From: Phiber Optik <phiber@eff.org>
Date: Mon, 8 Feb 93 09:09:16 PST
To: jim@tadpole.com (Jim Thompson)
Subject: Re:  Compressed/Encrypted Voice using Modems
In-Reply-To: <9302081700.AA02209@ono-sendai>
Message-ID: <199302081708.AA13952@eff.org>
MIME-Version: 1.0
Content-Type: text/plain


> 
> haven't seen it.
> 
OK, fearing the worst (maybe I forgot to CC my message to cypherpunks, but I'm
sure I did), I'll repost my original message.  It was a God-sent that I got 
cut off last night while composing it, and expreserve preserved it.
Here it is:

> 
> > ... because in FSK systems which code 1 bit per symbol
> > (only two phases), bps = baud.  But then and ONLY then....
> 
> Uhh, don't you mean two frequencies?  FSK is Frequency Shift Key, not
> Phase Shift Key (PSK).. ;-)
> 
> Actually, I KNOW you meant this, and it was probably just a typo,
> right?
> 
> -derek
> 
Woops!  Sorry.  To compensate, I'll give more information.  In the Bell 103
system (FSK), the frequencies are 2125Hz for answer, and 1170Hz for originate
carriers, with the frequency shifts being +/- 100Hz.  Compare with CCITT's
V.21, and substitute the carrier frequencies with 1750 and 1080Hz.  Same
+/- 100Hz shifting.

Someone else mentioned the almighty Claude Shannon in another message concern-
ing maximum bit-rate of a voice channel, and I wanted to clear up what was 
said.  Shannon's capacity formula said capacity in bits-per-second equals
bandwidth of channel in hertz times the base-2 (binary) logarithm of one plus
the signal (in watts) to noise (in watts) ratio.  As a side note, I say watts
because commonly, today, you measure signal and noise levels in decibels (dB),
and the S/N ratio is in dBm's (decibels per milliwatt).
In the phone system, we say a voice frequency channel (VFC) has a bandwidth of
4kHz.  In-band signalling is approximately from .3 to 3kHz.  This formula
(yielding the Shannon limit) is based on a "Gaussian Band Limited Channel"
(GBLC), which is an approximation of a VFC, with a signal wave of S watts
at the input of an "ideal" low-pass filter, subjected to Gaussian noise with
a mean power of N watts (uniformly).  Written, it's C = W log2(1 + S/N).
A simple example you can do in your head is W=3000Hz, pick an S/N of 1023,
1+1023 is 1024, and base-2 log of 1024 is simply 10, 3000 * 10 is 30000, so
Shannon's limit for these values is C = 30000bps.  Play with it.  Bear in mind,
Shannon didn't consider intersymbol interference.  Nyquist did.  Compare this
to Harry Nyquist's 2-bit rule, 2W, or double the bandwidth, and get the maximum
bit rate (this line of thinking led him to the infamous Nyquist sampling
theorem, sample at a rate twice the bandwidth of a channel, and you have all
the information you need to reconstruct it at the receiving end).  But Nyquist
deals only with binary systems.  Shannon's formula shows that theoretically
you could increase the data rate indefinitely by increasing the S/N ratio.
We achieve this in modern modulation systems by using multilevel systems,
(M-ary for short, with M > 2), and hence the protocols I described in my
previous message.  We can apply Nyquist's 2-bit rule to the multilevel system
by saying 2W log2 M bps is achievable, with an acceptable error rate.  As we
increase M (number of bits per symbol), so we have to find ways to increase
the signal to noise ratio, to maintain an acceptable error rate.
The whole thing is stupendously interesting to me, as I hope it is to the
rest of you folks.  To blow your mind with sheer genius, read Shannon's
classic "A Mathematical Theory of Communication" in Bell System Tech Journal,
July and October of '48 at your local university.  Also Nyquist's "Certain
Topics in Telegraph Transmission Theory", April '28.  Know your roots.

Good night.