Shannon–Hartley theorem

The Shannon–Hartley theorem gives the maximum reliable data rate of a band-limited channel with additive white Gaussian noise: bandwidth multiplied by the base-two logarithm of one plus the signal-to-noise ratio.

Channel capacity: The highest information rate at which a communication channel can support arbitrarily reliable transmission. The theorem gives channel capacity for the specific case of bandwidth-limited Gaussian noise.
Bandwidth (signal processing): The range of frequencies occupied by a signal or available to a communication channel. It scales the theorem's maximum data rate directly.
Digital modulation: The encoding of digital information in changes to a carrier signal's amplitude, frequency, or phase. Modulation schemes trade signal quality and bandwidth against rates below the theorem's limit.
Claude Shannon: An American mathematician and engineer who founded modern information theory. Shannon derived the capacity result underlying the theorem.
Signal-to-noise ratio: The ratio of signal power to noise power, often expressed in decibels. In the theorem, capacity rises logarithmically with this ratio.
Hertz: The SI unit of frequency, equal to one cycle per second. Channel bandwidth is measured in hertz in the capacity formula.
Error-correcting code: A coding method that adds structured redundancy so transmitted data can be recovered despite errors. Codes approach the capacity limit by correcting noise-induced errors.
A Mathematical Theory of Communication: Claude Shannon's 1948 paper that established the foundations of information theory. The paper presented the theoretical framework from which the channel-capacity result emerged.
Additive white Gaussian noise: A noise model in which independent Gaussian disturbances are added across a channel with uniform spectral density. This is the noise assumption under which the theorem's capacity formula applies.
Decibel: A logarithmic unit expressing a ratio of power or other quantities. Signal-to-noise ratios are often reported in decibels but must be converted to linear form for the formula.

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