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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).
As with a prefix code, the representation of a string as a concatenation of such words is unique. A bifix code is a set of words which is both a prefix and a suffix code. [8] An optimal prefix code is a prefix code with minimal average length. That is, assume an alphabet of n symbols with probabilities () for a prefix code C.
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
Shannon coding; Shannon–Fano coding; Shannon–Fano–Elias coding; Shannon's source coding theorem; Signaling compression; Silence compression; Smallest grammar ...
It also developed the concepts of information entropy, redundancy and the source coding theorem, and introduced the term bit (which Shannon credited to John Tukey) as a unit of information. It was also in this paper that the Shannon–Fano coding technique was proposed – a technique developed in conjunction with Robert Fano.