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Shannon's Source Coding Theorem
In information theory, Shannon's source coding theorem (or noiseless coding theorem) establishes the limits to possible data compression, and the operational meaning of the Shannon entropy. Named after Claude Shannon, the source coding theorem shows that (in the limit, as the length of a stream of independent and identically-distributed random variable (i.i.d.) data tends to infinity) it is impossible to compress the data such that the code rate (average number of bits per symbol) is less than the Shannon entropy of the source, without it being virtually certain that information will be lost. However it is possible to get the code rate arbitrarily close to the Shannon entropy, with negligible probability of loss. The source coding theorem for symbol codes places an upper and a lower bound on the minimal possible expected length of codewords as a function of the entropy of the input word (which is viewed as a random variable) and of the size of the target alphabet. Statements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Information Theory
Information theory is the scientific 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 is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, 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 (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a die (with six equally likely outcomes). Some other important measures in information theory are mutual information, channel capacity, error exponents, and relative entropy. Important sub-fields of information theory include sourc ... [...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 h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Presentation Layer Protocols
A presentation conveys information from a speaker to an audience. Presentations are typically demonstrations, introduction, lecture, or speech meant to inform, persuade, inspire, motivate, build goodwill, or present a new idea/product. Presentations usually require preparation, organization, event planning, writing, use of visual aids, dealing with stress, and answering questions. “The key elements of a presentation consists of presenter, audience, message, reaction and method to deliver speech for organizational success in an effective manner.” Presentations are widely used in tertiary work settings such as accountants giving a detailed report of a company's financials or an entrepreneur pitching their venture idea to investors. The term can also be used for a formal or ritualized introduction or offering, as with the presentation of a debutante. Presentations in certain formats are also known as keynote address. Interactive presentations, in which the audience is involved, ... [...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] |
Coding Theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. There are four types of coding: # Data compression (or ''source coding'') # Error control (or ''channel coding'') # Cryptographic coding # Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, ZIP data compression makes data files smaller, for purposes such as to reduce Internet traffic. Data compression and er ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell System Technical Journal
The ''Bell Labs Technical Journal'' is the in-house scientific journal for scientists of Nokia Bell Labs, published yearly by the IEEE society. The managing editor is Charles Bahr. The journal was originally established as the ''Bell System Technical Journal'' (BSTJ) in New York by the American Telephone and Telegraph Company (AT&T) in 1922, published under this name until 1983, when the breakup of the Bell System placed various parts of the system into separate companies. The journal was devoted to the scientific fields and engineering disciplines practiced in the Bell System for improvements in the wide field of electrical communication. After the restructuring of Bell Labs in 1984, the journal was renamed to ''AT&T Bell Laboratories Technical Journal''. In 1985, it was published as the ''AT&T Technical Journal'' until 1996, when it was renamed to ''Bell Labs Technical Journal''. History The ''Bell System Technical Journal'' was published by AT&T in New York City through its ... [...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 probabi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noisy-channel Coding Theorem
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (digital information) 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. The Shannon limit or Shannon capacity of a communication channel refers to the maximum rate of error-free data that can theoretically be transferred over the channel if the link is subject to random data transmission errors, for a particular noise level. It was first described by Shannon (1948), and shortly after published in a book by Shannon and Warren Weaver entitled '' The Mathematical Theory of Communication'' (1949). This founded the modern discipline of information theory. Overview Stated by Claude Shann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Channel Coding
In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is the sender encodes the message with redundant information in the form of an ECC. The redundancy allows the receiver to detect a limited number of errors that may occur anywhere in the message, and often to correct these errors without retransmission. The American mathematician Richard Hamming pioneered this field in the 1940s and invented the first error-correcting code in 1950: the Hamming (7,4) code. ECC contrasts with error detection in that errors that are encountered can be corrected, not simply detected. The advantage is that a system using ECC does not require a reverse channel to request retransmission of data when an error occurs. The downside is that there is a fixed overhead that is added to the message, thereby requiring ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs' Inequality
200px, Josiah Willard Gibbs In information theory, Gibbs' inequality is a statement about the information entropy of a discrete probability distribution. Several other bounds on the entropy of probability distributions are derived from Gibbs' inequality, including Fano's inequality. It was first presented by J. Willard Gibbs in the 19th century. Gibbs' inequality Suppose that : P = \ is a discrete probability distribution. Then for any other probability distribution : Q = \ the following inequality between positive quantities (since pi and qi are between zero and one) holds: : - \sum_^n p_i \log p_i \leq - \sum_^n p_i \log q_i with equality if and only if : p_i = q_i for all ''i''. Put in words, the information entropy of a distribution P is less than or equal to its cross entropy with any other distribution Q. The difference between the two quantities is the Kullback–Leibler divergence or relative entropy, so the inequality can also be written: : D_(P\, Q) \equiv \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Equipartition Property
In information theory, the asymptotic equipartition property (AEP) is a general property of the output samples of a stochastic source. It is fundamental to the concept of typical set used in theories of data compression. Roughly speaking, the theorem states that although there are many series of results that may be produced by a random process, the one actually produced is most probably from a loosely defined set of outcomes that all have approximately the same chance of being the one actually realized. (This is a consequence of the law of large numbers and ergodic theory.) Although there are individual outcomes which have a higher probability than any outcome in this set, the vast number of outcomes in the set almost guarantees that the outcome will come from the set. One way of intuitively understanding the property is through Cramér's large deviation theorem, which states that the probability of a large deviation from mean decays exponentially with the number of samples. Such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
