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Shannon–Fano–Elias coding produces a binary prefix code, allowing for direct decoding. Let bcode(x) be the rational number formed by adding a decimal point before a binary code. For example, if code(C) = 1010 then bcode(C) = 0.1010. For all x, if no y exists such that
Unfortunately, Shannon–Fano coding 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. Fano's version of Shannon–Fano coding is used in the IMPLODE compression method, which is part of the ZIP file format ...
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).
Elias coding is a term used for one of two types of lossless coding schemes used in digital communications: Shannon–Fano–Elias coding, a precursor to arithmetic coding, in which probabilities are used to determine codewords; Universal coding using one of Elias' three universal codes, each with predetermined codewords: Elias delta coding
Package-merge algorithm: Optimizes Huffman coding subject to a length restriction on code strings; Shannon–Fano coding; Shannon–Fano–Elias coding: precursor to arithmetic encoding [5] Entropy coding with known entropy characteristics. Golomb coding: form of entropy coding that is optimal for alphabets following geometric distributions
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More precisely, the source coding theorem states that for any source distribution, the expected code length satisfies [(())] [ (())], where is the number of symbols in a code word, is the coding function, is the number of symbols used to make output codes and is the probability of the source symbol. An entropy coding attempts to ...
A code is non-singular if each source symbol is mapped to a different non-empty bit string; that is, the mapping from source symbols to bit strings is injective.. For example, the mapping = {,,} is not non-singular because both "a" and "b" map to the same bit string "0"; any extension of this mapping will generate a lossy (non-lossless) coding.