Shannon's Law

Shannon's Law, formulated by Claude Shannon, a mathematician who helped build the foundations for the modern computer, is a statement in information theory that expresses the maximum possible data speed that can be obtained in a data channel. Shannon's Law says that the highest obtainable error-free data speed, expressed in bits per second (bps), is a function of the bandwidth and the signal-to-noise ratio.

Let c be the maximum obtainable error-free data speed in bps that a communications channel can handle. Let b be the channel bandwidth in hertz. Let s represent the signal-to-noise ratio. Then Shannon's law is stated as follows:

c = b log2 (1 + s)

The function log2 represents the base-2 logarithm. All logarithms are exponents. The base-2 logarithm of a number x is the number y such that 2y = x.

No practical communications system has yet been devised that can operate at close to the theoretical speed limit defined by Shannon's law. Some systems, using sophisticated encoding and decoding, can approach half of the so-called Shannon limit for a channel having fixed bandwidth and signal-to-noise ratio.

This was last updated in September 2005

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