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Shannon–Fano–Elias coding : ウィキペディア英語版
Shannon–Fano–Elias coding
In information theory, Shannon–Fano–Elias coding is a precursor to arithmetic coding, in which probabilities are used to determine codewords.〔

== Algorithm description ==

Given a discrete random variable ''X'' of ordered values to be encoded, let p(x) be the probability for any ''x'' in ''X''. Define a function
:\bar F(x) = \sum_p(x_i) + \frac 12 p(x)
Algorithm:
:For each ''x'' in ''X'',
::Let ''Z'' be the binary expansion of \bar F(x).
::Choose the length of the encoding of ''x'', L(x), to be the integer \left\lceil \log_2 \frac \right\rceil + 1
::Choose the encoding of ''x'', code(x), be the first L(x) most significant bits after the decimal point of ''Z''.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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