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The capacity is the highest achievable rate. Consider a codeword of length sent through the AWGN channel with noise level . When received, the codeword vector variance is now , and its mean is the codeword sent.
An application of the channel capacity concept to an additive white Gaussian noise (AWGN) channel with B Hz bandwidth and signal-to-noise ratio S/N is the Shannon–Hartley theorem: C = B log 2 ( 1 + S N ) {\displaystyle C=B\log _{2}\left(1+{\frac {S}{N}}\right)\ }
AWGN channel capacity with the power-limited regime and bandwidth-limited regime indicated. Here, = ; B and C can be scaled proportionally for ...
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 ...
Here an AWGN channel is assumed. In digital communication or data transmission , E b / N 0 {\displaystyle E_{b}/N_{0}} ( energy per bit to noise power spectral density ratio ) is a normalized signal-to-noise ratio (SNR) measure, also known as the "SNR per bit".
On the contrary, in the limit of small signal to noise ratios the mutual information approaches the AWGN channel capacity, which is the supremum among all possible choices of symbol statistical distributions. At intermediate values of signal to noise ratios the mutual information (MI) is well approximated by: [17]
There are some specific cases for which the capacity is known, such as the AWGN channel and fading channel. [2] Capacity of the broadcast channel: The capacity of the broadcast channel, or the case in which a single transmitter is sending information to many receivers, is unknown in general, though it is known for several specific cases. [3] [4]
"Turbo Equalization: Principles and New Results" Archived 27 February 2009 at the Wayback Machine, an IEEE Transactions on Communications article about using convolutional codes jointly with channel equalization. IT++ Home Page The IT++ is a powerful C++ library which in particular supports turbo codes; Turbo codes publications by David MacKay