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It is an application of the noisy-channel coding theorem to the archetypal case of a continuous-time analog communications channel subject to Gaussian noise. The theorem establishes Shannon's channel capacity for such a communication link, a bound on the maximum amount of error-free information per time unit that can be transmitted with a ...
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 feedback capacity is known as a closed-form expression only for several examples such as the trapdoor channel, [14] Ising channel, [15] [16]. For some other channels, it is characterized through constant-size optimization problems such as the binary erasure channel with a no-consecutive-ones input constraint [ 17 ] , NOST channel [ 18 ] .
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:
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.
Forney constructed a concatenated code = to achieve the capacity of the noisy-channel coding theorem for . In his code, In his code, The outer code C out {\displaystyle C_{\text{out}}} is a code of block length N {\displaystyle N} and rate 1 − ϵ 2 {\displaystyle 1-{\frac {\epsilon }{2}}} over the field F 2 k {\displaystyle F_{2^{k}}} , and k ...
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In general, a stronger code induces more redundancy that needs to be transmitted using the available bandwidth, which reduces the effective bit-rate while improving the received effective signal-to-noise ratio. The noisy-channel coding theorem of Claude Shannon can be used to compute the maximum achievable communication bandwidth for a given ...