# PAM5 and 8B10B and FEC and SAME_BAUD

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Rich,

You sent today an email to the Reflector, that I reproduce
below, that left me perplexed. I sent you a fast response,
but I would like now to be more detailed.

You seem to affirm that you can have it all: use PAM-5 and
include 8b/10b and FEC and still be able to transmit all this
information at 5 Gbaud (serial). I think that this is not true.
I will explain this assuming, for simplicity that we use
instead four parallel transmitters at 1.25 Gbaud each.
The final result will be the same as if we had used one
transmitter at 5 Gbaud and collected together four
consecutive PAM-5 symbols to form one unit.

The raw data consists of 8 bits at 1.25 Gbaud that come
from the MAC layer. These 8 bits represent 2^8 = 256
possible symbols. Using four PAM-5 transmitters at
1.25 Gbaud the number of possible 4-dimensional symbols
is 5^4 = 625. That is, in the 800 psec baud interval you
can transmit 1 out of 625 possible symbols. One such
symbol, for example, could be:

{-1, +2, 0, -1}

Meaning that the A-transmitter sent a "-1", the B-
transmitter sent a "+2", and so on.

Since we have 625 possible symbols (or points in
this 4-dimensional space) and we only need 256
different symbols for the raw data, we have more
than twice the number of points than we really
need for raw data:

625 > 2 * 256 = 512

It is this fact that enables to add Trellis coding
and get 6 dB coding gain using FEC.

Now, if you also want to add the 8b/10b coding,
your "raw" data becomes now something more than
512 symbols: 256 for Current RD(-) and another
256 symbols for Current RD(+) plus another 12
symbols corresponding to valid special code groups,
like K28.5 and K28.7. In total, your "raw" data after
adding 8b/10b consists of 524 different symbols.

Since we have 625 possible points (5^4) we still
have enough points to cover the needed 524 symbols
corresponding to this "raw" data, but we are left with
only 625 - 524 = 101 unused points. This redundancy
is too small and does not allow us to add Trellis
Coding. In other words: we can not get any coding gain
or FEC. The only way to get coding gain in this case
would be either by going to PAM-6 (to get a total
of 6^4 = 1296 symbols, which is greater than
2*524 = 1048) or to increase the baud rate above
1.25 Gbaud.

But assume, for instance, that we sacrifice the
coding gain altogether and we decide to use just
PAM-5 to get 625 possible symbols in order to
accomodate the needed 524 symbols of the 8b/10b
coding.  I do not see any sense in adding the 8b/10b
coding , because once we went to 5-level symbols
for transmission we lost the two main properties
that make the 8b/10b coding attractive: DC balance
and low running disparity. How could you add these
two properties to a 5-level transmission scheme ?
When you use PAM-5 you have to add a scrambler
anyway in order to get the "quasi DC balance", as
the PCS of the 1000BASE-T does.

Summarizing: you can not have a PAM-5 serial at
5 Gbaud (or a PAM-5 4-WDM at 1.25 Gbaud) that
also includes the 8b/10b and FEC. Either you must
go to PAM-6 or increase the baud rate. And in any
case, I do not see the value in adding the 8b/10b
coding when we use a 5-level transmission scheme.

Jaime

Jaime E. Kardontchik
Micro Linear
San Jose, CA 95131
email: kardontchik.jaime@xxxxxxxxxxx
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In a message dated 3/1/00 6:49:49 PM, rtaborek@xxxxxxxxxxx wrote:

>
>Ed,
>
>.....
>
>You point out that FEC requires a higher line rate, which mitigates the
benefits
>of FEC. This is true for a traditional Binary signaled system.
>
>However, for a MultiLevel system such as PAM5, an additional level can easily
>accomodate the FEC overhead. Several HSSG PAM5 proposals as well as
1000BASE-T
>utilize FEC in this fashion. As an example, my 5 Gbaud PAM5 proposal used 4
of
>the levels to respresent 2 bits and the 5th level to represent FEC as well as
>special characters. In terms mapping, one 8B/10B code-group could be mapped
to
>4
>PAM5 symbols creating a PAM5x4 "code-group" symbol. Note that the PAM5x4
symbol
>period is 800 ps, and is used to convey 10 bits and that the PAM5 symbol
period
>is 200 ps = 5Gbaud. You can find more detail on thge latter example in:
>http://grouper.ieee.org/groups/802/3/tutorial/july99/mastut.pdf
>
>It is possible to add FEC to MultiLevel signaling WITHOUT increasing the line