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This sets the theoretical limit that any modulation system cannot go beyond. It has
been the target for system designers since it was discovered. The limit will show up
below in the error rate curves of various modulation schemes.
Many ways exist for jamming electrons down wires or waves across the airways. In
all these cases, the channel has a bandwidth. Sometimes the bandwidth is limited by
physics; sometimes the Federal Communications Commission (FCC) limits it. In both
cases, Shannon’s Capacity Theorem applies: putting God and the FCC on equal math-
ematical footing.
A quick aside about the FCC: After college, we constructed and ran a pirate radio sta-
tion out of a private house. We broadcast as WRFI for about two years, playing the music
we felt like playing and rebroadcasting the BBC as our newscast. I was a DJ and a periph-
eral player. We had fake airwave names to hide our identities; mine was Judge Crater.
Finally, after a great run, the FCC showed up at our door to shut us down. They had
tracked us down in a specially modified station wagon with a directional antenna molded
into the roof. They only had to follow a big dashboard display arrow to our door. It turns
out the DJ at the time was playing a Chicago blues album. The FCC agents confessed
that they liked the music so much that they pulled over until the album was complete
before they knocked on the door. The DJ opened the door, the FCC employee folded open
his wallet just like Jack Webb on Dragnet, and the DJ got a look at the laminated FCC
business card. Both sides, in turn, dissolved in laughter. Two hours, and some refresh-
ments later, they departed with our crystal, a very civilized conflict. But I digress.
Here are a couple of web sites and a PDF on Shannon’s Capacity Theorem:

www.owlnet.rice.edu/ engi202/capacity.html
www.cs.ncl.ac.uk/old/modules/1996-97/csc210/shannon.html
www.elec.mq.edu.au/ cl/files_pdf/elec321/lect_capacity.pdf

Every method of sending data across a channel has a mathematical footing. Often,
the method itself leads to a closed mathematical form for the capacity of the method.
Once the method is implemented, then the implementation can be tested using
Shannon’s Capacity Theorem. Calibrated levels of noise can be added to a perfect chan-
nel and the data-carrying capability can be measured. The testing methods are very
complex and are shown at www.elec.mq.edu.au/ cl/files_pdf/elec321/lab_ber.pdf.

Baseband Transmission

Given a wire, it’s entirely possible to turn the voltage off and on to form pulses on the
wire. In its crudest form, this is baseband transmission, a method of communication
distinct from modulated transmission, which we’ll discuss later.