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Topic: Huffman coding

Related Topics

Arithmetic coding

Channel coding

Prefix code

Entropy encoding

Adaptive Huffman coding

Arithmetic encoding

Gray code

Coding theory

Data compression

Range encoding

Code word

Binary tree

Lossless data compression

Information entropy

Radix sort

	PlanetMath: Huffman coding
		Huffman coding is a method of lossless data compression, and a form of entropy encoding.
		The mapping is obtained by the path from the root of the Huffman tree to the leaf associated with a symbol's weight.
		This is version 4 of Huffman coding, born on 2002-03-08, modified 2003-09-04.
	planetmath.org /encyclopedia/HuffmanCoding.html (659 words)

	Huffman coding - Wikipedia, the free encyclopedia
		Huffman coding is such a widespread method for creating prefix-free codes that the term "Huffman code" is widely used as a synonym for "prefix-free code" even when such a code is not produced by Huffman's algorithm.
		Huffman, unable to prove any codes were the most efficient, was about to give up and start studying for the final when he hit upon the idea of using a frequency-sorted binary tree and quickly proved this method the most efficient.
		Huffman coding with unequal letter costs is the generalization in which this assumption is no longer assumed true: the letters of the encoding alphabet may have non-uniform lengths, due to characteristics of the transmission medium.
	en.wikipedia.org /wiki/Huffman_coding (2061 words)

	Huffman coding - Wikipedia, the free encyclopedia
		It was developed by David A. Huffman as a PhD student at MIT in 1952, and published in A Method for the Construction of Minimum-Redundancy Codes.
		Huffman coding is optimal when the probability of each input symbol is a negative power of two.
		Huffman coding with unequal letter costs is the generalization in which the letters of the encoding alphabet may have non-uniform lengths.
	www.encyclopedia-online.info /Huffman_coding (1297 words)

	Adaptive Huffman coding - Wikipedia, the free encyclopedia
		Adaptive Huffman coding is an adaptive coding technique based on Huffman coding, building the code as the symbols are being transmitted, having no initial knowledge of source distribution, that allows one-pass encoding and adaptation to changing conditions in data.
		Code is represented as a tree structure in which every node has a corresponding weight and a unique number.
		Paul E. Black, adaptive Huffman coding at the NIST Dictionary of Algorithms and Data Structures.
	en.wikipedia.org /wiki/Adaptive_Huffman_coding (578 words)

	Huffman Coding
		David Huffman in 1954 designed a lossless coding procedure for a frame of values that has the smallest possible average code length.
		Huffman codes are not unique.) The average number of bits per value is then 0.41 + 0.22 + 0.23 + 0.14 + 0.14 = 2.2 which is less than the 3 in the binary coding* with equal probability.
		Huffman coding is used in the final step of creating an MP3 file.
	webphysics.davidson.edu /faculty/dmb/py115/huffman_coding.htm (592 words)

	Data Compression -- Section 3
		Rather than using a Huffman code based upon the characteristics of the current message ensemble, the code used could be based on statistics for a class of transmissions to which the current ensemble is assumed to belong.
		3.3 Universal Codes and Representations of the Integers
		The result is an instantaneously decodable code since the total length of a codeword is exactly one greater than twice the number of zeros in the prefix; therefore, as soon as the first 1 of a codeword is encountered, its length is known.
	www.ics.uci.edu /~dan/pubs/DC-Sec3.html (4346 words)

	Lossless Data Compression
		The design of the Huffman code is optimal (for a fixed blocklength) assuming that the source statistics are known a priori.
		A code tree is thus generated and the Huffman code is obtained from the labeling of the code tree.
		Huffman codes are optimal in the sense that no other lossless fixed-to-variable length code has a lower average rate.
	www.data-compression.com /lossless.html (932 words)

	Huffman coding (Site not responding. Last check: 2007-10-21)
		Huffman codes belongs into a family of codes with a variable codeword length.
		Decreasing of redundancy in data by Huffman codes is based on the fact that distinct symbols have distinct probabilities of incidence.
		Extended Huffman codes have the charachteristic that the coding sheme is coding group of symbols rather than a single symbol.
	oldwww.rasip.fer.hr /research/compress/algorithms/fund/huffman (371 words)

	Huffman coding - Hydrogenaudio Knowledgebase
		Huffman codes have the property to have a unique prefix, they can therefore be decoded correctly in spite of their variable length.
		It is an ideal complement of the perceptual coding: During big polyphonies, the perceptual coding is very efficient, due to the fact that many sounds are masked or lessened, but little information is identical, so the Huffman algorithm is very seldomly efficient.
		Huffman source code an ANSI C implementation of the algorithm.
	wiki.hydrogenaudio.org /index.php?title=Huffman_coding (218 words)

	Huffman Coding: A CS2 Assignment
		As we'll see, Huffman coding compresses data by using fewer bits to encode more frequently occurring characters so that not all characters are encoded with 8 bits.
		Note that this tree is different from the tree we used to illustrate Huffman coding above, and the bit patterns for each character are different, but the total number of bits used to encode "go go gophers" is the same.
		This table is constructed from a coding tree using root-to-leaf paths to generate the bit sequence that encodes each character.
	www.cs.duke.edu /csed/poop/huff/info (3345 words)

	Frank Rietta's Work, Research, and Play: A Little Huffman Coding with Java Tricks
		A Huffman code is a way to utilize a binary tree to construct a minimal-length encoding for messages where certain characters or groups of characters have known frequencies.
		Huffman codes are the most efficient compression method for random data and are often found as steps in other compression algorithms such as JPEG and Deflate (ZIP).
		To construct a Huffman tree, first initialize a series of nodes, which are simply data structures holding the represented character and its frequency within the message.
	www.rietta.com /blog/2005/05/little-huffman-coding-with-java-tricks.html (604 words)

	Huffman Coding
		Thus, in Morse code the letter 'e' is represented by a code frame of length 1 (a single dot), whereas the letter 'z' is represented by a code frame of length 4 (dash-dash-dot-dot).
		Unblocked codes, such as Morse code, are sometimes referred to as "compressed" codes, because they shorten or "compress" the amount of time or space required to transmit and/or store a given amount of information.
		To obtain the code for each source symbol, trace the path from the symbol on the left to the final single point on the right, then read the sequence of 0's and 1's backwards through the tree from right to left.
	www.skylondaworks.com /sc_huff.htm (819 words)

	Adaptive Huffman Coding
		Huffman coding suffers from the fact that the uncompresser need have some knowledge of the probabilities of the characters in the compressed files.
		Adaptive Huffman coding also works at a universal level, but is far more effective than static huffman coding at a local level because the tree is constantly evolving.
		This algorithm is called adaptive huffman coding because the tree is adaptive- it is created simultaneously with either the compressed or uncompressed file as it reads in the other.
	www.cs.duke.edu /csed/curious/compression/adaptivehuff.html (1951 words)

	Huffman coding
		Note: The worst case for Huffman coding (or, equivalently, the longest Huffman coding for a set of characters) is when the distribution of frequencies follows the Fibonacci numbers.
		Huffman coding is one of many lossless compression algorithms.
		Huffman is optimal for character coding (one character-one code word) and simple to program.
	www.nist.gov /dads/HTML/huffmanCoding.html (324 words)

	Arithmetic coding - Wikipedia, the free encyclopedia
		Compression algorithms that use arithmetic coding start by determining a model of the data -- basically a prediction of what patterns will be found in the symbols of the message.
		Arithmetic coding and range encoding can be regarded as different interpretations of the same coding methods; arithmetic coders can be regarded as range encoders/decoders, and vice-versa.
		The corresponding arithmetic coding interpretation can be found by regarding the non-negative integers in the range as being the numerators of fractions in the interval [0,1).
	en.wikipedia.org /wiki/Arithmetic_coding (1935 words)

	Practical Huffman Coding
		The first code was derived directly from the tree; code2, code3 and the code labeled canonical are some other prefix codes with the same length.
		There are 4 codes with length 4 (that is where the 4 comes from), so the next length 4 code would start at 0100.
		In practice the log2(alphabetsize) for the nonzero bits in this canonical code is the one that is important for memory layout.
	www.compressconsult.com /huffman (3148 words)

	Huffman coding Computer Encyclopedia Enterprise Resource Directory Complete Guide to Internet (Site not responding. Last check: 2007-10-21)
		A {data compression} technique which varies the length of the encoded symbol in proportion to its information content, that is the more often a symbol or token is used, the shorter the binary string used to represent it in the compressed stream.
		Huffman codes can be properly decoded because they obey the prefix property, which means that no code can be a prefix of another code, and so the complete set of codes can be represented as a binary tree, known as a Huffman tree.
		Huffman coding was first described in a seminal paper by D.A. Huffman in 1952.
	www.jaysir.com /computer-encyclopedia/h/huffman-coding-computer-terms.htm (120 words)

	DataCompression.info - Huffman Coding (Site not responding. Last check: 2007-10-21)
		David Huffman developed a form of encoding that creates the most efficient set of prefix codes for a given text.
		The decoder is one pass and uses a huffman code table at the beginning of the compressed file to decode the file.
		This type of Huffman coding follows some specific rules regarding the structure of the Huffman tree that simplify the process of transmitting the tree.
	datacompression.info /Huffman.shtml (3319 words)

	Data Compression -- Section 4
		The basis for algorithm FGK is the Sibling Property, defined by Gallager [Gallager 1978]: A binary code tree has the sibling property if each node (except the root) has a sibling and if the nodes can be listed in order of nonincreasing weight with each node adjacent to its sibling.
		The intuitive explanation of algorithm V's advantage over algorithm FGK is as follows: as in algorithm FGK, the code tree constructed by algorithm V is the Huffman code tree for the prefix of the ensemble seen so far.
		Another reasonable assumption about adaptive coding is that the weights in the current tree correspond closely to the probabilities associated with the source.
	www.ics.uci.edu /~dan/pubs/DC-Sec4.html (1768 words)

	Reference.com/Encyclopedia/Huffman coding
		Note that, in general, a Huffman code need not be unique, but it is always one of the codes minimizing
		An exhaustive list of papers on Huffman coding on its variations is given by "Code and Parse Trees for Lossless Source Encoding"
		Huffman's original article: D.A. Huffman, " A method for the construction of minimum-redundancy codes" (PDF), Proceedings of the I.R.E., sept 1952, pp 1098-1102
	www.reference.com /browse/wiki/Huffman_coding (1920 words)

	Adaptive Huffman Coding
		The key is to have both encoder and decoder to use exactly the same initialization and update_model routines.
		The Huffman tree could look very different after node swapping (Fig 7.2), e.g., in the third tree, node A is again swapped and becomes the #5 node.
		Note: Code for a particular symbol changes during the adaptive coding process.
	www.cs.cf.ac.uk /Dave/Multimedia/node212.html (279 words)

	Huffman coding
		Richard Suchenwirth 2002-04-11 - In Huffman coding, characters (or other data items) are represented as bit sequences of varying length, so that the most frequent items have the shortest bit sequences.
		Therefore I decided for the slightly wasteful approach of using regexp to determine and chop off matching prefixes (this is possible because Huffman trees match the Fano condition that no code is the prefix of another code).
		Such strings would be both (simply) encrypted and loss-free compressed (trailing zeros added in the final conversion would be ignored on decoding, because no code consists of all zeros - I had to change Y from 00000 in Huffman's original map to 000001 to obtain that added safety).
	wiki.tcl.tk /3235 (454 words)

	DataCompression.info - Adaptive Huffman Coding (Site not responding. Last check: 2007-10-21)
		Traditional Huffman Coding uses a static dictionary, which means each item in the file is encoded the same way.
		Adaptive Huffman coding modifies the table as characters are encoded, which allows the encoder to adapt to changing conditions in the input data.
		The code for incorporating the last symbol grabs an extra input bit, but since this is usually the EOT symbol, the bug doesn't always cause problems.
	datacompression.info /AdaptiveHuffman.shtml (660 words)

	Encoding - Huffman Coding (Site not responding. Last check: 2007-10-21)
		There are many different reasons for and ways of encoding data, and one of these ways is Huffman coding.
		The idea behind Huffman coding is simply to use shorter bit patterns for more common characters, and longer bit patterns for less common characters.
		The code for each of the letters is the sequence of 0's and 1's that lead to it on the tree, starting from the symbol with a probability of 1.
	educ.queensu.ca /~compsci/units/encoding/huffman.html (493 words)

	Huffman coding (Site not responding. Last check: 2007-10-21)
		Huffman coding (aka static Huffman coding) is an effective and widely used lossless data compression scheme.
		Huffman coding is described in many (text)books on algorithms and data structures (e.g.
		You can also find articles on Huffman coding of varying quality on the net (e.g.
	www.cs.helsinki.fi /u/vkarvone/2005k/ds-project/huffman.html (121 words)

	Compression Links: Huffman Coding area
		Huffman codes and Fibonacci numbers by Alex Vinokur
		This page contains a paper "Improved Huffman coding using recursive splitting" that describes a program that attempts to improve on Huffman compression by manipulation of the data stream.
		Professor David A. Huffman (August 9, 1925 - October 7, 1999) - author of "Huffman Codes".
	www.compression-links.info /Huffman (3125 words)

	adaptive Huffman coding (Site not responding. Last check: 2007-10-21)
		As characters are processed, frequencies are updated and codes are changed (or, the coding tree is modified).
		Note: The total message length can be less than that produced by a static Huffman coding since the coding can be different at different places in the message.
		Explanation of algorithm FGK and Vitter's Algorithm (algorithm V), two different adaptive Huffman coding algorithms.
	www.nist.gov /dads/HTML/adaptiveHuffman.html (134 words)

	The Laws of Cryptography: Huffman Coding Algorithm
		Here is a Huffman code program in 6 files, coded in Java.
		The code here does not create and transmit the decoding tree or information needed to create the decoding tree such as the frequency table.
		Code Length: 2.3 Input file (as a String): aaaaabbbbbcccccccccccccccdddddddddddddddddeeeeeeeeeeeeeeeeeeffffffffffffffffffffffffffffffffffffffff Encoded file (as a String): 10011001100110011001100010001000100010001011011011011011011011011011011011011011011011101101101101101101101101101101101101101101101101101111111111111111111111111111111111111111111111111111110000000000000000000000000000000000000000 Decoded file (as a String): aaaaabbbbbcccccccccccccccdddddddddddddddddeeeeeeeeeeeeeeeeeeffffffffffffffffffffffffffffffffffffffff ten42%
	www.cs.utsa.edu /~wagner/laws/Ahuffmanc.html (851 words)

	Bidirectional Huffman Coding - Fraenkel, Klein (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		Some affix Huffman codes are exhibited, and necessary conditions for the existence of such codes are given.
		For some symbol strings, it might be required to process the bitstream all the way from the end to the beginning of the frame, until...
		2 the redundancy of binary Huffman codes (context) - Johnsen - 1980
	citeseer.ist.psu.edu /fraenkel89bidirectional.html (574 words)

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