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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.
Shannon–Hartley theorem; Channel capacity, in electrical engineering, computer science, and information theory, is the theoretical maximum rate at which ...
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 ...
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.
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:
In wired communication, the field of information theory (in particular, the Shannon–Hartley theorem) motivates the need for studying the signal-to-noise ratio (SNR). In a wireless communication, when a collection of channels is active at the same time, the interference from the other channels is considered as noise, which motivates the need ...
The dominant equation here is the Shannon–Hartley theorem, and analog limitations of this type can be understood as factors that affect either the analog bandwidth of a signal or as factors that affect the signal-to-noise ratio. The bandwidth of wired systems can be in fact surprisingly narrow, with the bandwidth of Ethernet wire limited to ...