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The shannon also serves as a unit of the information entropy of an event, which is defined as the expected value of the information content of the event (i.e., the probability-weighted average of the information content of all potential events). Given a number of possible outcomes, unlike information content, the entropy has an upper bound ...
The concept of information entropy was introduced by Claude Shannon in his 1948 paper "A Mathematical Theory of Communication", [2] [3] and is also referred to as Shannon entropy. Shannon's theory defines a data communication system composed of three elements: a source of data, a communication channel, and a receiver. The "fundamental problem ...
Common values of b are 2, Euler's number e, and 10, and the unit of entropy is shannon (or bit) for b = 2, nat for b = e, and hartley for b = 10. [ 1 ] Mathematically H may also be seen as an average information, taken over the message space, because when a certain message occurs with probability p i , the information quantity −log( p i ...
The most common unit of information is the bit, or more correctly the shannon, [2] based on the binary logarithm. Although bit is more frequently used in place of shannon, its name is not distinguished from the bit as used in data processing to refer to a binary value or stream regardless of its entropy (information content). Other units ...
Shannon entropy (information entropy), being the expected value of the information of an event, is inherently a quantity of the same type and with a unit of information. The International System of Units, by assigning the same unit (joule per kelvin) both to heat capacity and to thermodynamic entropy implicitly treats information entropy as a quantity of dimension one, with 1 nat = 1.
The Shannon information is closely related to entropy, which is the expected value of the self-information of a random variable, quantifying how surprising the random variable is "on average". This is the average amount of self-information an observer would expect to gain about a random variable when measuring it.
If the base of the logarithm is 2, then the unit of uncertainty is the shannon (more commonly known as bit). If it is the natural logarithm, then the unit is the nat. Hartley used a base-ten logarithm, and with this base, the unit of information is called the hartley (aka ban or dit) in his honor. It is also known as the Hartley entropy or max ...
Other information-theoretic measures such as conditional information, mutual information, or total correlation can be expressed in terms of joint entropy and are thus related by the corresponding inequalities. Many inequalities satisfied by entropic vectors can be derived as linear combinations of a few basic ones, called Shannon-type inequalities.