There has been a lot of work done in field of information theory and signal processing. Basically, signal that is sent over a transmission medium undergoes a change and get modified. In engineering terms, signals degrade over time. Signal in a transmission medium undergoes change due to many factors.

There are many ways to combat noise in a channel. In a noisy channel, Shannon-Hartley theorem gives the maximum rate at which information can be transmitted in a communication medium with a given bandwidth in presence of noise.

Consider dial-up phone lines at our home. Today its fiber, but assume we got a dial up connected linked to our phone line and the digital data must go through phone line that is designed to carry voice data. A standard voice phone supports frequency at a range of 300 Hz to 3300 Hz.

The bandwidth of the line is ( 3300 – 300 ) = 3000 Hz or 3 KHz.

Shannon-Hartley theorem states that the capacity of a channel can be related with Bandwidth and S/N ( Signal to Noise Ratio ) of the system.

In mathematical terms, [1]

Capacity of a channel = B log_{2}( 1 + S/N )

Where,

B = Bandwidth of the system

S/N – Signal to Noise Ratio

SNR or Signal to Noise ratio is expressed in dB which is SNR = 10 log_{10} ( S/N )

Consider a typical SNR of 30dB in the system. S/N then becomes 1000.

Then capacity of the channel is given by C = 3000 * log_{2}( 1000 ) = 30 Kbps

The same formula to calculate the capacity can be applied to all form of communication links, may it be coaxial, fibers etc. But it should be noted that the above capacity is theoretical upper limit of the channel. The capacity of the channel can be increased by increasing the bandwidth of the signal or reducing the noise in the channel, which requires a bit of ingenuity.

References:

[1] Haykin, Simon. *An introduction to analog and digital communication*. John Wiley, 1994.