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Uniquely Decodable Code
In coding theory a variable-length code is a code which maps source symbols to a variable number of bits. Variable-length codes can allow sources to be compressed and decompressed with zero error (lossless data compression) and still be read back symbol by symbol. With the right coding strategy an independent and identically-distributed source may be compressed almost arbitrarily close to its entropy
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Variable-width Encoding
A variable-width encoding is a type of character encoding scheme in which codes of differing lengths are used to encode a character set (a repertoire of symbols) for representation in a computer. Most common variable-width encodings are multibyte encodings, which use varying numbers of bytes (octets) to encode different characters. (Some authors, notably in Microsoft documentation, use the term multibyte character set, which is a misnomer, because representation size is an attribute of the encoding, not of the character set). Early variable width encodings using less than a byte per character were sometimes used to pack English text into fewer bytes in adventure games for early microcomputers
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Shannon–Fano–Elias Coding
In information theory, Shannon–Fano–Elias coding is a precursor to arithmetic coding, in which probabilities are used to determine codewords.[1]Contents1 Algorithm description1.1 Example2 Algorithm analysis2.1 Prefix code 2.2 Code length3 ReferencesAlgorithm description[edit] Given a discrete random variable X of ordered values to be encoded, let p ( x ) displaystyle p(x) be the probability for any x in X
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Entropy Encoding
In information theory an entropy encoding is a lossless data compression scheme that is independent of the specific characteristics of the medium. One of the main types of entropy coding creates and assigns a unique prefix-free code to each unique symbol that occurs in the input. These entropy encoders then compress data by replacing each fixed-length input symbol with the corresponding variable-length prefix-free output codeword. The length of each codeword is approximately proportional to the negative logarithm of the probability
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Unary Coding
Unary coding,[nb 1] sometimes called thermometer code, is an entropy encoding that represents a natural number, n, with n ones followed by a zero (if natural number is understood as non-negative integer) or with n − 1 ones followed by a zero (if natural number is understood as strictly positive integer). For example 5 is represented as 111110 or 11110. Some representations use n or n − 1 zeros followed by a one. The ones and zeros are interchangeable without loss of generality
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Asymmetric Numeral Systems
Asymmetric numeral systems
Asymmetric numeral systems
(ANS) [1] is a family of entropy coding methods introduced by dr Jarosław (Jarek) Duda [2], used in data compression since 2014[3] due to improved performance compared to the previously used methods, being up to 30 times faster. [4]. 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
Facebook
Zstandard
Zstandard
compressor [5] (also used e.g
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Golomb Coding
Golomb coding
Golomb coding
is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb
Solomon W. Golomb
in the 1960s. Alphabets following a geometric distribution will have a Golomb code as an optimal prefix code,[1] making Golomb coding
Golomb coding
highly suitable for situations in which the occurrence of small values in the input stream is significantly more likely than large values.Contents1 Rice coding 2 Overview2.1 Construction of codes 2.2 Use with signed integers3 Simple algorithm 4 Example 5 Use for run-length encoding 6 Adaptive Run-Length Golomb-Rice encoding 7 Applications 8 References 9 External linksRice coding[edit] 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
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Adaptive Huffman Coding
Adaptive Huffman coding
Huffman coding
(also called Dynamic Huffman coding) is an adaptive coding technique based on Huffman coding. It permits building the code as the symbols are being transmitted, having no initial knowledge of source distribution, that allows one-pass encoding and adaptation to changing conditions in data. The benefit of one-pass procedure is that the source can be encoded in real time, though it becomes more sensitive to transmission errors, since just a single loss ruins the whole code.Contents1 Algorithms1.1 FGK Algorithm 1.2 Vitter algorithm1.2.1 Algorithm for adding a symbol 1.2.2 Function Slide_And_Increment(p) 1.2.3 Example2 References 3 External linksAlgorithms[edit] There are a number of implementations of this method, the most notable are FGK (Faller-Gallager-Knuth) and Vitter algorithm. FGK Algorithm[edit] It is an online coding technique based on Huffman coding
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Canonical Huffman Code
A canonical Huffman code
Huffman code
is a particular type of Huffman code
Huffman code
with unique properties which allow it to be described in a very compact manner. Data compressors generally work in one of two ways. Either the decompressor can infer what codebook the compressor has used from previous context, or the compressor must tell the decompressor what the codebook is. Since a canonical Huffman codebook can be stored especially efficiently, most compressors start by generating a "normal" Huffman codebook, and then convert it to canonical Huffman before using it. In order for a symbol code scheme such as the Huffman code
Huffman code
to be decompressed, the same model that the encoding algorithm used to compress the source data must be provided to the decoding algorithm so that it can use it to decompress the encoded data
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Modified Huffman Coding
Modified Huffman coding
Huffman coding
is used in fax machines to encode black on white images (bitmaps). It combines the variable length codes of Huffman coding
Huffman coding
with the coding of repetitive data in run-length encoding. See also[edit] Fax
Fax
CompressionExternal links[edit]"Modified Huffman coding
Huffman coding
from UNESCO"
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Range Encoding
Range encoding
Range encoding
is an entropy coding method defined by G. Nigel N. Martin in a 1979 paper,[1] which effectively rediscovered the FIFO arithmetic code first introduced by Richard Clark Pasco in 1976.[2] Given a stream of symbols and their probabilities, a range coder produces a space efficient stream of bits to represent these symbols and, given the stream and the probabilities, a range decoder reverses the process. Range coding is very similar to arithmetic encoding, except that encoding is done with digits in any base, instead of with bits, and so it is faster when using larger bases (e.g. a byte) at small cost in compression efficiency.[3] After the expiration of the first (1978) arithmetic coding patent,[4] range encoding appeared to clearly be free of patent encumbrances. This particularly drove interest in the technique in the open source community
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Shannon Coding
In the field of data compression, Shannon coding, named after its creator, Claude Shannon, is a lossless data compression technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). It is suboptimal in the sense that it does not achieve the lowest possible expected code word length like Huffman coding
Huffman coding
does, and never better but sometimes equal to the Shannon-Fano coding. The method was the first of its type, the technique was used to prove Shannon's noiseless coding theorem in his 1948 article "A Mathematical Theory of Communication",[1] and is therefore a centerpiece of the information age. This coding method gave rise to the field of information theory and without its contribution, the world would not have any of the many successors; for example Shannon-Fano coding, Huffman coding, or arithmetic coding
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Shannon–Fano Coding
In the field of data compression, Shannon–Fano coding, named after Claude Shannon
Claude Shannon
and Robert Fano, is a technique for constructing a prefix code based on a set of symbols and their probabilities (estimated or measured). It is suboptimal in the sense that it does not achieve the lowest possible expected code word length like Huffman coding.[citation needed] The technique was proposed in Shannon's "A Mathematical Theory of Communication", his 1948 article introducing the field of information theory
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Tunstall Coding
In computer science and information theory, Tunstall coding is a form of entropy coding used for lossless data compression.Contents1 History 2 Properties 3 Algorithm 4 Example 5 Limitations 6 ReferencesHistory[edit] Tunstall coding was the subject of Brian Parker Tunstall's PhD thesis in 1967, while at Georgia Institute of Technology
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Zentralblatt MATH
zbMATH, formerly Zentralblatt MATH, is a major international reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society (EMS), FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media. It uses the Mathematics Subject Classification codes for organising the reviews by topic.Contents1 History 2 Services 3 See also 4 References 5 External linksHistory[edit] Mathematicians Richard Courant, Otto Neugebauer and Harald Bohr, together with the publisher Ferdinand Springer, took the initiative for the foundation of a new mathematical reviewing journal. Harald Bohr, the brother of the famous physicist Niels Bohr, worked in Copenhagen. Courant and Neugebauer were professors at the University of Göttingen
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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
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