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Re: [10GBT] Modified 128 point cross constellation mapping

Hello Weizhuang and Chen,

Thank you for all your efforts in addressing the PAM12 constellation issue.

This 128-point cross constellation is actually the Compapiano-Glazer
rectangular constellation for N=7 (see, e.g., Fig.3 on Page 635 of Forney et
al.'s classical paper, "Efficient Modulation for Band-limited Channels,"
IEEE J-SAC, Sept. 1984).

While this cross constellation does indeed reduce the transmit power in the
absence of THP as you correctly state, unfortunately, all N=odd
Compapiano-Glazer constellations are inefficient in the presence of THP. The
holes that appear in the 4 corners of the N=odd constellations might as well
be put in the center in the presence of THP, which is probably why Dariush
placed it there in dabiri_1_0304.pdf.

To understand why, consider an observer who measures statistics of the
transmit signal at the output of the transmitter and the
echo/NEXT/FEXT/ANEXT impairments at input of the receiver, when the THP is
fully engaged. Whether or not the cross constellation is used or the
original PAM12 constellation is used, this observer will see identical
statistics in the measurements of the signal and all the impairments.
Furthermore, the dynamic range of the received signal at the input of the
receiver will also be identical, which implies that the BER at the receiver
output will be identical, and off with respect to the theoretical
calculations that donít consider these inefficiencies.

The inefficiencies exist in both cases, because holes exist in the THP
expanded constellation in both cases. Such inefficiencies do not exist in
any N=even constellation, and the PAM8 proposal uses N=6 in the
Compapiano-Glazer family of rectangular constellations (also shown in the
figure referenced above).


>From: weizhuang xin <>
>Reply-To: "IEEE P802.3an" <>
>Subject: [10GBT] Modified 128 point cross constellation mapping
>Date: Fri, 27 Aug 2004 17:59:40 -0700
>Hi All,
>Attached is a revised 128-point cross constellation mapping from what we
>sent previously. Please note there are 16 co-sets in this 2D
>constellation mapping, and the co-set labels are Gray code coded. The
>un-coded bits are still protected with 12 dB partitioning as before.
>Weizhuang Xin
>Keyeye Communications, Inc.
><< Modified128-pointcrossconstellationmapping.pdf >>

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