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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 ...
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 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 ] .
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 ...
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 ...
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:
In the case of communication of information over a noisy channel, this abstract concept was formalized in 1948 by Claude Shannon in a paper entitled A Mathematical Theory of Communication, in which information is thought of as a set of possible messages, and the goal is to send these messages over a noisy channel, and to have the receiver ...
However, suppose that when a value is sent across the channel, the value that is received is + (mod 5) where represents the noise on the channel and may be any real number in the open interval from −1 to 1. Thus, if the recipient receives a value such as 3.6, it is impossible to determine whether it was originally transmitted as a 3 or as a 4 ...