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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 ...
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
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).
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To decode an Elias delta-coded integer: Read and count zeros from the stream until you reach the first one. Call this count of zeros L.; Considering the one that was reached to be the first digit of an integer, with a value of 2 L, read the remaining L digits of the integer.
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