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Shannon Theory. Risanuri Hidayat 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. Shannon's Theorem.

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shannon theory

Shannon Theory

Risanuri Hidayat

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.

shannon s theorem
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.
shannon s theorem1
Shannon's Theorem
  • 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.
shannon s theorem2
Shannon's Theorem
  • Here is a graph showing the relationship between C/B and S/N (in dB):
examples
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.
examples1
Examples
  • 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.