more on Spectrum Gold Rush

[David Farber <dave () farber net>]

Begin forwarded message:

From: "David P. Reed" <dpreed () reed com>
Date: September 1, 2006 6:02:38 PM EDT
To: dave () farber net
Cc: ip () v2 listbox com
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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