Posted by Dave Platt on 09/30/07 17:42

In article <46ff32e0$0$32538$4c368faf@roadrunner.com>,
Green Xenon [Radium] <glucegen1@excite.com> wrote:

>Within physical-possibility, what is the largest amount of
>bits-per-symbol [assuming a baud-rate of only 1-bit-per-symbol]

You just made a meaningless statement. Baud rate is measured in
symbols per second, not bits per symbol. I assume that you meant to
say "assuming a baud-rate of one symbol per second."

> that can
>be reached without the highest-voltage causing any clipping, generating
>any temperatures above 70 Fahrenheit, resulting in any harm to
>anyone/anything [including the equipment itself], or shortening the life
>of the equipment and without the lowest-voltage being lost in the noise?
>What is the maximum-possible amount of discrete levels between the
>highest and lowest voltage in such a signal?

And, another important constraint for actual usability is this: you
have to make sure that the minimum-detectable difference between two
different symbol levels can be detected reliably and accurately at
_all_ levels. In the language of analog-to-digital converts this is
referred to as "linearity" and "no missing codes".

[As a counterexample: the human hearing system can hear down to 0 dBa
or so... a sound level which is just barely above the noise created by
the random collision of air molecules with the eardrum. And, we can
hear sounds up to around 120 decibels above that, before damage starts
to result. That's a pretty wide dynamic range. However, it's not
linear... if we're listening to a loud sound (say, at 110 dB or so),
small sounds are completely lost... you can't hear somebody whispering
10 feet away when you're listening to a rock concert.]

>An 8-bit signal can have a maximum of 256 different voltage levels
>between the highest and lowest voltage. Right? Go too high and the
>signal clips, go too low and the signal will not be recognized.

Right.

At audio-quality sampling rates (say, 50,000 baud) you can buy
converters that are linear down to around 22 bits, I think...
marketers call them "24-bit" converters but they aren't actually
linear down to those levels. At instrumentation rates like 1 baud (1
sample per second), with filtering and averaging being applied to
eliminate the noise, you can do rather better.

I don't know quite what the state-of-the-art is for measuring signals
at such low baud rates as you are referring to. I'd guess that it's
somewhere in the range of 28-30 bits.

30 bits is roughly a billion-to-one ratio between the smallest signal
and the largest. Crudely put, it would mean that you might have a
circuit which has to handle voltages of up to 1000 volts, and has to
be able to generate, and then measure voltage differences of a
*millionth* of a volt, at all of these levels. That's going to be
technologically difficult, to say the least.

The *theoretical* limit is somewhat higher than this, but not enough
to help you achieve what you wish. It'll be limited at the low end by
the thermal noise level (a 50-ohm resistance at room temperature
generates -174 dBm of noise over a 1 Hz bandwidth) and at the high end
by whatever voltage you think your equipment can handle without
damage.

Even being extremely generous, and saying 32 bits of linear resolution
(and thus reliable data) per symbol, you aren't going to get video
across it. 32 bits per second is somewhere between "fast Morse code"
and "old Teletype teleprinter or ticker-tape" bandwidth.

Note that this is the generation and measurement limit and assumes an
interference-free communication link (e.g. a well-shielded cable), and
is *not* what you can get away with in a real-world radio
transmission! The background noise level on LF radio frequencies is
higher than this, due to both manmade and atmospheric electrical
noise.

As another poster has pointed out, there's a damned good reason why
nobody uses very-low-baud-rate modulations to send large amounts of
high-speed data over a narrow-bandwidth channel, despite a century or
more of research and study and competition in the fields of radio and
electronic communication. It just doesn't work, and the reasons why
it doesn't are well understood by those who practice in the field.

--
Dave Platt <dplatt@radagast.org> AE6EO
Friends of Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

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