PAM-5, what are your BERs ?
Edward Chang was right on target.
He wrote on Feb 23:
> In the past, the multiple voltage-level coding
> was adopted by two LAN standards, ATM and
> Ethernet. Both of them were twisted-pair
> applications, and the BER were 10^(-10).
> I proposed BER of 10^(-12) in both working
> groups to be consistent with the LAN optical
> links' BER; however, for some reason, they
> remain 10^(-10), officially in both standards.
What was the reason ?
Multilevel voltage coding was not the reason.
On the contrary, it was a remedy. The real reason
was the strong ISI at the maximum link lengths
that these Standards wanted to support.
Multi-level voltage coding was adopted to
lower the baud rate or the frequency content
of the signal in order to make the ISI smaller
and get a better BER.
However, the remaining ISI in these Copper links
remained high enough that the eye at the
input of the receiver remained still
completely closed. It is this closed eye that
limited the achievable BER in the Copper media
to 10^(-10). Post-equalizers, no matter how
sophisticated they were, are not able to
completely reverse the effects of eye closening
on the achievable BER.
---> Conclusion ? In order to get a BER of
10^(-12) you have to have a clear
open eye at the input of the receiver.
The maximum supported link length
is set accordingly to meet this basic
condition: open eye.
Now we can go to the basic two PAM-5 proposals:
1) PAM-5 serial at 5 Gbaud
Using 1300 nm lasers lasers at 5 Gbaud the
optical eye is completely closed already at
~170 meters due to heavy ISI (installed MMF,
500 MHz*km bandwidth).
Oscar claimed a support of 500 meters of
installed MMF and pointed out that
DFEs (equalizers) have been successfuly used
in 100 and 1000 Mbps Copper networks.
However, the specs and experience of the 100 Mbps
and 1000 Mbps links over Copper - where the eye
at the input of the receiver is completely
closed at the target link length due to ISI -
put the achievable BERs around 10^(-10) only.
Even using sophisticated equalizers.
What is the experimental support that a BER
of 10^(-12) could be achieved when a strong ISI
closes completely the eye at the input of the
receiver ? I think that none and that the
experience points to the contrary. Why then
could an equalizer running at 5 GHz achieve
here what sophisticated equalizers running
40 times slower (125 MHz) were not able to achieve
in the Copper Ethernets ? Parallel processing
could enable perhaps to meet the timing
constraints of the design by running multiple
equalizers at a lower clock, but will not
eliminate the basic limitation on achievable
BERs once the eye at the input of the receiver
is already completely closed.
Let us see now the case PAM-5 at 1.25 Gbaud:
2) PAM-5 4-WDM at 1.25 Gbaud
Let us compare this approach to two other well
known on-off approaches: 1 GbE and 4-WDM at
3.125 Gbaud using the 8b/10b coding. Let us
assume again 1300 nm lasers and installed
500 MHz*km MMF.
The figures below (I hope will not get distorted
during transmission) show the power levels of
the three systems. For 1 GbE I assumed no ISI.
For PAM-5 I assumed 400 meters link length
(there is no ISI up to this distance, ISI= 0 dB).
For 4-WDM at 3.125 Gbaud I assumed 300 meters link
length and about 3 dB optical loss due to ISI.
| | 1 GbE, 1.25 Gbaud, no ISI
| | | | |
| | | | |
| | | | | PAM-5 4-WDM at 1.25 Gbaud
| | | | | no ISI.
| | | | |
|**** ****| 8b/10b 4-WDM at 3.125 Gbaud
|**** ****| 3 dB ISI loss
( the asterisks denote closening of the eye due
2a) 1 GbE
By definition, the optical power difference
between the '0' and '1' levels in the 1 GbE
case is 1:
optical signal power = 10*log(1) = 0 dB
optical SNR = 0 dB (reference)
And we get a BER of 10^(-12).
2b) PAM-5 4-WDM at 1.25 Gbaud
In the PAM-5 case, notice that using the
"open fiber control" method that I described
in a previous email, we get the same launched
power per channel as in the 1 GbE Ethernet.
However, in PAM-5 the power difference
between levels is 0.25 (this is the well
known 6 dB optical power penalty loss of
the PAM-5 modulation). Let us now add
the 6 dB electrical coding gain provided
by the Viterbi decoding: the effective distance
between levels doubles. Summarizing, in PAM-5
4-WDM at 1.25 Gbaud, the effective optical
signal power difference between levels is:
effec optical signal power diff =
10*log(2*0.25) = - 3 dB
where the factor 2 inside the log comes
from the coding gain.
The noise power at the input of the
receiver is the same as in 1 GbE because
we use the same baud rate. Hence,
effec optical SNR = - 3 dB
This is not bad compared to the 0 dB of 1 GbE.
Furthermore, notice that we could even bring
back the SNR for PAM5 to 0 dB (the 1 GbE
reference) if a new laser safety proposal
to move the maximum safe power from -4 dBm
to -1 dBm is accepted. See P. Kolesar et al
presentation in the next March meeting.
2c) 8b/10b 4-WDM at 3.125 Gbaud
In this case the eye is half closed due
to ISI. Hence the optical power difference
optical signal power = 10*log(0.5)
= - 3 dB
and the electrical noise power at the input
of the receiver is larger, since the receiver
needs more bandwidth:
elec noise power = 10*log[(3.125/1.25)^2]
= 8 dB
Hence, the optical SNR is
optical SNR = - 3 - 8/2 = -7 dB
This case is clearly worse than the 1 GbE
case in terms of optical SNR. And the
Task Force considers that this system
can achieve the needed 10^(-12) BER.
PAM-5 4-WDM at 1.25 Gbaud has no
ISI, a clear and wide open eye at
the input of the receiver, an optical SNR
only slightly less than the SNR of present
1 GbE transceivers and better than
the proposed 8b/10b 4-WDM at 3.125G
Hence, it is a good choice if one
wants to reach the required BER of
Note: the above analysis, based on simple
static SNRs, is not a substitute for a
much more careful analysis regarding
the viabibility of any PAM-5 approach.
However, a simple back-of-the-envelope
analysis is very useful to make a quick
comparison between different PAM-5 proposals
in order to find out which PAM-5 architecture,
a) one working under strong ISI conditions
that close the optical eye completely; or
b) another using a lower baud rate
and working with minimal ISI so that
the optical eye at the input of the
receiver is widely open,
which one has more chance to meet the required
BER of 10^(-12), and discard accordingly the
one that does not have a chance.
Jaime E. Kardontchik
San Jose, CA 95131