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226 CHAPTER NINE
Physical Layer
All that said, digital communication comes down to one thing: sending data over a chan-
nel. Another fundamental theorem came out of Shannon’s work (first mentioned in
Chapter 8). It comes down to an equation that is the fundamental, limiting case for the
transmission of data through a channel:

C B log 11 S>N2
2
C is the capacity of the channel in bits per second, B is the bandwidth of the channel
in cycles per second, and S/N is the signal-to-noise ratio in the channel.
Intuitively, this says that if the S/N ratio is 1 (the signal is the same size as the noise),
we can put almost 1 bit per sine wave through the channel. This is just about baseband
signaling, which we’ll discuss shortly. If the channel has low enough noise and supports
an S/N ratio of about 3, then we can put almost 2 bits per sine wave through the channel.
The truth is, Shannon’s capacity limit has been difficult for engineers to even
approach. Until lately, much of the available bandwidth in communication channels has
been wasted. It is only in the last couple of years that engineers have come up with
methods of packing data into sine waves tight enough to approach Shannon’s limit.
Shannon’s Capacity Theorem plots out to the curve in Figure 9-1.
There is a S/N limit below which there canot be error free transmission. C is the
capacity of the channel in bits per second, B is the bandwidth of the channel in cycles

Bits per Hertz
66

44
2 2
Eb/No
0
-2 -1 0 123456 789 1011 121314151617 181920

-8
FIGURE 9-1 Shannon’s capacity limit