Bzzzt! Glad to see people outside of the SP world actually know about
the Shannon capacity theorem, but the description here isn't 100% correct.
Raz you are confusing Shannon with Nyquist. The theoretical data rate you
can pass through an analog telephone channel is 64kbps. When the analog
signal is received at the exchange, it is filtered and then quantised into
256 levels. Since the bandwidth of the channel is roughly 4kHz, Nyquist
theory states that a sampling rate of twice that (8kHz) is required to
accurately sample all the frequency components.
Thus we have 8 bit data sampled at 8kHz which gives us a serial data rate
Now, theoretically, if I can take 64kbps data from my computer, build it
into blocks of 8 bits, assign each block an analog value EXACTLY equal to
the values used at the exchange and transmit it at a clock rate EXACTLY
equal to that used at the exchange, then I can get 64kbps throughput down
an analog phone line.
OK. Now this is where Shannon's capacity theorem comes in. Obviuosly
the analog signal will be corrupted by noise between my house and the
exchange. Obviously I cannot set my quantisation levels exactly to that used
at the exchange. And Obviously I cannot set my tx clock to exactly that used
by the exchange.
All these errors that enter the corrupted data are modelled as noise.
Additive noise represents the noise picked up during transmission, quantisation
noise represents errors in the quantisation of the analog waveform, and clock
noise represents errors between the rx and tx clocks. The number of
quantisation levels also represents the dynamic range of the channel (ie the
number of distinct variations allowable on the channel). Shannon's theorem
provides a relationship between channel bandwidth, noise and dynamic range of
the channel to give us an (annoyingly) reliable estimate of a channels
Unfortunately I do not have my textbook handy, which gives the Shannon
capacity equation and a worked example of estimating the capacity of a phone
line. If I find the example tonight, I will post it tomorrow.
Now to finally address Raz's statement, S/N ratio on the channel is what
is limiting modem development to 33.6 kbps. The Shannon limit on the average
Australian phone line is around 35kbps. Obvoiusly if you live next to an
exchange you will get a higher channel capacity, but if you live in the
outback your capacity will be pretty poor. If telstra relaid all its
cabling with super low noise cabling, your channel capacity would increase
and modems would be able to run on higher data rates, possible over 40 kbps.
As an example of Shannons theory being put to work, satellite earth stations
have problems during rainstorms, as this increases the path loss (ie. S/N)
on their channel (air and space between the satellite and their ground
station). When the rain comes, the S/N ratio degrades, and thus they must
reduce the data rates on the digital channels to maintain an acceptable
bit error rate. Therefore less overseas phone calls can be made during
a rain storm!
And now to the disclaimer. All this info is off the top of my head. I'm sure
its pretty right, and will check it tonight. If any of what I have said
is wrong, please feel free to correct me in the strongest possible way!
End of lecture...
Joshua Pitcher email@example.com
P.O. Box 253 http://www.progsoc.uts.edu.au/~jpitcher
Like a software house, except the software's free, and it's
usable, and it works, and if it breaks they'll quickly tell you how to
fix it, and ...
> > The line that you are dialling in with is analogue only to the first
> > optimux/exchange. It is generally safe to assume that it will have
> > the same (analogue) characteristics from call to call, so if you are
> > seeing different characteristics for two different paths into the
> > same modem, the problem is almost certainly arising at the UTS
> > end. Because 9514 is digitial all the way into UTS's premises (I
> > believe) the problem (if indeed it exists) is actually with the
> > equipment on UTS's premises. At a guess, this equipment belongs to
> > UTS and is therefore the domain of ITD.
> UTS's voice feeds are digital, and go into our (digital) PBX (a NEC
> 2400 IMS to be specific). the lines however are translated from
> digital internally inside the PBX (or PABX if you prefer) to analogue
> (so that the modem can understand it) before being pumped to the
> modem. now.. i think you should be lucky to get 28.8 because we have a
> 2400 SDS here at work (an older model of the 2400 range), and it cant
> punch anything beyond 20,100 baud. we have had to get external lines
> right off the MDF to get faster speeds than that.
> i think you might find though that it is Optus' equipment that makes
> the diff if Telstra's 330 switch (which redirects off to the Optus
> 9514 switch, which it has been doing for some 6 months or so now) runs
> faster. and i guess you would probably need to look and find where
> Optus' main trunk line to Telstra's sydney local network is, and this
> may be different from the trunk it is using to get from 330 to
> 9514. Maybe Telstra are deliberately (conspiracy theory here :)) doing
> funny business on all traffic heading down to Optus on this main
> trunk, keep people using Telstra local services maybe? *shrug*
> a couple of ways to test this would be to talk to a design engineer
> and find out what trunks go where, and also to try dialing into the
> 9514 switch from an Optus local service (since it would stay inside
> their network).
> another point is that it is not unheard of for PCM (the same
> modulation modems use for sending data) compression to be used on
> voice line over long distance or heavy use trunks. this _will_ affect
> the maximum speed you can get out of a modem on a voice line across
> such a trunk. data lines and hence ISDN lines are typically guaranteed
> not to have such compression.
> > Perhaps they bought bargain basement equipment.
> at the time the PBX was installed it was only the second installation
> of such equipment in *.au (after the ABC), and such equipment is
> extensively used throughout *.au (99% of line men/engineers got their
> initial PBX training on them). the NEC 2400 boxen are quite amazing
> for what they achieve, even more so for when they were released. and
> if you had ever seen the regulations you need to hop through in order
> to get telephony equipment approved you probably appreciate it more.
> Matthew Keenan Network Administrator First Pacific Stockbrokers
> Sydney, Australia