Shannon–Fano coding: Difference between revisions

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* '''Fano's method''' divides the source symbols into two sets ("0" and "1") with probabilities as close to 1/2 as possible. Then those sets are themselves divided in two, and so on, until each set contains only one symbol. The codeword for that symbol is the string of "0"s and "1"s that records which half of the divides it fell on. This method was proposed in a later [[technical report]] by Fano (1949).
 
Shannon–Fano codes are [[Optimization (mathematics)|suboptimal]] in the sense that they do not always achieve the lowest possible expected codeword length, as [[Huffman coding]] does.<ref name="Kaur">{{cite journal |last1=Kaur |first1=Sandeep |last2=Singh |first2=Sukhjeet |title=Entropy Coding and Different Coding Techniques |journal=Journal of Network Communications and Emerging Technologies |date=May 2016 |volume=6 |issue=5 |page=5 |url=https://pdfs.semanticscholar.org/4253/7898a836d0384c6689a3c098b823309ab723.pdf |archive-url=https://web.archive.org/web/20191203151816/https://pdfs.semanticscholar.org/4253/7898a836d0384c6689a3c098b823309ab723.pdf |url-status=dead |archive-date=2019-12-03 |access-date=3 December 2019}}</ref> However, Shannon–Fano codes have an expected codeword length within 1 bit of optimal. Fano's method usually produces encoding with shorter expected lengths than Shannon's method. However, Shannon's method is easier to analyse theoretically.
 
Shannon–Fano coding should not be confused with [[Shannon–Fano–Elias coding]] (also known as Elias coding), the precursor to [[arithmetic coding]].