[IP] more on Spectrum Gold Rush
Begin forwarded message:
From: "David P. Reed" <dpreed@xxxxxxxx>
Date: September 1, 2006 6:02:38 PM EDT
To: dave@xxxxxxxxxx
Cc: ip@xxxxxxxxxxxxxx
Subject: Re: [IP] more on Spectrum Gold Rush
Dave -
The Shannon-Hartley Theorem does not provide a limit to the
communications capacity of the electromagnetic field, as Brett would
have it. The Shannon-Hartley theorem describes a "channel" which is
an abstraction for a single receiver which is receiving the
superposition of a single signal and a gaussian noise source with
bounded energy. It doesn't have any general application beyond a
radio that exists at a single point in space, under that limited set
of assumptions.
The Shannon Hartley theorem exists as part of a broad and useful
mathematical theory, called information theory. There are indeed
limits that can be calculated by using information theory, given
physical assumptions. However, the following are fundamental
problems in using the Shannon-Hartley theorem.
1) the physical universe is not a gaussian process. Any assumption
of that sort should be tested against reality - otherwise it is
merely a statement of rhetorical faith, or merely an assumption made
to make analysis possible. Lightning strikes, for example, are not
obviously gaussian in their effect on radios - and meteor trails,
used practically to assist radio communications in some applications,
are not gaussian.
2) Channels other than the simple channel described in the S-H
theorem (such as so-called mult-terminal systems) have very different
communications capacities. The simplest such channel is the multiple-
access channel, which happens when 2 or more signals are superposed
on a noise source (which may or may not be gaussian). These
channels seem more appropriate for modeling large-scale networked
communications. For example, one somewhat clear analysis done by
Xie and Kumar under plausible assumptions (of the gaussian sort
challenged above, caveat lector) concludes that the limit of capacity
increases linearly with the number of transceivers in a shared medium.
The last point suggests that it may be the case that under suitable
cooperative behavior (rules) radios can be designed to communicate
without very serious limits.
There is clearly much to do to realize the capabilities suggested by
these comments. But Brett Ellis is making a political point, not a
technical point, and his politics of scarcity should be recognized as
such.
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