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To determine the channel capacity, it is necessary to find the capacity-achieving distribution () and evaluate the mutual information (;). Research has mostly focused on studying additive noise channels under certain power constraints and noise distributions, as analytical methods are not feasible in the majority of other scenarios.
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.
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.
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 converse of the capacity theorem essentially states that () is the best rate one can achieve over a binary symmetric channel. Formally the theorem states: Formally the theorem states:
For the case of channel capacity, the algorithm was independently invented by Suguru Arimoto [1] and Richard Blahut. [2] In addition, Blahut's treatment gives algorithms for computing rate distortion and generalized capacity with input contraints (i.e. the capacity-cost function, analogous to rate-distortion). These algorithms are most ...
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; and of course; the bit - a new way of seeing the most fundamental unit of ...
The channel capacity of the classical ideal channel with respect to a quantum ideal channel is C ( C m , C n × n ) = 0. {\displaystyle C(\mathbb {C} ^{m},\mathbb {C} ^{n\times n})=0.} This is equivalent to the no-teleportation theorem: it is impossible to transmit quantum information via a classical channel.