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Slepian–Wolf Coding
__NOTOC__ In information theory and communication, the Slepian–Wolf coding, also known as the Slepian–Wolf bound, is a result in distributed source coding discovered by David Slepian and Jack Wolf in 1973. It is a method of theoretically coding two lossless compressed correlated sources. Problem setup Distributed coding is the coding of two, in this case, or more dependent sources with separate encoders and a joint decoder. Given two statistically dependent independent and identically distributed finite-alphabet random sequences X^n and Y^n, the Slepian–Wolf theorem gives a theoretical bound for the lossless coding rate for distributed coding of the two sources. Theorem The bound for the lossless coding rates as shown below: : R_X\geq H(X, Y), \, : R_Y\geq H(Y, X), \, : R_X+R_Y\geq H(X,Y). \, If both the encoder and the decoder of the two sources are independent, the lowest rate it can achieve for lossless compression is H(X) and H(Y) for X and Y respectively, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, 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 is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering (field), information engineering, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a dice, die (with six equally likely outcomes). Some other important measures in information theory are mutual informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, weather science, climate change, and information systems including the transmission of information in telecommunication. The thermodynamic concept was referred to by Scottish scientist and engineer William Rankine in 1850 with the names ''thermodynamic function'' and ''heat-potential''. In 1865, German physicist Rudolf Clausius, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of hea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timeline Of Information Theory
A timeline of events related to information theory, quantum information theory and statistical physics, data compression, error correcting codes and related subjects. * 1872 – Ludwig Boltzmann presents his H-theorem, and with it the formula Σ''p''i log ''p''i for the entropy of a single gas particle * 1878 – J. Willard Gibbs defines the Gibbs entropy: the probabilities in the entropy formula are now taken as probabilities of the state of the ''whole'' system * 1924 – Harry Nyquist discusses quantifying "intelligence" and the speed at which it can be transmitted by a communication system * 1927 – John von Neumann defines the von Neumann entropy, extending the Gibbs entropy to quantum mechanics * 1928 – Ralph Hartley introduces Hartley information as the logarithm of the number of possible messages, with information being communicated when the receiver can distinguish one sequence of symbols from any other (regardless of any associated meaning) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchronization (computer Science)
In computer science, synchronization refers to one of two distinct but related concepts: synchronization of processes, and synchronization of data. ''Process synchronization'' refers to the idea that multiple processes are to join up or handshake at a certain point, in order to reach an agreement or commit to a certain sequence of action. ''Data synchronization'' refers to the idea of keeping multiple copies of a dataset in coherence with one another, or to maintain data integrity. Process synchronization primitives are commonly used to implement data synchronization. The need for synchronization The need for synchronization does not arise merely in multi-processor systems but for any kind of concurrent processes; even in single processor systems. Mentioned below are some of the main needs for synchronization: '' Forks and Joins:'' When a job arrives at a fork point, it is split into N sub-jobs which are then serviced by n tasks. After being serviced, each sub-job waits until al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Synchronization
Data synchronization is the process of establishing consistency between source and target data stores, and the continuous harmonization of the data over time. It is fundamental to a wide variety of applications, including file synchronization and mobile device synchronization. Data synchronization can also be useful in encryption for synchronizing public key servers. File-based solutions There are tools available for file synchronization, version control ( CVS, Subversion, etc.), distributed filesystems (Coda, etc.), and mirroring (rsync, etc.), in that all these attempt to keep sets of files synchronized. However, only version control and file synchronization tools can deal with modifications to more than one copy of the files. * File synchronization is commonly used for home backups on external hard drives or updating for transport on USB flash drives. The automatic process prevents copying already identical files, thus can save considerable time relative to a manual copy, al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Compression
In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. Typically, a device that performs data compression is referred to as an encoder, and one that performs the reversal of the process (decompression) as a decoder. The process of reducing the size of a data file is often referred to as data compression. In the context of data transmission, it is called source coding; encoding done at the source of the data before it is stored or transmitted. Source coding should not be confused with channel coding, for error detection and correction or line coding, the means for mapping data onto a signal. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Ziv
Jacob Ziv ( he, יעקב זיו; born 1931) is an Israeli electrical engineer who, along with Abraham Lempel, developed the LZ family of lossless data compression algorithms. Biography Ziv was born in Tiberias, British mandate Palestine, on 27 November 1931. He received the B.Sc., Dip. Eng., and M.Sc. degrees, all in electrical engineering, from the Technion – Israel Institute of Technology in 1954, and 1957, respectively, and the D.Sc. degree from the Massachusetts Institute of Technology in 1962. Ziv joined the Technion – Israel Institute of Technology in 1970 and is Herman Gross Professor of Electrical Engineering and a Technion Distinguished Professor. His research interests include data compression, information theory, and statistical communication theory. Ziv was Dean of the Faculty of Electrical Engineering from 1974 to 1976 and Vice President for Academic Affairs from 1978 to 1982. Since 1987 Ziv has spent three sabbatical leaves at the Information Research De ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aaron D
According to Abrahamic religions, Aaron ''′aharon'', ar, هارون, Hārūn, Greek (Septuagint): Ἀαρών; often called Aaron the priest ()., group="note" ( or ; ''’Ahărōn'') was a prophet, a high priest, and the elder brother of Moses. Knowledge of Aaron, along with his brother Moses, exclusively comes from religious texts, such as the Hebrew Bible, Bible and the Quran. The Hebrew Bible relates that, unlike Moses, who grew up in the Egyptian royal court, Aaron and his elder sister Miriam remained with their kinsmen in the eastern border-land of Egypt ( Goshen). When Moses first confronted the Egyptian king about the enslavement of the Israelites, Aaron served as his brother's spokesman ("prophet") to the Pharaoh (). Part of the Law given to Moses at Sinai granted Aaron the priesthood for himself and his male descendants, and he became the first High Priest of the Israelites. Aaron died before the Israelites crossed the Jordan river. According to the Book of Numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas M
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Illinois * Thomas, Indiana * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts, entertainment, and media * ''Thomas'' (Burton novel) 1969 novel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Of Error
In statistics, the term "error" arises in two ways. Firstly, it arises in the context of decision making, where the probability of error may be considered as being the probability of making a wrong decision and which would have a different value for each type of error. Secondly, it arises in the context of statistical modelling (for example regression) where the model's predicted value may be in error regarding the observed outcome and where the term probability of error may refer to the probabilities of various amounts of error occurring. Hypothesis testing In hypothesis testing in statistics, two types of ''error'' are distinguished. *Type I errors which consist of rejecting a null hypothesis that is true; this amounts to a false positive result. *Type II errors which consist of failing to reject a null hypothesis that is false; this amounts to a false negative result. The probability of error is similarly distinguished. * For a Type I error, it is shown as α (alpha) and is kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
