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[10GBT] Bit-to-Symbol Mapping Losses in the PAM12 proposal

Hi All,

The bit-to-symbol mapping on slide 24 of powell_1_0704.pdf results in a 2D
constellation shown on slide 9 of dabiri_1_0304.pdf. I took the liberty of
snipping off that slide and attaching it herewith in order to ease this
technical discussion.

The problem with this mapping is two-fold. Firstly, it results in an
inefficient use of the 12 PAM levels available for the encoding since it
eliminates 16 points in the center of the 2D constellation. There are many
ways to calculate this inefficieny - loss of capacity in the 0-412.5MHz
frequency band used in the PAM12 proposal, reduction in SNR with respect to
a hypothetical, optimal PAM12 system, etc. For the purposes of our technical
discussion, I will use the latter measure.

A simple calculation of the back-channel overhead, the 64B/65B overhead, the
LPDC coding overhead and the 10Gb/s data rate, shows that in an "optimally
encoded" PAM12 system, the modulation rate should have been approximately
780Ms/s. From the DFE SNR curves output by solarsep_varlen7a.m code, the
optimal DFE SNR for Model 3 at this modulation rate shows that there is a
1.1dB additional SNR margin available in this optimal PAM12 system over the
proposed practical 825Ms/s PAM12 system.

(As an aside, a PAM8 system with the same overhead as in the PAM12 proposal
would operate at a symbol rate of ~950Ms/s and I have an e-mail in to
cabling experts on this task force to confirm that we can handle cabling
environmental variations with such an overhead. This "low overhead" PAM8
system is easy to implement with a simple framing scheme and would result in
an additional 1dB SNR margin for PAM8.)

In addition to the 1.1dB bit-to-symbol mapping loss in the PAM12 proposal,
there is an additional problem that arises due to the proposed 2D
constellation. If the THP filter is loaded with ZERO coefficients, then the
average symbol amplitude in the 2D constellation is sqrt(53)=7.28. If the
THP filter is fully utilized, the PAM12 constellation will smear to cause an
uniform distribution from 0-12, which results in an average symbol amplitude
of sqrt(1/3)*12=6.928. The difference in power between these two extremes is
0.43dB, a fact that was also pointed out on slide 10 of
zimmerman_1_0504.pdf. Furthermore, the results presented in jones_1_0504.pdf
show that there are perfectly valid receivers possible for the PAM12
proposal that use ZERO THP coefficients at all line lengths. The main effect
of this transmit power variation is that emissions compliance measurements
would then become a function of the link partner's receiver structure.

Finally, a parting thought which is an important consideration for my
continued opposition to the PAM12 proposal. If this task force ever approves
a constellation with a hole in the center, 10GBASE-T will become the  butt
of ribald jokes in the larger community of communications experts who
understand these inefficiencies. While this may not be a technical issue, I
consider it a fate worse than death for those of us who have reputations to
maintain in this community.

Sailesh Rao.

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PAM12 constellation.pdf