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Re: [802.3_50G] 答复: [802.3_50G] Relating DER, BER and Q in Draft 1.2

It is more complicated than this, and I think there are some errors in the chain below.   I’m sorry I can’t give you a good single reference to all this.  It is scattered in work from Pete Anslow, Jonathan King, Rich Mellitz, Adee Ran and others some of which may not be published.   I don’t think it has been fully analyzed for all the situations yet, and due to the error burst effects I’m not sure a completely rigorous analysis is possible.


DER0 is the probability of a PAM4 symbol error when all the previous symbols are correct.    If there is no correlation between errors (no error extension or error bursts) then without pre-coding the BER is 0.5*DER0 (assumes Gray coding where one symbol error only creates one bit error in the two bits that make up the symbol).   However with a DFE with no tap weight constraints a single initial symbol can create error bursts of average length 4 symbols (error extension factor 0.75) (but with burst lengths from one to infinite length).  Limiting tap weights can reduce this error burst effect and 120D is attempting to do this.    Adding pre-coding will cause there to be a single symbol error at the start of the burst and a single symbol error at the end of the burst if this is a single tap classic DFE.   This is an approximation for multi-tap DFE’s where the first tap is dominant, but is likely to fall apart if that is not the case.  


When discussing Q values it also gets more complicated.  For PAM4 in the vertical domain, noise can create errors on the middle two levels when the noise is both positive and negative.  (in comparison to NRZ where only noise of one sign can create an error.).    The result is that for a given Q (Signal to Noise ratio relative to the small eye) the PAM4 symbol error ratio will be 1.5*NRZ bit error ratio.   (I’m not sure whether COM takes this into account or not.).


When looking in the horizontal (jitter) direction to a first approximation I don’t think this factor of 1.5 exists, as the jitter will close the eye (closest to the sampling threshold) in a similar manner that it does for NRZ.   However there may be a second order effect that the deterministic pattern dependent jitter will tend to make only one sign of the uncorrelated jitter detrimental so there may be a correction to be made in the other direction.


From: Vinu Arumugham [mailto:00000960f69b1502-dmarc-request@xxxxxxxx]
Sent: Thursday, March 23, 2017 11:55 AM
To: STDS-802-3-50G@xxxxxxxxxxxxxxxxx
Subject: Re: [802.3_50G]
答复: [802.3_50G] Relating DER, BER and Q in Draft 1.2



Thanks for the pointers.

Reviewing Annex 120D:


Table 120D–8 shows DER0 is 1e-5.

There is no BER spec. Instead, Table 120D–6 specifies a PCS symbol error ratio (SER) of 1e-4.

With precoding, BER=2*DER0. Without precoding, BER=DER0. But precoding is optional.

So it looks like this was overcome by specifying SER instead of BER.

SER=10*DER0, independent of precoding.

Looks consistent.


120D.3.1.1 says:

"J4 is defined as the time interval that includes all but 10–4 of the jitter probability density distribution, ..."

120D.3.2.1 says:

 Q4 is 3.8906.

But Q4=Q(3.8906) = 5e-5 which is inconsistent with J4=1e-4.

Q4 should be 3.7 instead?

Same applies to


Clause 136:

Table 136-13 has a DER0 value of 1E-4.

136.1 specifies BER of 2.4E-4. " ... BER better than 10–4".






On 03/21/2017 02:21 AM, Yang Zhiwei wrote:

Hi Vinu,

I'm not sure how the DER0 and BER values are derived for CR, but to my understanding the basic consideration should be same with other. You can refer to "ran_020415_25GE_adhoc" for DER0 calculation. and "cideciyan_02a_1111" for PreFEC BER calculation for radom error.

As to the Q=5E-5, you can get it by Q(3.8906) there Q(x) is the Q function defined in Equation 95-1 and in mathematical also 0.5*erfc(x/sqrt(2)).

Hope a some helpful for you and may be someone can provide more details for the calculation process.




Best Regards!

Yang Zhiwei

Senior SI and Architecture Engineer, ZTE

+86 18675573560


收件人: STDS-802-3-50G@xxxxxxxxxxxxxxxxx;

20170318 06:02

[802.3_50G] Relating DER, BER and Q in Draft 1.2



Table 136-13 has a DER value of 1E-4. 136.1         specifies BER of 2.4E-4.
        calculates Q for 5E-5.

Could someone please point to the contribution(s) that relate       these values?