Editing Huffman coding (section)

== Applications ==
[[Arithmetic coding]] and Huffman coding produce equivalent results &mdash; achieving entropy &mdash; when every symbol has a probability of the form 1/2<sup>''k''</sup>.  In other circumstances, arithmetic coding can offer better compression than Huffman coding because &mdash; intuitively &mdash; its "code words" can have effectively non-integer bit lengths, whereas code words in prefix codes such as Huffman codes can only have an integer number of bits. Therefore, a code word of length ''k'' only optimally matches a symbol of probability 1/2<sup>''k''</sup> and other probabilities are not represented optimally; whereas the code word length in arithmetic coding can be made to exactly match the true probability of the symbol.  This difference is especially striking for small alphabet sizes.{{Citation needed|date=December 2021}}

Prefix codes nevertheless remain in wide use because of their simplicity, high speed, and [[Arithmetic coding#History and patents|lack of patent coverage]].  They are often used as a "back-end" to other compression methods.  [[Deflate]] ([[PKZIP]]'s algorithm) and multimedia [[codec]]s such as [[JPEG]] and [[MP3]] have a front-end model and [[quantization (signal processing)|quantization]] followed by the use of prefix codes; these are often called "Huffman codes" even though most applications use pre-defined variable-length codes rather than codes designed using Huffman's algorithm.