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It connects Hartley's result with Shannon's channel capacity theorem in a form that is equivalent to specifying the M in Hartley's line rate formula in terms of a signal-to-noise ratio, but achieving reliability through error-correction coding rather than through reliably distinguishable pulse levels.
This result is known as the Shannon–Hartley theorem. [11] When the SNR is large (SNR ≫ 0 dB), the capacity ¯ is logarithmic in power and approximately linear in bandwidth. This is called the bandwidth-limited regime.
The channel capacity can be calculated from the physical properties of a channel; for a band-limited channel with Gaussian noise, using the Shannon–Hartley theorem. Simple schemes such as "send the message 3 times and use a best 2 out of 3 voting scheme if the copies differ" are inefficient error-correction methods, unable to asymptotically ...
Shannon's diagram of a general communications system, showing the process by which a message sent becomes the message received (possibly corrupted by noise) This work is known for introducing the concepts of channel capacity as well as the noisy channel coding theorem. Shannon's article laid out the basic elements of communication:
the mutual information, and the channel capacity of a noisy channel, including the promise of perfect loss-free communication given by the noisy-channel coding theorem; the practical result of the Shannon–Hartley law for the channel capacity of a Gaussian channel; as well as; the bit—a new way of seeing the most fundamental unit of information.
This relationship is described by the Shannon–Hartley theorem, which is a fundamental law of information theory. SNR can be calculated using different formulas depending on how the signal and noise are measured and defined.
The Shannon–Hartley theorem says that the limit of reliable information rate (data rate exclusive of error-correcting codes) of a channel depends on bandwidth and signal-to-noise ratio according to: < (+) where
In the famous Shannon–Hartley theorem, the C/N ratio is equivalent to the S/N ratio. The C/N ratio resembles the carrier-to-interference ratio (C/I, CIR), and the carrier-to-noise-and-interference ratio, C/(N+I) or CNIR. C/N estimators are needed to optimize the receiver performance. [1]