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Topic: Arithmetic encoding

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Range encoding

Entropy coding

Huffman coding

Coding theory

Code word

Hamming distance

Information theory

	Arithmetic coding - Wikipedia, the free encyclopedia
		Rather than try to simulate infinite precision, most arithmetic coders instead operate at a fixed limit of precision that they know the decoder will be able to match, and round the calculated fractions to their nearest equivalents at that precision.
		There is profound similarity between arithmetic coding and range encoding, so much so that their performances can usually be expected to be almost identical, with range encoding only being a few bits behind if there is indeed any difference.
		The idea behind range encoding is that, instead of starting with the interval [0,1) and dividing it into sub-intervals proportional to the probability of each symbol, the encoder starts with a large range of non-negative integers, such as 000,000,000,000 to 999,999,999,999, and divides it into sub-ranges proportional to the probability of each symbol.
	en.wikipedia.org /wiki/Arithmetic_coding (1736 words)

	PlanetMath: arithmetic encoding
		Arithmetic coding is a technique for achieving near-optimal entropy encoding.
		Since arithmetic encoders are typically implemented on binary computers, the actual output of the encoder is generally the shortest sequence of bits representing the fractional part of a rational number in the final interval.
		This is version 1 of arithmetic encoding, born on 2002-03-08.
	planetmath.org /encyclopedia/ArithmeticEncoding.html (237 words)

	esp@cenet description view (Site not responding. Last check: 2007-10-19)
		Arithmetic coding was introduced by Rissanen, "Generalized Kraft Inequality and Arithmetic Coding," IBM Journal of Research and Development, Volume 20, No. 3, May 1976, at pp.
		Since a number is being encoded or generated to represent symbol strings, the LIFO method and means of Langdon et al imports that the least significant bits are generated first, while the most significant bits are generated last.
		The arithmetic encoding process can be viewed as the summation of properly shifted numbers as may be found, for example, in the process of ordinary multiplication.
	v3.espacenet.com /textdes?&DB=EPODOC&IDX=EP21283 (5231 words)

	PlanetMath: entropy encoding
		An entropy encoding is a coding scheme that involves assigning codes to symbols so as to match code lengths with the probabilities of the symbols.
		Typically, entropy encoders are used to compress data by replacing symbols represented by equal-length codes with symbols represented by codes proportional to the negative logarithm of the probability.
		Two of the most common entropy encoding techniques are Huffman encoding and arithmetic encoding.
	planetmath.org /encyclopedia/EntropyEncoding.html (149 words)

	Arithmetic Code Discussion and Implementation
		Arithmetic coding is similar to Huffman coding; they both achieve their compression by reducing the average number of bits required to represent a symbol.
		In case you were sleeping, this is the string that was encoded in the encoding example.
		The standard form of arithmetic coding's encoding is based on fractional ranges on a probability line between 0 and 1.
	michael.dipperstein.com /arithmetic (3321 words)

	Arithmetic Coding
		Arithmetic coding is a general technique for coding the outcome of a stochastic process based on an adaptive model.
		Encoding proceeds a byte at a time and provides output a bit at a time; decoding proceeds a bit at a time and provides output a byte at a time.
		The arithmetic coder is distributed with several illustrative models, culminating in PPMC, prediction by partial matching with model C. When introduced in the 1980s, PPM provided the best known compression on general text and binary data such as images.
	www.colloquial.com /ArithmeticCoding/javadoc/tutorial.html (1274 words)

	Entropy encoding - Wikipedia, the free encyclopedia
		An entropy encoding is a coding scheme that assigns codes to symbols so as to match code lengths with the probabilities of the symbols.
		Three of the most common entropy encoding techniques are Huffman coding, range encoding, and arithmetic encoding.
		If the approximate entropy characteristics of a data stream are known in advance (especially for signal compression), a simpler static code such as unary coding, Elias gamma coding, Fibonacci coding, Golomb coding, or Rice coding may be useful.
	en.wikipedia.org /wiki/Entropy_encoding (189 words)

	Arithmetic Coding (AC)
		The biggest drawbak of the arithmetic coding is it´s low speed since of several needed multiplications and divisions for each symbol.
		A fast variant of arithmetic coding, which uses less multiplications and divisions, is a range coder, which works byte oriented.
		Range encoding was first proposed by this paper from G. Martin in 1979, which describes the algorithm not very clearly.
	www.data-compression.info /Algorithms/AC (1298 words)

	Bijective Arithmetic Encoding with Really Good End Treatment
		Arithmetic encoding, as presented so far, works just fine when we're writing an endless stream of symbols from some source to some sink.
		Still, the rest of the arithmetic encoding process is so nearly perfect that we find this blatant waste of bits to be annoying, and we present a better way.
		Every such encoding, including the popular Huffman encoding, is a special case of arithmetic encoding that limits the size of the range to negative powers of two, and so the same end treatment we use for arithmetic encoding works for these types of codes as well.
	www3.sympatico.ca /mt0000/biacode/biacode.html (2909 words)

	Hacking Data Compression - Lesson 11
		Encoding the free characters and the pointers separately made sense, because they really have no relation to each other.
		The free characters and the match lengths were encoded adaptively with the a single frequency table, by using "character" 253+length to represent the match length (where length goes from 3 to F).
		The position was encoded with a static-frequency model, which assumed that matches were most often found in the most recently seen data.
	www.fadden.com /techmisc/hdc/lesson11.htm (2080 words)

	[No title]
		The basic concept behind the Modified Run Length Encoding method (mod-RLE) is to modify the lengths of the symbol runs in the source data stream such that the resulting run length can be used to determine the length of the original run.
		The transform was employed only on runs of length 3 or greater where the encoded run is of length 2+((N-1)/2) and N is the length of the original run.
		The first is the output stream from an arithmetic coder which is used to encode all variable length codes of size 8 bits and less.
	www.geocities.com /m99datacompression/papers/rle2.html (1172 words)

	Untitled
		This means that the new encoded number will have to fall somewhere in the 50th to 60th percentile of the currently established range.
		In the event that the encoded word has a string of 0s or 9s in it, the high and low values will slowly converge on a value, but may not see their most significant digits match immediately.
		During the encoding process, the modeling code has to take a character to be encoded and convert it to a probability range.
	www.dogma.net /markn/articles/arith/part1.htm (5152 words)

	Compressing References
		I compared using zlib on the byte stream generated by a move-to-front encoding with using a Arithmetic encoding on the indices generated by a move-to-front scheme.
		However, these results do not include the size of the dictionaries for the arithmetic encoding, and arithmetic encoding is rather expensive to compress and decompress.
		The resulting indicies are encoded as a byte stream and compressed as described in Section 6.
	www.cs.umd.edu /users/pugh/java/latex2html/pack/node5.html (1085 words)

	Hacking Data Compression - Lesson 6
		This week's subject is arithmetic encoding, a method of encoding symbols that can produce output which is extremely close in size to the entropy of the input.
		When encoding, we want to output bits and shift whenever the most significant bits of high and low are the same.
		Arithmetic coding will encode symbols according to their probabilities in a manner which gets very close to the entropy if the input (the factors reducing effectiveness are message termination overhead, use of finite-precision arithmetic, and the scaling of frequencies so that they don't exceed the maximum).
	www.fadden.com /fadden.com/techmisc/hdc/lesson06.htm (3751 words)

	The Encoder (Site not responding. Last check: 2007-10-19)
		The central concept behind range encoding is this: given a large-enough range of integers, and a probability estimation for the symbols, the initial range can easily be divided into sub-ranges whose sizes are proportional to the probability of the symbol they represent.
		Arithmetic coding can be thought of as a form of range encoding with the range starting at zero and extending to one.
		In delta encoded transmission over a network where only a single copy of the file is available at each end of the communication channel special error control codes are used to detect which parts of the file has changed since its previous version.
	www.the-encoder.info (1861 words)

	Compressing Coin Flips (Three Concepts: Information) (Site not responding. Last check: 2007-10-19)
		The process is demonstrated in figure 2, which shows the encoding of the string "0100#", where "#" is used to denote the end of the input.
		The encoding continues this way until the termination symbol, needed in decoding, is encountered.
		When our arithmetic coder is not given the bias as a parameter, it calculates it from the data, and codes it into the beginning of the compressed file.
	www.helsinki.fi /~mmmietti/infoproj1 (1665 words)

	[No title]
		Arithmetic coding is a state-of-the-art lossless entropy data compression method which offers better compression performance than the well-established Huffman entropy coding process.
		The JPEG standard specifies a particular arithmetic coding scheme to be used optionally as alternative to Huffman coding.
		The encoding and decoding processes should be correct anyway, however, in the sense that they are complementary to each other and thus retain data integrity.
	sylvana.net /jpeg-ari/uncompressed/READ.txt (746 words)

	A Study of Arithmetic Genetic Encoding for Highly Randomized Fitness Landscapes
		This paper presents hypotheses, directions and preliminary results of research in Genetic Algorithms, specifically in the case of arithmetic weight encoding for highly stochastic static fitness landscapes.
		Genetic algorithms can be applied to many scenarios where the encoding may be neither numeric nor string-based in nature.
		But in this case, we concentrate on the type of genetic algorithm in which the genome encodes an array of numbers representative of some parameters to be optimized.
	personal.vsnl.com /udayan/age1.htm (1103 words)

	Rate-constrained Conditional Replenishment Video Coding with Adaptive Change Detection
		Context-based arithmetic encoding [8] is one of the binary bitmap-based shape coding scheme used in the object-based MPEG-4 standard [7].
		For encoding the pixels in the two top and left rows of a macroblock, parts of the template are defined by the shape information of the already transmitted macroblocks on the top and left side of the current macroblock.
		For encoding the state transition, a context-based arithmetic encoder is used.
	www.stanford.edu /class/ee368b/Projects/chiao (2395 words)

	Entropy encoding -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		An entropy encoding is a (Act of writing in code or cipher) coding scheme that assigns codes to symbols so as to match code lengths with the (Click link for more info and facts about probabilities) probabilities of the symbols.
		According to (Click link for more info and facts about Shannon's theorem) Shannon's theorem, the optimal code length for a symbol is -logP, where b is the number of symbols used to make output codes and P is the probability of the input symbol.
		Three of the most common entropy encoding techniques are (Click link for more info and facts about Huffman coding) Huffman coding, (Click link for more info and facts about range encoding) range encoding, and (Click link for more info and facts about arithmetic encoding) arithmetic encoding.
	www.absoluteastronomy.com /encyclopedia/e/en/entropy_encoding.htm (171 words)

	ASPN : Python Cookbook : arithmetic coder (Site not responding. Last check: 2007-10-19)
		A simple but slow way of compression using arithmetic coding.
		The encoded result is two numbers, 'N' and 'Nbits'.
		To decode the number, pass those two and the statistics table to the decode() function.
	aspn.activestate.com /ASPN/Cookbook/Python/Recipe/306626 (418 words)

	CISC-834: Real World Applications and their Algorithms (Site not responding. Last check: 2007-10-19)*
		What is the word length needed for unambiguous encoding using the integer arithmetic version of the arithmetic encoding algorithm.
		Decode the code you obtained to verify that the encoding was correct.
		Generate a binary sequence of length L with P(0) = 0.8, and use the arithmetic encoding algorithm to encode it.
	www.qucis.queensu.ca /home/daver/834/A2.html (170 words)

	Results
		Huffman or arithmetic), we calculated the zero-order entropy for the original image and for the transformed image.
		We suggest that this improvement could be due to the improved predictor (GAP) or to the fact that the authors used arithmetic encoding to produce their final compressed output.
		JPEG encoders normally use Huffman encoding which is slightly less efficient than arithmetic encoding.
	www.stanford.edu /class/ee368b/Projects/dhavelin/results.htm (892 words)

	Glossary (Site not responding. Last check: 2007-10-19)
		DPCM encoding scheme, which results in increased compression rate with an acceptable quality loss.
		Whenever a phrase already stored in the dictionary reoccurrs in the charstream, it is encoded with its index number in the dictionary.
		The encoding algorithm completes one encoding step each time it produces output, thus completing the encoding of the current character sequence and moving on to the next.
	oldwww.rasip.fer.hr /research/compress/glossary/Glossary.htm (941 words)

	ipedia.com: Arithmetic coding Article (Site not responding. Last check: 2007-10-19)
		Arithmetic coding in data compression is the process of encoding a stream of data into a large binary fraction.
		Arithmetic coding actually refers to half of an arithmetic coding data compression system.
		An arithmetic encoder takes a string of symbols as input and produces a rational number in the interval [0, 1) as output.
	www.ipedia.com /arithmetic_coding.html (448 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		An intoduction to Arithmetic Coding is given here (not the fastest link on the web...).
		Prograssive Transmission: by encoding each bitplane separately it is possible to stop the decoding process at any bitrate and still be able to reconstract the image at the chosen quality.
		It isn't fully-embedded but it is possible to perform lossy compression by encoding fewer bitplanes (max 15 bitplanes in my implementation for lossless compression).
	www.geocities.com /capecanaveral/Lab/2336/wave.html (325 words)

	compress
		The i_encode, i_update and i_decompress routines are for bitplane arithmetic encoding.
		To use these routines, a context array of unsigned chars which has a length equal to the number of bits in each pixel must be initialised to 1 unless more knowledge concerning the probability distribution of the data is known.
		After each pixel is encoded by i_encode and stored in the file outf, i_update must be called to adjust the context and observation variables.
	www.csse.monash.edu.au /software/mil/compress.html (392 words)

	DataCompression.info - Arithmetic Coding (Site not responding. Last check: 2007-10-19)
		Arithmetic coding is a method of encoding data using a variable number of bits.
		An arithmetic encoder doesn't have to use an integral number of bits to encode a symbol.
		In this particular case, A and B are a compressor and decompressor that use arithmetic coding.
	datacompression.info /ArithmeticCoding.shtml (2621 words)

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