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This formula's way of introducing frequency-dependent noise cannot describe all continuous-time noise processes. For example, consider a noise process consisting of adding a random wave whose amplitude is 1 or −1 at any point in time, and a channel that adds such a wave to the source signal. Such a wave's frequency components are highly ...
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.
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.
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.
In the above formula, P is measured in units of power, such as watts (W) or milliwatts (mW), and the signal-to-noise ratio is a pure number. However, when the signal and noise are measured in volts (V) or amperes (A), which are measures of amplitude, [ note 1 ] they must first be squared to obtain a quantity proportional to power, as shown below:
The landmark event establishing the discipline of information theory and bringing it to immediate worldwide attention was the publication of Claude E. Shannon's classic paper "A Mathematical Theory of Communication" in the Bell System Technical Journal in July and October 1948.
Here, information is measured in shannons, nats, or hartleys. ... Let have probability mass function (). The unconditional entropy of is calculated ...
In information theory, the source coding theorem (Shannon 1948) [2] informally states that (MacKay 2003, pg. 81, [3] Cover 2006, Chapter 5 [4]): N i.i.d. random variables each with entropy H(X) can be compressed into more than N H(X) bits with negligible risk of information loss, as N → ∞; but conversely, if they are compressed into fewer than N H(X) bits it is virtually certain that ...