is 50 ps. 100 MHz with 50 ps of Jitter looks very clean at first sight on a scope. Check the power supplies (discussed above).