Application of General MAP Detection Theory for PAM Signals to the Analysis of TDECQ and SSPRQ

Transmitter and dispersion eye closure quaternary (TDECQ) has been selected by the IEEE Ethernet Standard as a vital test to enable the 4-level pulse amplitude modulation (PAM4) format for 400 Gb/s operation over fiber optic cables and short stress pattern random quaternary (SSPRQ) is exclusively elected as the testing signal for TDECQ and some other important tests. The authors find that the SSPRQ is an un-equiprobable sequence whereas the other PAM4 test patterns, such as PRBS15Q and PRBS31Q (or in general, PRBSnQ) are equiprobable. This motivates us to use a general maximum a posteriori probability (MAP) detection theory to handle the situation. We show the penalty using the SSPRQ signal, compared with the PRBSnQ, is unfortunately 0.135 dB in energy per bit to noise power density ratio
$(\text{EbNo})$
, coming from both the average energy decrease due to the un-equiprobability and the deviation from MAP detection at the given SER. The TDECQ tester with SSPRQ will predict a different BER compared with that using a BER tester.