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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 specified bandwidth in the presence of the noise interference, assuming that the signal power is bounded, and that the Gaussian noise process is characterized by a ...
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.
Shannon originally wrote down the following formula for the entropy of a continuous distribution, known as differential entropy: = ().Unlike Shannon's formula for the discrete entropy, however, this is not the result of any derivation (Shannon simply replaced the summation symbol in the discrete version with an integral), and it lacks many of the properties that make the discrete entropy a ...
Information-theoretic analysis of communication systems that incorporate feedback is more complicated and challenging than without feedback. Possibly, this was the reason C.E. Shannon chose feedback as the subject of the first Shannon Lecture, delivered at the 1973 IEEE International Symposium on Information Theory in Ashkelon, Israel.
For example, David Ellerman's analysis of a "logic of partitions" defines a competing measure in structures dual to that of subsets of a universal set. [14] Information is quantified as "dits" (distinctions), a measure on partitions. "Dits" can be converted into Shannon's bits, to get the formulas for conditional entropy, and so on.
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:
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A misleading [1] information diagram showing additive and subtractive relationships among Shannon's basic quantities of information for correlated variables and . The area contained by both circles is the joint entropy H ( X , Y ) {\displaystyle \mathrm {H} (X,Y)} .