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[10GBT] Information bits, coded bits and framing complexity

Hi All,

In coded modulation communication systems, such as the PAM8 and PAM12
proposals on the table, it is customary to speak of information bits and
coded bits. Information bits represent the actual data being transmitted and
the coded bits are the remainder in the modulation scheme.

For the cabling media under consideration, it is natural to consider a 4D
symbol as the unit entity since there are 4 wire pairs in the media. For a
10GBASE-T system that employs k coded bits over an M-level 4D-PAM system,
the transmitted symbol rate can be calculated using the formula:

Symbol Rate (Ms/s) = 10000/(4*log2(M) Ė k)

The PAM8 proposal uses k=2, M=8. Using a simple integer for k allows this
PAM8 system to also use simple data frames that span exactly 1 LDPC code
block each.

For k=2, M=8, the symbol rate is

10000/(4*log2(8)-2) = 1000Ms/s

With a little expenditure of clock generation complexity, we can also
achieve rational values for k. Naturally, the smaller the k, the more
efficient the coded modulation scheme. Therefore, for instance, if k=1.5,
M=8, the symbol rate becomes

10000/(4*log2(8)-1.5) = 952.381 Ms/s

and the resulting PAM8 system can also be made to use data frames that span
exactly 1 LDPC block each. It provides an additional 1dB of SNR margin,
adding another 1dB to the Total EMI Penalty of PAM12.

For PAM12, using k=2 results in a symbol rate of

10000/(4*log2(12)-2) = 810.3826 Ms/s

If a more efficient coding scheme that achieves k=1.5 is employed, the
symbol rate becomes

10000/(4*log2(12)-1.5) = 778.8253 Ms/s

However, the symbol rate proposed in powell_1_0704.pdf for the PAM12 system
is 825Ms/s, which corresponds to k=2.2186bits. The number of information
bits in each 4D PAM12 symbol is 10000/825 = 12.1212bits. Therefore, not only
is the PAM12 proposal using a sub-optimal modulation rate (mainly due to the
bit-to-symbol mapping losses described earlier), but it is also using a
complex data framing scheme spanning 33 LDPC blocks each in order to achieve
this sub-optimality.

Sailesh Rao.

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