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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 ...
Shannon–Fano coding methods gave rise to the field of information theory and without its contributions, the world would not have any of the many successors; for example Huffman coding, or arithmetic coding.
The technique for finding this code is sometimes called Huffman–Shannon–Fano coding, since it is optimal like Huffman coding, but alphabetic in weight probability, like Shannon–Fano coding. The Huffman–Shannon–Fano code corresponding to the example is { 000 , 001 , 01 , 10 , 11 } {\displaystyle \{000,001,01,10,11\}} , which, having ...
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
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 ...
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.
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To make the code a canonical Huffman code, the codes are renumbered. The bit lengths stay the same with the code book being sorted first by codeword length and secondly by alphabetical value of the letter: B = 0 A = 11 C = 101 D = 100 Each of the existing codes are replaced with a new one of the same length, using the following algorithm: