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Shannon capacity of a graph. If G is an undirected graph, it can be used to define a communications channel in which the symbols are the graph vertices, and two ...
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.
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 Shannon capacity of a graph G is bounded from below by α(G), and from above by ϑ(G). [5] In some cases, ϑ(G) and the Shannon capacity coincide; for instance, for the graph of a pentagon, both are equal to √ 5. However, there exist other graphs for which the Shannon capacity and the Lovász number differ. [6]
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.
The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication", [2] [3] and is also referred to as Shannon entropy. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel, and a receiver. The "fundamental problem ...
Furthermore, later on in the Wiki article, the authors have set Hartley's expression equal to Shannon's channel capacity to find a relationship between M and the S/N ratio. If Hartley's is a rate, and Shannon's is a capacity, then it wouldn't make a lot of sense to set the two equal to each other. First Harmonic 12:04, 5 September 2006 (UTC)
Shannon capacity may mean Channel capacity, the capacity of a channel in communications theory; Shannon capacity of a graph This page was last edited on 6 ...