Andrey Andreyevich Markov was a Russian mathematician best known for his work on stochastic processes. A primary subject of his research later became known as the Markov chain. He was also a strong, close to master-level chess player.
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as either "1" or "0", but other representations such as true/false, yes/no, on/off, or +/− are also widely used.
Basic English is a controlled language based on standard English, but with a greatly simplified vocabulary and grammar. It was created by the linguist and philosopher Charles Kay Ogden as an international auxiliary language, and as an aid for teaching English as a second language. It was presented in Ogden's 1930 book Basic English: A General Introduction with Rules and Grammar.
Claude Elwood Shannon was an American mathematician, electrical engineer, computer scientist and cryptographer known as the "father of information theory". He is credited alongside George Boole for laying the foundations of the Information Age.
Information theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering.
In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable , which takes values in the alphabet and is distributed according to , the entropy is
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term.
The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing. In practice, it is used to select band-limiting filters to keep aliasing below an acceptable amount when an analog signal is sampled or when sample rates are changed within a digital signal processing function.
Image compression is a type of data compression applied to digital images, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior results compared with generic data compression methods which are used for other digital data.
In the field of data compression, Shannon–Fano coding, named after Claude Shannon and Robert Fano, is a name given to two different but related techniques for constructing a prefix code based on a set of symbols and their probabilities.
Richard Wesley Hamming was an American mathematician whose work had many implications for computer engineering and telecommunications. His contributions include the Hamming code, the Hamming window, Hamming numbers, sphere-packing, Hamming graph concepts, and the Hamming distance.
John Wilder Tukey was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his name. He is also credited with coining the term bit and the first published use of the word software.
"Communication Theory of Secrecy Systems" is a paper published in 1949 by Claude Shannon discussing cryptography from the viewpoint of information theory. It is one of the foundational treatments of modern cryptography. His work has been described as a "turning point, and marked the closure of classical cryptography and the beginning of modern cryptography." It is also a proof that all theoretically unbreakable ciphers must have the same requirements as the one-time pad.
In information theory, the noisy-channel coding theorem, establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data nearly error-free up to a computable maximum rate through the channel. This result was presented by Claude Shannon in 1948 and was based in part on earlier work and ideas of Harry Nyquist and Ralph Hartley.
A timeline of events related to information theory, quantum information theory and statistical physics, data compression, error correcting codes and related subjects.
In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels.
The Shannon–Weaver model is one of the first and most influential models of communication. It was initially published in the 1948 paper A Mathematical Theory of Communication and explains communication in terms of five basic components: a source, a transmitter, a channel, a receiver, and a destination. The source produces the original message. The transmitter translates the message into a signal, which is sent using a channel. The receiver translates the signal back into the original message and makes it available to the destination. For a landline phone call, the person calling is the source. They use the telephone as a transmitter, which produces an electric signal that is sent through the wire as a channel. The person receiving the call is the destination and their telephone is the receiver.
The pragmatic theory of information is derived from Charles Sanders Peirce's general theory of signs and inquiry. Peirce explored a number of ideas about information throughout his career. One set of ideas is about the "laws of information" having to do with the logical properties of information. Another set of ideas about "time and thought" have to do with the dynamic properties of inquiry. All of these ideas contribute to the pragmatic theory of inquiry. Peirce set forth many of these ideas very early in his career, periodically returning to them on scattered occasions until the end, and they appear to be implicit in much of his later work on the logic of science and the theory of signs, but he never developed their implications to the fullest extent. The 20th century thinker Ernst Ulrich and his wife Christine von Weizsäcker reviewed the pragmatics of information; their work is reviewed by Gennert.
The Bell Labs Technical Journal was the in-house scientific journal for scientists of Nokia Bell Labs, published yearly by the IEEE society.
In the field of data compression, Shannon coding, named after its creator, Claude Shannon, is a lossless data compression technique for constructing a prefix code based on a set of symbols and their probabilities. It is suboptimal in the sense that it does not achieve the lowest possible expected code word length like Huffman coding does, and never better than but sometimes equal to the Shannon–Fano coding.
