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The channel capacity is defined as ... If G is an undirected graph, it can be used to define a communications channel in which the symbols are the graph vertices, ...
In graph theory, the Shannon capacity of a graph is a graph invariant defined from the number of independent sets of strong graph products. It is named after American mathematician Claude Shannon . It measures the Shannon capacity of a communications channel defined from the graph, and is upper bounded by the Lovász number , which can be ...
Some authors refer to it as a capacity. But such an errorless channel is an idealization, and if M is chosen small enough to make the noisy channel nearly errorless, the result is necessarily less than the Shannon capacity of the noisy channel of bandwidth , which is the Hartley–Shannon result that followed later.
Graph showing the proportion of a channel’s capacity (y-axis) that can be used for payload based on how noisy the channel is (probability of bit flips; x-axis). The basic mathematical model for a communication system is the following:
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions. Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion. RNA secondary structure prediction from a multiple sequence alignment.
Bandwidth in hertz is a central concept in many fields, including electronics, information theory, digital communications, radio communications, signal processing, and spectroscopy and is one of the determinants of the capacity of a given communication channel.
The BSC has a capacity of 1 − H b (p) bits per channel use, where H b is the binary entropy function to the base-2 logarithm: A binary erasure channel (BEC) with erasure probability p is a binary input, ternary output channel. The possible channel outputs are 0, 1, and a third symbol 'e' called an erasure.
Graph showing the proportion of a channel’s capacity (y-axis) that can be used for payload based on how noisy the channel is (probability of bit flips; x-axis). The channel capacity of the binary symmetric channel, in bits, is: [2] = (),