On 12/08/2022 7:34 am, David P. Reed via Starlink wrote:
>
> I'll give you another example of a serious misuse of a theorem outside 
> its range of applicability:
>
> Shannon proved a channel capacity theorem: C = W log(S / N). The proof 
> is mathematical, and correct.
>
Indeed.
>
> But hiding in the assumptions are some very strong and rarely 
> applicable conditions. It was a very useful result in founding 
> information theory.
>
> But... it is now called "Shannon's Law" and asserted to be true and 
> applicable to ALL communications systems.
>
...and it is. But it needs to be applied correctly.
>
> This turns out not to be correct. And it is hardly ever correct in 
> practice.
>
Ahem ... if it's proven, it's correct, even in practice ;-)
>
> An example of non-correct application turns out to be when multiple 
> transmissions of electromagnetic waves occur at the same time. EE 
> practice is to treat "all other signals" as Gaussian Noise. They are 
> not - they never are
>
Therein lies the problem. Correct theorem, incorrectly applied.
>
> .
>
> So, later information theorists discovered that where there are 
> multiple signals received by a single receiving antenna, and only a 
> little noise (usually from the RF Front End of the receiver, not the 
> environment) the Slepian-Wolf capacity theorem applies C = W 
> log(\sum(S[i]. i=1,N) /W).
>
Note: N here isn't the noise power (just the number of signals).
>
> That's a LOT more capacity than Shannon's Law predicts, especially in 
> narrowband signalling.
>
Only if you lump in correlated signals with noise, which is an incorrect 
(or rather, over-simplified) application of the Shannon-Hartley theorem.
>
> And noise itself is actually "measurement error" at the receiver, 
> which is rarely Gaussian, in fact it really is quite predictable 
> and/or removable.
>
Noise in the Shannon sense is random and therefore not predictable or 
correlated. Interference can be both predictable and correlated, and 
therefore can sometimes be removed / to an extent. Modelling 
interference as noise means not exploiting its inherent properties, and 
yes that means ending lower capacity. But that doesn't mean that either 
theorem is inapplicable - Shannon's fundamental limit still holds, even 
in the multi-user case, as long as the noise you plug in is the "little 
noise" from the RF front end and leave the interference out.

The point I guess is that models are just models, and the more you know 
about what it is that you are dealing with, the better you can model.

Which, I suppose, applies to managing queues also. The more you know 
what's in them and how it'll respond when you manage it, the better.

-- 
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Dr. Ulrich Speidel

School of Computer Science

Room 303S.594 (City Campus)

The University of Auckland
u.speidel@auckland.ac.nz  
http://www.cs.auckland.ac.nz/~ulrich/
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