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.
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 Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".[1]
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 to the number of input weights if these weights are sorted.[2] However, although optimal among methods encoding symbols separately, Huffman coding is not always optimal among all compression methods - it is replaced with arithmetic coding[3] or asymmetric numeral systems[4] if a better compression ratio is required.
^Huffman, D. (1952). "A Method for the Construction of Minimum-Redundancy Codes" (PDF). Proceedings of the IRE. 40 (9): 1098–1101. doi:10.1109/JRPROC.1952.273898.
^Van Leeuwen, Jan (1976). "On the construction of Huffman trees" (PDF). ICALP: 382–410. Retrieved 2014-02-20.
^Ze-Nian Li; Mark S. Drew; Jiangchuan Liu (2014-04-09). Fundamentals of Multimedia. Springer Science & Business Media. ISBN 978-3-319-05290-8.
^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.
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Adaptive Huffmancoding (also called Dynamic Huffmancoding) is an adaptive coding technique based on Huffmancoding. It permits building the code as the...
entropy coding attempts to approach this lower bound. Two of the most common entropy coding techniques are Huffmancoding and arithmetic coding. If the...
fewer bits used in total. Arithmetic coding differs from other forms of entropy encoding, such as Huffmancoding, in that rather than separating the input...
decompress the encoded data. In standard Huffmancoding this model takes the form of a tree of variable-length codes, with the most frequent symbols located...
necessarily a prefix code. Prefix codes are also known as prefix-free codes, prefix condition codes and instantaneous codes. Although Huffmancoding is just one...
possible expected code word length like Huffmancoding does, and never better than but sometimes equal to the Shannon–Fano coding (Fano's method). The...
property": there is no valid code word in the system that is a prefix (start) of any other valid code word in the set. Huffmancoding is the most known algorithm...
arithmetic coding techniques have also expired. Range coding conceptually encodes all the symbols of the message into one number, unlike Huffmancoding which...
lossless data compression file format that uses a combination of LZ77 and Huffmancoding. It was designed by Phil Katz, for version 2 of his PKZIP archiving...
signal. Huffmancoding is an entropy encoding method and variable-length code algorithm that assigns more common values with shorter binary codes that require...
of arithmetic coding (which uses a nearly accurate probability distribution), with a processing cost similar to that of Huffmancoding. In the tabled...
this set of codes in an adaptive coding scheme; "Rice coding" can refer either to that adaptive scheme or to using that subset of Golomb codes. Whereas a...
priority number associated with it earlier), it is popped-off and ignored. Huffmancoding requires one to repeatedly obtain the two lowest-frequency trees. A...
using threaded code may be an ideal optimization. Huffman threaded code consists of lists of tokens stored as Huffmancodes. A Huffmancode is a variable-length...
to produce bit sequences are Huffmancoding (also used by the deflate algorithm) and arithmetic coding. Arithmetic coding achieves compression rates close...
only have results at the leaves of the tree, such as the Huffman tree used in Huffmancoding, or the implicit classification tree used in Twenty Questions...
Steve Huffman (born 1983 or 1984), also known by his Reddit username spez (/spɛz/), is an American web developer and entrepreneur. He is the co-founder...
in Dayton, Ohio Huffmancoding, a data compression algorithm (Huffman tree) by David A. HuffmanHuffman Dam, near Fairborn, Ohio Huffman Historic District...
Bzip2 uses two reversible transformations; BWT, then Move to front with Huffmancoding for symbol reduction (the actual compression element). PPMd – Dmitry...
differencing connection. Entropy coding originated in the 1940s with the introduction of Shannon–Fano coding, the basis for Huffmancoding which was developed in...
Predictive coding – used in DPCM Entropy encoding – the two most common entropy encoding techniques are arithmetic coding and Huffmancoding Adaptive dictionary...
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