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



Sailesh,

You made my day! LOL!

Sterling

sailesh rao wrote:

> 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.
>
> Regards,
> Sailesh Rao.
> srao@phyten.com
>
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