Shannon (unit)

Units of
information
Information-theoretic
Data storage
Quantum information

The shannon (symbol: Sh) is a unit of information named after Claude Shannon, the founder of information theory. IEC 80000-13 defines the shannon as the information content associated with an event when the probability of the event occurring is ⁠1/2⁠. It is understood as such within the realm of information theory, and is conceptually distinct from the bit, a term used in data processing and storage to denote a single instance of a binary signal. A sequence of n binary symbols (such as contained in computer memory or a binary data transmission) is properly described as consisting of n bits, but the information content of those n symbols may be more or less than n shannons depending on the a priori probability of the actual sequence of symbols.[1]

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, which is reached when the possible outcomes are equiprobable. The maximum entropy of n bits is n Sh. A further quantity that it is used for is channel capacity, which is generally the maximum of the expected value of the information content encoded over a channel that can be transferred with negligible probability of error, typically in the form of an information rate.

Nevertheless, the term bits of information or simply bits is more often heard, even in the fields of information and communication theory, rather than shannons; just saying bits can therefore be ambiguous. Using the unit shannon is an explicit reference to a quantity of information content, information entropy or channel capacity, and is not restricted to binary data,[2] whereas "bits" can as well refer to the number of binary symbols involved, as is the term used in fields such as data processing.

  1. ^ Since the information associated with an event outcome that has a priori probability p, e.g. that a single given data bit takes the value 0, is given by H = −log p, and p can lie anywhere in the range 0 < p ≤ 1, the information content can lie anywhere in the range 0 ≤ H < ∞.
  2. ^ Olivier Rioul (2018). "This is IT: A primer on Shannon's entropy and Information" (PDF). L'Information, Séminaire Poincaré. XXIII: 43–77. Retrieved 2021-05-23. The Système International d'unités recommends the use of the shannon (Sh) as the information unit in place of the bit to distinguish the amount of information from the quantity of data that may be used to represent this information. Thus, according to the SI standard, H(X) should actually be expressed in shannons. The entropy of one bit lies between 0 and 1 Sh.