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Information-theoretic
Information theory is the mathematical study of the quantification, storage, and communication of information. The field was established and formalized by Claude Shannon in the 1940s, though early contributions were made in the 1920s through the works of Harry Nyquist and Ralph Hartley. It is at the intersection of electronic engineering, mathematics, statistics, computer science, neurobiology, physics, and electrical engineering. A key measure in information theory is 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 (which has two equally likely outcomes) provides less information (lower entropy, less uncertainty) than identifying the outcome from a roll of a die (which has six equally likely outcomes). Some other important measures in information theory are mutual information, channel capacity, error exponents, and relative entropy. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information-theoretic Security
A cryptosystem is considered to have information-theoretic security (also called unconditional security) if the system is secure against adversaries with unlimited computing resources and time. In contrast, a system which depends on the computational cost of cryptanalysis to be secure (and thus can be broken by an attack with unlimited computation) is called computationally secure or conditionally secure. Overview An encryption protocol with information-theoretic security is impossible to break even with infinite computational power. Protocols proven to be information-theoretically secure are resistant to future developments in computing. The concept of information-theoretically secure communication was introduced in 1949 by American mathematician Claude Shannon, one of the founders of classical information theory, who used it to prove the one-time pad system was secure. Information-theoretically secure cryptosystems have been used for the most sensitive governmental communic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information
Information is an Abstraction, abstract concept that refers to something which has the power Communication, to inform. At the most fundamental level, it pertains to the Interpretation (philosophy), interpretation (perhaps Interpretation (logic), formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any Media (communication), medium can be said to convey some amount of information. Whereas digital signals and other data use discrete Sign (semiotics), signs to convey information, other phenomena and artifacts such as analog signals, analogue signals, poems, pictures, music or other sounds, and current (fluid), currents convey information in a more continuous form. Information is not knowledge itself, but the meaning (philosophy), meaning that may be derived from a representation (mathematics), representation through interpretation. The concept of ''information'' is relevant or connected t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmic Complexity Theory
In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that produces the object as output. It is a measure of the computational resources needed to specify the object, and is also known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It is named after Andrey Kolmogorov, who first published on the subject in 1963 and is a generalization of classical information theory. The notion of Kolmogorov complexity can be used to state and prove impossibility results akin to Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program ''P'' computing a lower bound for each text's Kolmogorov complexity can return a value essentially larger than ''P'''s own len ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Exponent
In information theory, the error exponent of a channel code or source code over the block length of the code is the rate at which the error probability decays exponentially with the block length of the code. Formally, it is defined as the limiting ratio of the negative logarithm of the error probability to the block length of the code for large block lengths. For example, if the probability of error P_ of a decoder drops as e^, where n is the block length, the error exponent is \alpha. In this example, \frac approaches \alpha for large n. Many of the information-theoretic theorems are of asymptotic nature, for example, the channel coding theorem states that for any rate less than the channel capacity, the probability of the error of the channel code can be made to go to zero as the block length goes to infinity. In practical situations, there are limitations to the delay of the communication and the block length must be finite. Therefore, it is important to study how the prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutual Information
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual Statistical dependence, dependence between the two variables. More specifically, it quantifies the "Information content, amount of information" (in Units of information, units such as shannon (unit), shannons (bits), Nat (unit), nats or Hartley (unit), hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of Entropy (information theory), entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable. Not limited to real-valued random variables and linear dependence like the Pearson correlation coefficient, correlation coefficient, MI is more general and determines how different the joint distribution of the pair (X,Y) is from the product of the marginal distributions of X and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantification (science)
In mathematics and empirical science, quantification (or quantitation) is the act of counting and measuring that maps human sense observations and experiences into quantity, quantities. Quantification in this sense is fundamental to the scientific method. Natural science Some measure of the undisputed general importance of quantification in the natural sciences can be gleaned from the following comments: * "these are mere facts, but they are quantitative facts and the basis of science." * It seems to be held as universally true that "the foundation of quantification is measurement." * There is little doubt that "quantification provided a basis for the objectivity of science." * In ancient times, "musicians and artists ... rejected quantification, but merchants, by definition, quantified their affairs, in order to survive, made them visible on parchment and paper." * Any reasonable "comparison between Aristotle and Galileo shows clearly that there can be no unique lawfulness discov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Coin
In probability theory and statistics, a sequence of Independence (probability theory), independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin. In theoretical studies, the assumption that a coin is fair is often made by referring to an ideal coin. John Edmund Kerrich performed experiments in coin flipping and found that a coin made from a wooden disk about the size of a Crown (British coin), crown and coated on one side with lead landed heads (wooden side up) 679 times out of 1000. In this experiment the coin was tossed by balancing it on the forefinger, flipping it using the thumb so that it spun through the air for about a foot before landing on a flat cloth spread over a table. Edwin Thompson Jaynes claimed that when a coin is caught in the hand, instead of being allowed to bounce, the physical bias in the coin is insignificant compared to the met ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Detection And Correction
In information theory and coding theory with applications in computer science and telecommunications, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Definitions ''Error detection'' is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. ''Error correction'' is the detection of errors and reconstruction of the original, error-free data. History In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ZIP (file Format)
ZIP is an archive file format that supports lossless compression, lossless data compression. A ZIP file may contain one or more files or directories that may have been compressed. The ZIP file format permits a number of Data compression, compression algorithms, though DEFLATE is the most common. This format was originally created in 1989 and was first implemented in PKWARE, Inc.'s PKZIP utility, as a replacement for the previous ARC (file format), ARC compression format by Thom Henderson. The ZIP format was then quickly supported by many software utilities other than PKZIP. Microsoft has included built-in ZIP support (under the name "compressed folders") in versions of Microsoft Windows since 1998 via the "Plus! 98" addon for Windows 98. Native support was added as of the year 2000 in Windows ME. Apple has included built-in ZIP support in macOS, Mac OS X 10.3 (via BOMArchiveHelper, now Archive Utility) and later. Most :Free software operating systems, free operating s ... [...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 is 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 sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Source Coding
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 is 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 sign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
