Editing Huffman coding (section)

{{distinguish|Hamming code}}
{{Short description|Technique to compress data}}
{{Use dmy dates|date=May 2019|cs1-dates=y}}
[[Image:Huffman tree 2.svg|thumb|Huffman tree generated from the exact frequencies of the text "this is an example of a huffman tree". Encoding the sentence with this code requires 135 (or 147) bits, as opposed to 288 (or 180) bits if 36 characters of 8 (or 5) bits were used (This assumes that the code tree structure is known to the decoder and thus does not need to be counted as part of the transmitted information). The frequencies and codes of each character are shown in the accompanying table.

{| class="wikitable sortable"
!Char!!Freq!!Code
|-
|space||7||111
|-
|a    ||4||010
|-
|e    ||4||000
|-
|f    ||3||1101
|-
|h    ||2||1010
|-
|i    ||2||1000
|-
|m    ||2||0111
|-
|n    ||2||0010
|-
|s    ||2||1011
|-
|t    ||2||0110
|-
|l    ||1||11001
|-
|o    ||1||00110
|-
|p    ||1||10011
|-
|r    ||1||11000
|-
|u    ||1||00111
|-
|x    ||1||10010
|}
]]
In [[computer science]] and [[information theory]], a '''Huffman code''' is a particular type of optimal [[prefix code]] that is commonly used for [[lossless data compression]]. The process of finding or using such a code is '''Huffman coding''', an algorithm developed by [[David A. Huffman]] while he was a [[Doctor of Science|Sc.D.]] student at [[Massachusetts Institute of Technology|MIT]], and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".<ref name=":0">{{Cite journal | last1 = Huffman | first1 = D. |author-link1=David A. Huffman| title = A Method for the Construction of Minimum-Redundancy Codes | doi = 10.1109/JRPROC.1952.273898 | journal = [[Proceedings of the IRE]]| volume = 40 | issue = 9 | pages = 1098–1101 | year = 1952 | url = http://compression.ru/download/articles/huff/huffman_1952_minimum-redundancy-codes.pdf}}</ref>

The output from Huffman's algorithm can be viewed as a [[variable-length code]] table for encoding a source symbol (such as a character in a file).  The algorithm derives this table from the estimated probability or frequency of occurrence (''weight'') for each possible value of the source symbol.  As in other [[entropy encoding]] methods, more common symbols are generally represented using fewer bits than less common symbols.  Huffman's method can be efficiently implemented, finding a code in time [[linear time|linear]] to the number of input weights if these weights are sorted.<ref>{{cite journal | first = Jan | last = Van Leeuwen | author-link = Jan van Leeuwen | url = http://www.staff.science.uu.nl/~leeuw112/huffman.pdf | title = On the construction of Huffman trees | journal = ICALP | year =1976 | pages = 382–410 | access-date = 20 February 2014}}</ref>  However, although optimal among methods encoding symbols separately, Huffman coding [[#Optimality|is not always optimal]] among all compression methods – it is replaced with [[arithmetic coding]]<ref name="LiDrew2014">{{cite book|author1=Ze-Nian Li|author2=Mark S. Drew|author3=Jiangchuan Liu|title=Fundamentals of Multimedia|url=https://books.google.com/books?id=R6vBBAAAQBAJ|date=9 April 2014|publisher=Springer Science & Business Media|isbn=978-3-319-05290-8}}</ref> or [[asymmetric numeral systems]]<ref name=PCS2015>[https://ieeexplore.ieee.org/document/7170048 J. Duda, K. Tahboub, N. J. Gadil, E. J. Delp, ''The use of asymmetric numeral systems as an accurate replacement for Huffman coding''], Picture Coding Symposium, 2015.</ref> if a better compression ratio is required.