Hi Take-san,
> I meant QRAXX as “Q-ary Repeat-Accumulate Codes for Weak Signal
> Communications” in Nico’s literature but I do not have any intent to modify
> wsjt-X “QRA64” mode to this discussion.
Understood. But why not scale the well-known results from Nico’s excellent
QRA64 mode to see what should be possible?
>
> By the increase of symbol length to 64mS (FT64) and 74.7mS (FT128) from 32mS
> (from 160mS FT8 symbol length speed up by factor 5), the gain is 10LOG(64/32)
> = +3dB and 10LOG(74.7/32) = +4dB.
You have shown that the *symbol* SNR (Es/N0) will be doubled if we use 64FSK
instead of 8FSK, but what matters is the *bit* SNR, Eb/N0.
A single 64FSK symbol conveys 6 bits of information, whereas the 8FSK symbol
conveys only 3 bits. You neglected to factor this into your calculations. While
the 64ms 64FSK symbol contains twice the energy of the 32ms 8FSK symbol, the
energy-per-bit is the same, either way.
There *is* a slight modulation-detection-efficiency advantage to using 64FSK
instead of 8FSK if the symbol detection is done noncoherently on a
symbol-by-symbol basis, but the gain is fraction of a dB. Furthermore, any
such advantage vanishes if the 8FSK demodulator is configured to detect
sequences of, say, 2 or 3 symbols rather than individual symbols.
In any case, the 64FSK vs 8FSK advantage was already included in the scaled
QRA64 example that I described earlier. I stand by my conclusions.
I also fully agree with Joe’s objection to your "second" +4dB term. Each FT8
message conveys 75 bits. If we send five of them serially, then we are sending
375 bits. If we were to combine the essential information into a single
packet, it would need to convey a total of 11 callsigns (the Fox call, 5 calls
to be printed with RR73, and 5 calls to be printed with signal reports_ plus 5
signal reports. This is a total of 11*28 + 5*3 where I have conservatively used
only 3 bits for each signal report. Thus, the available savings is
10*log10(375/323) = 0.6 dB.
73, Steve k9an
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