Sean Breheny wrote:
> I understand that, I was just wondering where the 35kbit/sec number
> comes from. It sounds like a rule of thumb and not a theoretical
> limit. If it were a theoretical limit, it should apply in a lab-type
> setting, too, and yet it would be fairly easy to inject a signal into
> a telephone codec which got any arbitrary sequence of codes out of the
> ADC, which could then deliver a data rate of 64 kbits/sec. Even with a
> kilometer of wire in front of the codec, it could be done in the lab
> by doing system identification on the wire to determine the transfer
> function and then pre-distorting the signal to compensate.
>=20
> In fact, this must actually be possible (not quite 64kbps) in a
> real-world situation on a high-quality phone line since 56 kbps modems
> do work on at least one analog end.

56k works in the ISP-to-end user direction because the end user's modem
uses a 14- to 16-bit ADC to measure the voltage coming down the line, and
with enough training, it can syncrhonize itself precisely to the 8-kHz
sampling rate of the digital part of the system, and it can distinguish
about 128 unique voltage levels in each sample interval. Note that because
of u-law companding, these voltage levels are not linearly distributed,
which is why you need such a high-resolution ADC. It isn't 256 levels
becuase in the u-law system there are pairs of codes that are
indistinguishable, and furthermore, the phone company does some in-band
signalling by robbing (overwriting) one of the bits every now and then.=20

If both ends of the link are analog, then you have to treat the digital
part in the middle as a simple noisy channel, because there's no way to
syncrhonize to the sampling or calibrate to the telco's actual codec
voltage levels. As a result, you have an available bandwidth of about
3400-3700 Hz, and an effective S/N ratio of about 40-50 dB -- but keep in
mind that this is quantization noise in a companding codec, not simple AWGN=
..
That's why you end up with a limit of about 35 kbps in this mode -- 9 to 10
bits per baud at 3200-3400 baud.

-- Dave Tweed
--=20
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