|
Range Coding
Range coding (or range encoding) is an entropy coding method defined by G. Nigel N. Martin in a 1979 paper,, 100000)) using the probability distribution . The encoder breaks down the range [0, 100000) into three subranges: A: [ 0, 60000) B: [ 60000, 80000) : [ 80000, 100000) Since our first symbol is an A, it reduces our initial range down to [0, 60000). The second symbol choice leaves us with three sub-ranges of this range. We show them following the already-encoded 'A': AA: [ 0, 36000) AB: [ 36000, 48000) A: [ 48000, 60000) With two symbols encoded, our range is now [0, 36000) and our third symbol leads to the following choices: AAA: [ 0, 21600) AAB: [ 21600, 28800) AA: [ 28800, 36000) This time it is the second of our three choices that represent the message we want to encode, and our range becomes [21600, 28800). It may look harder to determine our sub-ranges in this case, but it is actually not: we can mer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy Coding
In information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method must have expected code length greater or equal to the entropy of the source. More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies \mathbb E_(d(x))\geq \mathbb E_ \log_b(P(x))/math>, where l is the number of symbols in a code word, d is the coding function, b is the number of symbols used to make output codes and P is the probability of the source symbol. An entropy coding attempts to approach this lower bound. Two of the most common entropy coding techniques are Huffman coding and arithmetic coding. If the approximate entropy characteristics of a data stream are known in advance (especially for signal compression), a simpler static code may be useful. These static codes i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Numeral System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" ( zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was spec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shannon–Fano Coding
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 (estimated or measured). * Shannon's method chooses a prefix code where a source symbol i is given the codeword length l_i = \lceil - \log_2 p_i\rceil. One common way of choosing the codewords uses the binary expansion of the cumulative probabilities. This method was proposed in Shannon's "A Mathematical Theory of Communication" (1948), his article introducing the field of information theory. * Fano's method divides the source symbols into two sets ("0" and "1") with probabilities as close to 1/2 as possible. Then those sets are themselves divided in two, and so on, until each set contains only one symbol. The codeword for that symbol is the string of "0"s and "1"s that records which half of the divides it fell on. This method was proposed in a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiscale Electrophysiology Format
Multiscale Electrophysiology Format (MEF) was developed to handle the large amounts of data produced by large-scale electrophysiology in human and animal subjects. MEF can store any time series data up to 24 bits in length, and employs lossless range encoded difference compression. Subject identifying information in the file header can be encrypted using 128-bit AES encryption in order to comply with HIPAA requirements for patient privacy when transmitting data across an open network. Compressed data is stored in independent blocks to allow direct access to the data, facilitate parallel processing and limit the effects of potential damage to files. Data fidelity is ensured by a 32-bit cyclic redundancy check in each compressed data block using the Koopman polynomial (0xEB31D82E), which has a Hamming distance of from 4 to 114 kbits. A formal specification and source code are available online. MEF_import is an EEGLAB plugin to import MEF data into EEGLAB. See also * Range encodin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy Encoding
In information theory, an entropy coding (or entropy encoding) is any lossless data compression method that attempts to approach the lower bound declared by Shannon's source coding theorem, which states that any lossless data compression method must have expected code length greater or equal to the entropy of the source. More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies \mathbb E_(d(x))\geq \mathbb E_ \log_b(P(x))/math>, where l is the number of symbols in a code word, d is the coding function, b is the number of symbols used to make output codes and P is the probability of the source symbol. An entropy coding attempts to approach this lower bound. Two of the most common entropy coding techniques are Huffman coding and arithmetic coding. If the approximate entropy characteristics of a data stream are known in advance (especially for signal compression), a simpler static code may be useful. These static codes ... [...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] |
Asymmetric Numeral Systems
Asymmetric numeral systems (ANS)J. Duda, K. Tahboub, N. J. Gadil, E. J. Delp''The use of asymmetric numeral systems as an accurate replacement for Huffman coding'' Picture Coding Symposium, 2015.J. Duda''Asymmetric numeral systems: entropy coding combining speed of Huffman coding with compression rate of arithmetic coding'' arXiv:1311.2540, 2013. is a family of entropy encoding methods introduced by Jarosław (Jarek) Duda from Jagiellonian University, used in data compression since 2014 due to improved performance compared to previous methods. ANS combines the compression ratio of arithmetic coding (which uses a nearly accurate probability distribution), with a processing cost similar to that of Huffman coding. In the tabled ANS (tANS) variant, this is achieved by constructing a finite-state machine to operate on a large alphabet without using multiplication. Among others, ANS is used in the Facebook Zstandard compressor [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fraction (mathematics)
A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A ''common'', ''vulgar'', or ''simple'' fraction (examples: \tfrac and \tfrac) consists of a numerator, displayed above a line (or before a slash like ), and a non-zero denominator, displayed below (or after) that line. Numerators and denominators are also used in fractions that are not ''common'', including compound fractions, complex fractions, and mixed numerals. In positive common fractions, the numerator and denominator are natural numbers. The numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. The denominator cannot be zero, because zero parts can never make up a whole. For example, in the fraction , the numerator 3 indicates that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Coding
Arithmetic coding (AC) is a form of entropy encoding used in lossless data compression. Normally, a string of characters is represented using a fixed number of bits per character, as in the ASCII code. When a string is converted to arithmetic encoding, frequently used characters will be stored with fewer bits and not-so-frequently occurring characters will be stored with more bits, resulting in fewer bits used in total. Arithmetic coding differs from other forms of entropy encoding, such as Huffman coding, in that rather than separating the input into component symbols and replacing each with a code, arithmetic coding encodes the entire message into a single number, an arbitrary-precision fraction ''q'', where . It represents the current information as a range, defined by two numbers. A recent family of entropy coders called asymmetric numeral systems allows for faster implementations thanks to directly operating on a single natural number representing the current information ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a rando ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Southampton
Southampton () is a port city in the ceremonial county of Hampshire in southern England. It is located approximately south-west of London and west of Portsmouth. The city forms part of the South Hampshire built-up area, which also covers Portsmouth and the towns of Havant, Waterlooville, Eastleigh, Fareham and Gosport. A major port, and close to the New Forest, it lies at the northernmost point of Southampton Water, at the confluence of the River Test and Itchen, with the River Hamble joining to the south. Southampton is classified as a Medium-Port City . Southampton was the departure point for the and home to 500 of the people who perished on board. The Spitfire was built in the city and Southampton has a strong association with the ''Mayflower'', being the departure point before the vessel was forced to return to Plymouth. In the past century, the city was one of Europe's main ports for ocean liners and more recently, Southampton is known as the home port of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A ''decimal numeral'' (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the #Decimal fractions, decimal fractions. That is, fraction (mathematics), fract ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Probability Distribution")
