Shannon's Theorem

Shannon's Theorem gives an upper bound to the capacity of a link, in bits per second (bps), as a function of the available bandwidth and the signal-to-noise ratio of the link.

The Theorem can be stated as:

C = B * log2(1+ S/N)

where C is the achievable channel capacity, B is the bandwidth of the line, S is the average signal power and N is the average noise power.

The signal-to-noise ratio (S/N) is usually expressed in decibels (dB) given by the formula:

10 * log10(S/N)

so for example a signal-to-noise ratio of 1000 is commonly expressed as

10 * log10(1000) = 30 dB.

Here is a graph showing the relationship between C/B and S/N (in dB): Examples

Here are two examples of the use of Shannon's Theorem.

Modem

For a typical telephone line with a signal-to-noise ratio of 30dB and an audio bandwidth of 3kHz, we get a maximum data rate of:

C = 3000 * log2(1001)

which is a little less than 30 kbps.

Satellite TV Channel

For a satellite TV channel with a signal-to noise ratio of 20 dB and a video bandwidth of 10MHz, we get a maximum data rate of:

C=10000000 * log2(101)

which is about 66 Mbps.

Reference

L L Peterson and B S Davie, Computer Networks:a systems approach (Morgan Kaufmann), 1996. ISBN: 1-55860-368-9 (Paperback ISBN: 1-55860-404-9 ) pp 94-95.