[e2e] Overly Overlay; Peer to peer is commonplace

[David P. Reed]

At 12:11 PM 1/2/2002 -0600, Nitin H Vaidya wrote:
>  * I presume you mean bit rate, when you say bandwidth above: Bit rate of
>    a link between a pair of nodes is not always an independent variable,
>    since all the "links" terminating at a given node may share the channel
>    with each other. Thus, bit rates of these links are correlated, not
>    independent (generally, a link's bit rate is correlated with those
>    links one or, possibly, more hops away).
>    Also, the bit rate can be tweaked by changing parameters such as the
>    modulation scheme.

This characterization remains muddy, and still shows evidence of trying to 
think of electromagnetic propagation as a set of wirelike links.

Signals do not interfere with each other in the physical medium - they are 
superposed on each other (a reversible process).  With space-time coding, 
for one interesting current example, they can in many cases be completely 
separated again.  (in fact, in a band-limited and space-bounded diffusive 
medium, it's been shown that as the number of transmitter reciever pairs 
increases with N, the communications capacity of the channel increases 
linearly with N. The *opposite* of what you'd expect if signals interfere 
and diffusion/multipath could be viewed as as noise).

So the tradeoff of achievable bitrates among a fixed set of transceivers in 
a medium is not derivable from the fundamental physics.  If you arbitrarily 
draw an fantasy topology on it and limit the computational capacity of the 
nodes to trivial processing (like memoryless linear filtering only, e.g. 
early twentieth-century tank circuits), then you come close to the 
approximation you suggest above.

Information theory has hardly started to be able to explain general 
"network channels" that arise when computational radios cooperatively 
coexist in a dense space.  Instead we use simple rules about point-to-point 
channels, and lump all other effects into our models as worst-case, 
assumed-to-be-gaussian noise processes.

But with respect to modeling radio networks as graphs, that is circular 
reasoning, assuming what you want to demonstrate.

Instead, I think you have to start modeling radio networks based on 
physics, and then see if graphs can model the real physics in a useful way.