more on Response to David Reed

[David Farber <dave () farber net>]

Begin forwarded message:

From: "David P. Reed" <dpreed () reed com>
Date: September 7, 2006 4:18:56 PM EDT
To: dave () farber net
Subject: Re: [IP] Response to David Reed

I don't think Brett's comments read on anything I said.

The major points I made were: 1) The Shannon-Hartley theorem does not  
define a limit to the capacity of the spectrum, which most definitely  
is what Brett was asserting.  2) Brett's comments were properly read  
as political, which his most recent letter confirms, which summarizes  
itself by "I have always advocated ...".

I'm not sure where Brett concludes that I suggested that  
sophisticated technology could remove all constraints on  
electromagnetic communications.   Rereading my letter, I find no such  
suggestion.   The only suggestion I find in my letter was that  
Brett's understanding of Shannon-Hartley theorem does not provide a  
limit to the capacity of the spectrum.

I suppose Brett is choosing to read into my letter some political  
proposal.  I was not making any such proposal there, other than a  
negative one - that Brett's argument that Shannon-Hartley Theorem is  
a compelling liimit that should define our spectrum policy is  
fundamentally incorrect.  In other words, he misreads the theorem,  
and further that it somehow is a law of electromagnetism.

You can read textbooks on electromagnetic physics at any level, and  
you will not find Shannon-Hartley.   You can read textbooks on  
cosmology and you will not find Shannon-Hartley either.   Shannon- 
Hartley is not a physical law - it is a mathematical theorem.  Like  
any theorem, it is a tautology, given its postulates.  The question  
is whether the situation it describes, a channel that has certain  
properties, describes a particular situation, or every situation.   
The SH theorem describes some simple situations quite well.  It's  
worth teaching.   But it does not describe the radio environment of  
any radio very accurately.

A "channel" is a mathematical object only: a function that combines a  
set of inputs to produce an output - not a physical phenomenon at  
all, but the most information-free abstraction.

Adding gaussian white noise to the signal at the receiver is the  
function of an AWGN channel, which is the ONLY channel the SH theorem  
describes.

Whatever limits there are, they do NOT derive from the Shannon  
Hartley theorem, which describe an AWGN channel, a *purely*  
mathematical construct (there is no physics in the Shannon-Hartley  
theorem - None!)   They can be properly derived from using  
information theory IF you base your theory on well-founded physical  
assumptions that are actually true facts.  That is, you must prove  
that the actual electromagnetic field that makes up the universe is  
Gaussian.   That is manifestly not true, and every astronomer knows  
that it is not.   There is structure everywhere - entropy is not  
maximized.  It's the basis of modern physics. It *is* true that in  
physics books, we say "posit a perfect vacuum with only two  
conducting bodies" and pure blackbody radiation at thermal  
equilibrium.   But we do that because we can analyze the situation -  
not because the world is Gaussian in fact.

Many people similarly probably believes that intro physics (college  
Physics I) uses simple linear differential equations because the  
universe has been proven to be continuous and differentiable.   That  
is not why intro physics courses use such models.  It is merely  
because they are tractable, and for many problems, the error is not  
too great.

Enough about Shannon-Hartley not addressing the laws of physics,  
which are crucial.   I could go on about the physics that are not  
included in Shannon Hartley, but it would be silly.

The other problem with Brett's comments is his statement "from the  
perspective of the receiver, the undesired signals are simply  
noise".   There is a difference between undesired signals and  
noise.   Noise is technically quite different from undesired  
signals.   What makes noise different is that noise is unpredictable,  
whereas signals are indeed predictable.   Signals are designed to be  
decoded.  Noise is not.   That distinction is crucial to an  
information theorist.   As I mentioned in my earlier note, the  
"multiple access channel" (which you can read about if you like in  
basic information theory texts, such as Cover and Thomas) are not  
covered by the Shannon Hartley theorem.   If you have two signals  
plus noise, the limit of the receiver's capacity is not, as Brett  
would imply in the "undesired signal is simply noise" in S-H theorem:
    R = W log(1 + S1/(S2+N)).

Instead the system of two transmitters and one receiver can achieve a  
rate of:

   R = W log(1+ (S1+S2)/N).

This is substantially larger than Brett's casual assertion would  
predict (S2 is in the numerator rather than the denominator!)   While  
it may be the case that the receiver actually considers S2 to be  
undesirable, nonetheless, it may be that it can act as a repeater for  
S2, which makes the system as a whole more efficient, since the  
transmitter of S2 can then get the gain inherent in using repeating  
and/or diversity as a result.

So in the context of the *system as a whole* this larger capacity has  
ramifications that multiply capacity.

It has recently been demonstrated (using information theory and a  
conservative physical propagation model) by Tse and others that the  
communications capacity of a set of radios operating as an adhoc net  
in a common medium can scale linearly in the number of radios.  This  
is not modeled by the Shannon-Hartley theorem.   In fact, the  
regulatory model of the US presumes the spectrum has a communications  
capacity that is independent of the number of radios in it - that in  
fact putting out more radios will either disrupt communications or at  
best share a limited resource.

The "limited resource" claim about spectrum is just plain wrong on a  
technical basis.  Advocacy has nothing to do with it.  In this letter  
and my previous letter, I am not advocating a policy solution.   I am  
merely pointing out that Brett's claims are centered around advocacy,  
and that his technical claims are wrong.









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