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Elias Delta Coding
Elias δ code or Elias delta code is a universal code encoding the positive integers developed by Peter Elias. Encoding To code a number ''X'' ≥ 1: # Let ''N'' = ⌊log2 ''X''⌋; be the highest power of 2 in ''X'', so 2''N'' ≤ ''X'' < 2''N''+1. # Let ''L'' = ⌊log2 ''N''+1⌋ be the highest power of 2 in ''N''+1, so 2''L'' ≤ ''N''+1 < 2''L''+1. # Write ''L'' zeros, followed by # the ''L''+1-bit binary representation of ''N''+1, followed by # all but the leading bit (i.e. the last ''N'' bits) of ''X''. An equivalent way to express the same process: #Separate ''X'' into the highest power of 2 it contains (2''N'') and the remaining ''N'' binary digits. #Encode ''N''+1 with Elias gamma coding. #Append the remaining ''N'' binary digits to this representation of ''N''+1. To represent a number [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Universal Code (data Compression)
In data compression, a universal code for integers is a prefix code that maps the positive integers onto binary codewords, with the additional property that whatever the true probability distribution on integers, as long as the distribution is monotonic (i.e., ''p''(''i'') ≥ ''p''(''i'' + 1) for all positive ''i''), the expected lengths of the codewords are within a constant factor of the expected lengths that the optimal code for that probability distribution would have assigned. A universal code is ''asymptotically optimal'' if the ratio between actual and optimal expected lengths is bounded by a function of the information entropy of the code that, in addition to being bounded, approaches 1 as entropy approaches infinity. In general, most prefix codes for integers assign longer codewords to larger integers. Such a code can be used to efficiently communicate a message drawn from a set of possible messages, by simply ordering the set of messages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Peter Elias
Peter Elias (November 23, 1923 – December 7, 2001) was a pioneer in the field of information theory. Born in New Brunswick, New Jersey, he was a member of the Massachusetts Institute of Technology faculty from 1953 to 1991. In 1955, Elias introduced convolutional codes as an alternative to block codes. He also established the binary erasure channel and proposed list decoding of error-correcting codes as an alternative to unique decoding. Career Peter Elias was a member of the Massachusetts Institute of Technology faculty from 1953 to 1991. His students included Elwyn Berlekamp and he was a colleague of Claude Shannon. From 1957 until 1966, he served as one of three founding editors of ''Information and Control''. Awards Elias received the Claude E. Shannon Award of the IEEE Information Theory Society (1977); the Golden Jubilee Award for Technological Innovation of the IEEE Information Theory Society (1998); and the IEEE Richard W. Hamming Medal (2002). Family background ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Elias Gamma Coding
Elias \gamma code or Elias gamma code is a universal code encoding positive integers developed by Peter Elias. It is used most commonly when coding integers whose upper bound cannot be determined beforehand. Encoding To code a number ''x'' ≥ 1: # Let N = \lfloor \log_2 x \rfloor be the highest power of 2 it contains, so 2''N'' ≤ ''x'' < 2''N''+1. # Write out N zero bits, then # Append the binary form of x, an (N+1)-bit binary number. An equivalent way to express the same process: # Encode N in unary; that is, as N zeroes followed by a one. # Append the remaining N binary digits of x to this representation of N. To represent a number x, Elias gamma (γ) uses 2 \lfloor \log_2(x) \rfloor + 1 bits. The code begins (the implied probability distribution for the code is added for clarity): Decoding To decode an Elias gamma-coded integer: #Read and count 0s from the stream until you reach the first 1. Call this count of zeroes ''N''. #Considering the one that was r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set. A function is bijective if it is invertible; that is, a function f:X\to Y is bijective if and only if there is a function g:Y\to X, the ''inverse'' of , such that each of the two ways for composing the two functions produces an identity function: g(f(x)) = x for each x in X and f(g(y)) = y for each y in Y. For example, the ''multiplication by two'' defines a bijection from the integers to the even numbers, which has the ''division by two'' as its inverse function. A function is bijective if and only if it is both injective (or ''one-to-one'')—meaning that each element in the codomain is mappe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Comparison Of Data Serialization Formats
This is a comparison of data serialization formats, various ways to convert complex objects to sequences of bits. It does not include markup languages used exclusively as document file format A document file format is a Text file, text or binary file format for storing documents on a computer storage, storage media, especially for use by computers. There currently exists a multitude of incompatible document file formats. Examples of ...s. Overview Syntax comparison of human-readable formats Comparison of binary formats See also * Comparison of document markup languages References {{reflist External linksXML-QL Proposal discussing XML benefits Data serialization formats Persist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Zigzag Code
A zigzag is a pattern made up of small corners at variable angles, though constant within the zigzag, tracing a path between two parallel lines; it can be described as both jagged and fairly regular. In geometry, this pattern is described as a skew apeirogon. From the point of view of symmetry, a regular zigzag can be generated from a simple motif like a line segment by repeated application of a glide reflection. Although the origin of the word is unclear, its first printed appearances were in French-language books and ephemera of the late 17th century. Examples of zigzags * The trace of a triangle wave or a sawtooth wave is a zigzag. * Pinking shears are designed to cut cloth or paper with a zigzag edge, to lessen fraying. * In sewing, a ''zigzag stitch'' is a machine stitch in a zigzag pattern. * The zigzag arch is an architectural embellishment used in Islamic, Byzantine, Norman and Romanesque architecture. * In seismology, earthquakes recorded in a "zigzag line" form b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
JPEG
JPEG ( , short for Joint Photographic Experts Group and sometimes retroactively referred to as JPEG 1) is a commonly used method of lossy compression for digital images, particularly for those images produced by digital photography. The degree of compression can be adjusted, allowing a selectable trade off between storage size and image quality. JPEG typically achieves 10:1 compression with noticeable, but widely agreed to be acceptable perceptible loss in image quality. Since its introduction in 1992, JPEG has been the most widely used image compression standard in the world, and the most widely used digital image format, with several billion JPEG images produced every day as of 2015. The Joint Photographic Experts Group created the standard in 1992, based on the discrete cosine transform (DCT) algorithm. JPEG was largely responsible for the proliferation of digital images and digital photos across the Internet and later social media. JPEG compression is used in a number of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Elias Omega Coding
Elias ω coding or Elias omega coding is a universal code encoding the positive integers developed by Peter Elias. Like Elias gamma coding and Elias delta coding, it works by prefixing the positive integer with a representation of its order of magnitude in a universal code. Unlike those other two codes, however, Elias omega recursively encodes that prefix; thus, they are sometimes known as recursive Elias codes. Omega coding is used in applications where the largest encoded value is not known ahead of time, or to compress data in which small values are much more frequent than large values. To encode a positive integer ''N'': #Place a "0" at the end of the code. #If ''N'' = 1, stop; encoding is complete. #Prepend the binary representation of ''N'' to the beginning of the code. This will be at least two bits, the first bit of which is a 1. #Let ''N'' equal the number of bits just prepended, minus one. #Return to Step 2 to prepend the encoding of the new ''N''. To decode an El ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Golomb-Rice Code
Golomb coding is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb in the 1960s. Alphabets following a geometric distribution will have a Golomb code as an optimal prefix code, making Golomb coding highly suitable for situations in which the occurrence of small values in the input stream is significantly more likely than large values. Rice coding Rice coding (invented by Robert F. Rice) denotes using a subset of the family of Golomb codes to produce a simpler (but possibly suboptimal) prefix code. Rice used this set of codes in an adaptive coding scheme; "Rice coding" can refer either to that adaptive scheme or to using that subset of Golomb codes. Whereas a Golomb code has a tunable parameter that can be any positive integer value, Rice codes are those in which the tunable parameter is a power of two. This makes Rice codes convenient for use on a computer, since multiplication and division by 2 can be implemente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
IEEE Transactions On Information Theory
''IEEE Transactions on Information Theory'' is a monthly peer-reviewed scientific journal published by the IEEE Information Theory Society. It covers information theory and the mathematics of communications. It was established in 1953 as ''IRE Transactions on Information Theory''. The editor-in-chief is Venugopal V. Veeravalli (University of Illinois Urbana-Champaign). As of 2007, the journal allows the posting of preprints on arXiv. According to Jack van Lint, it is the leading research journal in the whole field of coding theory. A 2006 study using the PageRank network analysis algorithm found that, among hundreds of computer science-related journals, ''IEEE Transactions on Information Theory'' had the highest ranking and was thus deemed the most prestigious. ''ACM Computing Surveys'', with the highest impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 an expected code length greater than 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 \operatorname E_ ell(d(x))\geq \operatorname E_ \log_b(P(x))/math>, where \ell is the function specifying 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 simple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Numeral Systems
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number ''eleven'' in the decimal or base-10 numeral system (today, the most common system globally), the number ''three'' in the binary or base-2 numeral system (used in modern computers), and the number ''two'' in the unary numeral system (used in tallying scores). The number the numeral represents is called its ''value''. Additionally, not all number systems can represent the same set of numbers; for example, Roman, Greek, and Egyptian numerals don't have a representation of the number zero. Ideally, a numeral system will: *Represent a useful set of numbers (e.g. all integers, or rational numbers) *Give every number represented a unique representation (or at lea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
