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- Shannon–Fano_coding abstract "In the field of data compression, Shannon–Fano coding, named after 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; however unlike Huffman coding, it does guarantee that all code word lengths are within one bit of their theoretical ideal . The technique was proposed in Shannon's "A Mathematical Theory of Communication", his 1948 article introducing the field of information theory. The method was attributed to Fano, who later published it as a technical report. Shannon–Fano coding should not be confused with Shannon coding, the coding method used to prove Shannon's noiseless coding theorem, or with Shannon–Fano–Elias coding (also known as Elias coding), the precursor to arithmetic coding.In Shannon–Fano coding, the symbols are arranged in order from most probable to least probable, and then divided into two sets whose total probabilities are as close as possible to being equal. All symbols then have the first digits of their codes assigned; symbols in the first set receive "0" and symbols in the second set receive "1". As long as any sets with more than one member remain, the same process is repeated on those sets, to determine successive digits of their codes. When a set has been reduced to one symbol, of course, this means the symbol's code is complete and will not form the prefix of any other symbol's code.The algorithm produces fairly efficient variable-length encodings; when the two smaller sets produced by a partitioning are in fact of equal probability, the one bit of information used to distinguish them is used most efficiently. Unfortunately, Shannon–Fano does not always produce optimal prefix codes; the set of probabilities {0.35, 0.17, 0.17, 0.16, 0.15} is an example of one that will be assigned non-optimal codes by Shannon–Fano coding.For this reason, Shannon–Fano is almost never used; Huffman coding is almost as computationally simple and produces prefix codes that always achieve the lowest expected code word length, under the constraints that each symbol is represented by a code formed of an integral number of bits. This is a constraint that is often unneeded, since the codes will be packed end-to-end in long sequences. If we consider groups of codes at a time, symbol-by-symbol Huffman coding is only optimal if the probabilities of the symbols are independent and are some power of a half, i.e., . In most situations, arithmetic coding can produce greater overall compression than either Huffman or Shannon–Fano, since it can encode in fractional numbers of bits which more closely approximate the actual information content of the symbol. However, arithmetic coding has not superseded Huffman the way that Huffman supersedes Shannon–Fano, both because arithmetic coding is more computationally expensive and because it is covered by multiple patents.[citation needed]Shannon–Fano coding is used in the IMPLODE compression method, which is part of the ZIP file format.".
- Shannon–Fano_coding thumbnail ShannonCodeAlg.svg?width=300.
- Shannon–Fano_coding wikiPageID "62544".
- Shannon–Fano_coding wikiPageRevisionID "598105137".
- Shannon–Fano_coding subject Category:Lossless_compression_algorithms.
- Shannon–Fano_coding comment "In the field of data compression, Shannon–Fano coding, named after 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; however unlike Huffman coding, it does guarantee that all code word lengths are within one bit of their theoretical ideal .".
- Shannon–Fano_coding label "Algoritmo de Huffman".
- Shannon–Fano_coding label "Codage de Shannon-Fano".
- Shannon–Fano_coding label "Codificação de Shannon-Fano".
- Shannon–Fano_coding label "Kodowanie Shannona-Fano".
- Shannon–Fano_coding label "Shannon-Fano-Kodierung".
- Shannon–Fano_coding label "Shannon–Fano coding".
- Shannon–Fano_coding label "Алгоритм Шеннона — Фано".
- Shannon–Fano_coding label "ترميز شانون-فانو".
- Shannon–Fano_coding label "シャノン符号化".
- Shannon–Fano_coding label "香农-范诺编码".
- Shannon–Fano_coding sameAs Shannon%E2%80%93Fano_coding.
- Shannon–Fano_coding sameAs Shannonovo-Fanovo_kódování.
- Shannon–Fano_coding sameAs Shannon-Fano-Kodierung.
- Shannon–Fano_coding sameAs Algoritmo_de_Huffman.
- Shannon–Fano_coding sameAs Codage_de_Shannon-Fano.
- Shannon–Fano_coding sameAs シャノン符号化.
- Shannon–Fano_coding sameAs 샤논-파노_부호화.
- Shannon–Fano_coding sameAs Kodowanie_Shannona-Fano.
- Shannon–Fano_coding sameAs Codificação_de_Shannon-Fano.
- Shannon–Fano_coding sameAs Q2645.
- Shannon–Fano_coding sameAs Q2645.
- Shannon–Fano_coding wasDerivedFrom Shannon–Fano_coding?oldid=598105137.
- Shannon–Fano_coding depiction ShannonCodeAlg.svg.