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Topic: Entropy coding

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Huffman coding

Arithmetic encoding

Coding theory

Arithmetic coding

Range encoding

Code word

Subband encoding

Information theory

Audio compression

Hamming distance

SRGB color space

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	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.
		This is version 1 of entropy encoding, born on 2002-03-08.
	www.planetmath.org /encyclopedia/EntropyEncoding.html (148 words)

	Patents in Class 341/107
		An arithmetic code decoding apparatus including a context index predictor which predicts a context index, a pipeline arithmetic code decoder which executes a decoding process of the bitstream using the predicted context index and outputs...
		In an encoding apparatus (10), a code table group exchange judgment unit (12) selects a group of code tables from a plurality of groups of code tables according to the property such as tonality of a spectrum signal D 11, and a quanti...
		An entropy encoding/decoding scheme uses an arithmetic encoder/decoder together with a context modeler for performing a context-based adaptive binary arithmetic coding, which is especially suited for video compression applications.
	www.freepatentsonline.com /CCL341-107.html (2217 words)

	A Bit-Wise Adaptable Entropy Coding Technique
		A recently invented coding technique for data compression is based on recursive interleaving of variable-to-variable-length binary source codes.
		A straightforward code design procedure can be used to produce an encoder with compression efficiency arbitrarily close to the theoretical limit, with increasing complexity as the limit is approached.
		When the bits collected in a bin form one of the code words, these bits are deleted from the bin and the value of the code word is encoded by placing oneor more new bit(s) in other bins.
	www.nasatech.com /Briefs/July02/NPO21101.html (999 words)

	Entropy Coding
		Entropy encoding is used regardless of the media’s specific characteristics.
		The data stream to be compressed is considered to be a simple digital sequence, and the semantic of the data is ignored.
		Entropy encoding is an example of lossless encoding as the decompression process regenerates the data completely.
	www.kom.e-technik.tu-darmstadt.de /projects/iteach/itbeankit/lessons/jpeg/Expert/Entropy_Coding/entropy_coding.html (109 words)

	Lossless Compression
		This is achieved by using a code in which the length of each codeword is proportional to the frequency that it is used, such as a Huffman code or arithmetic coding.
		Using optimal entropy encoding, it was found that the average coding rate for a 1:2 subsampling pyramid encoder operating on the test images was 6.76 bits per pixel of the original image.
		The advantage of this approach is that the code dictionary does not need to be sent in addition to the data, as it is implicitly defined by the structure of the output.
	www.stanford.edu /~mbax/ee392c/node5.html (808 words)

	Entropy Coding
		The term entropy coding summarises all procedures utilising the probability distribution and thus the entropy, in order to produce a code of ideal length.
		Entropy encoder assign short code words to frequently appearing symbols with high probability and in contrast longer code words to rare symbols.
		While arithmetic coding represents the optimum precisely, a clear deviation results in the case of applying Shannon Fano coding.
	www.binaryessence.com /dct/en000265.htm (181 words)

	Entropy Coding (EC)
		As established in Shannon's source coding theorem, there is a relationship between the symbol probability and it's corresponding bit sequence.
		Entropy coding can be done with a coding scheme, which uses a discrete number of bits for each symbol, for example Huffman coding, or with a coding scheme, which uses a discrete number of bits for several symbols.
		A tutorial on arithmetic coding from 1992 by Paul Howard and Jeffrey Vitter with table lookups for higher speed.
	www.data-compression.info /Algorithms/EC (1440 words)

	Entropy, Coding and Data Compression - Resonance - September 2001
		He introduced the concept of entropy of a probability distribution (which already was in use in thermodynamics as a measure of disorder) and showed how this determines the minimum possible rate of reliable communication.
		He also named the new subject `information theory' since entropy is a measure of the information content of a probability distribution.
		The entropy idea was later taken to ergodic theory in 1958 by A N Kolmogorov to solve the outstanding problem of isomorphism of Bernoulli shifts, thus giving birth to a very rich area of research known as entropy theory of measure preserving transformations.
	www.iisc.ernet.in /~academy/resonance/Sept2001/Sept2001p35-45.html (327 words)

	Image Compression - from DCT to Wavelets : A Review
		Entropy Coding (EC) achieves additional compression losslessly by encoding the quantized DCT coefficients more compactly based on their statistical characteristics.
		SBC has been used extensively first in speech coding [10] and later in image coding [31] because of its inherent advantages namely variable bit assignment among the subbands as well as coding error confinement within the subbands.
		Interaction of harmonic analysis with data compression, joint source-channel coding, image coding based on models of human perception, scalability, robustness, error resilience, and complexity are a few of the many outstanding challenges in image coding to be fully resolved and may affect image data compression performance in the years to come.
	www.acm.org /crossroads/xrds6-3/sahaimgcoding.html (5361 words)

	Effective Entropy Coding (Range Coding and Arithmetic Coding) - Sachin Garg
		For entropy coding, once the character probabilities are known, the individual symbols need to be assigned a range along a "probability line".
		The archive includes C++ classes for the entropy coders and code for order-0 model which was used for testing the coders and gathering results.
		For arithmetic coding, I have used Mark Nelson's code which was published with his 1991 DDJ article.
	sachingarg.com /compression/entropy_coding/64bit (1525 words)

	Arithmetic Coding (AC)
		Arithmetic coding (AC) is a special kind of entropy coding.
		The biggest drawbak of the arithmetic coding is it´s low speed since of several needed multiplications and divisions for each symbol.
		The subinterval from the coded symbol is then taken as the interval for the next symbol.
	www.data-compression.info /Algorithms/AC (1380 words)

	Entropy and entropy coding
		The basic idea of an entropy coder is to assign bit(s) to a symbol according to its probability.
		The source code of an arithmetic coder can be downloaded here(arith.tar.gz) or (source.zip).
		Calculate the entropy of the three test images: lenna,landsat and dsa.
	www.ee.latrobe.edu.au /~dennis/teaching/ELE42IPC/ELE42IPC_lab1/node1.html (407 words)

	Significantly Lower Entropy Estimates for Natural DNA Sequences
		Ziv and Lempel, 1977] may be viewed as entropy estimators, with LZ corresponding to a model that predicts based on a historical context of variable length.
		The motivation in designing these metrics was the possibility that coding regions might contain long nearly identical amino acid sequences, which despite their nearness when expressed as an amino acid sequence, are far apart when coded as nucleotides.
		Lauc, G., Ilic, I., and Heffer-Lauc, H. Entropies of coding and noncoding sequences of DNA and proteins.
	www.pnylab.com /pny/papers/cdna/cdna/cdna.html (7298 words)

	Dr. Dobb's \| A Rapid Entropy-Coding Algorithm \| July 22, 2001 (Site not responding. Last check: 2007-11-03)
		Entropy coding is an abstract problem weakly related to the type of data being compressed, while modeling of data compression depends intimately on the type of data being compressed.
		Entropy coding is well understood, while for many real-world types of data, the modeling issue remains mysterious.
		In arithmetic coding, this relationship between the number of bits of data in a system and the number of allowable states remains valid even when b is not an integer.
	www.ddj.com /184410168 (4509 words)

	EntropyCoder
		The input to the entropy coder is the quantized wavelet coefficients, or codewords, represented in sign magnitude.
		Creates a EntropyCoder object for the appropriate entropy coding parameters in the parameter list 'pl', and having 'src' as the source of quantized data.
		Since entropy coders themselves are always reversible, it returns the reversibility of the data that comes from the 'CBlkQuantDataSrcEnc' source object (i.e.
	www.jpeg.org /jpeg2000guide/software/jj2000/jj2000-5.1-Doc/doc/jj2000/j2k/entropy/encoder/EntropyCoder.html (672 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.
		Typically, entropy encoders are used to compress data by replacing symbols represented by equal-length codes with symbols represented by codes where the length of each codeword is proportional to the negative logarithm of the probability.
		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, Dynamic Markov Compression may be useful.
	en.wikipedia.org /wiki/Entropy_encoding (398 words)

	Arithmetic Coding and Huffman Coding in MatLab.
		Complete coding may be done by calling an easy to use main program (or main function), where input argument is the sequences you want to compress and the output is the compressed bitstream, as a vector of bytes.
		For signal compression a decorrelation process usually precede the entropy coding, but often the decorrelation is not perfect.
		Huffman coding is lossless, it is also often used in lossy compression as the final step after decomposition and quantization of a signal.
	www.ux.uis.no /~karlsk/proj99 (853 words)

	Sign Coding in an Embedded Wavelet Image Coder (Site not responding. Last check: 2007-11-03)
		While promising algorithms exist for efficiently coding the transform magnitudes, current wavelet image coding algorithms are not efficient at coding the sign of the transform coefficients.
		PSNR improvements up to.7 dB are possible from an efficient modeling and entropy coding of the coefficient signs, combined with a novel coding technique called sign extrapolation, which is used to improved the final estimate of insignificant coefficients without the transmission of any additional information.
		In current wavelet image coding systems, the inefficient coding of the sign of transform coefficients is accepted as a trade-off for the gains obtained through energy compaction.
	foulard.ee.cornell.edu /adeever/sc.html (564 words)

	Range coder by Arturo Campos
		The range coder is presented, a variation of arithmetic coding which does renormalization in bytes instead of bits thus running twice faster, and with 0.01% worse compression than an standard implementation of arithmetic coding.
		Arithmetic coding works doing an interval between 0-1 and further subdiving it, based on the cumulative probability of the symbol which is currently being processed.
		Init must be called before starting to encode symbols, both encode and renormalize code the symbols, and flushing is done when you have encoded all the symbols.
	www.arturocampos.com /ac_range.html (1323 words)

	The Laws of Cryptography: the Huffman Code
		Huffman codes are always optimal (the best possible), but this particular code has average code length equal to the entropy, and it is never possible to create a code with shorter average length.
		Most Huffman codes have average code length greater than the entropy (unless all frequencies are a fraction with numerator and denominator a power of 2).
		Even though Huffman's code is optimal (it yields the best possible code for a collection of symbols and frequencies), the other adaptive algorithms (LZ or LZW) usually do a much better job of compressing a file.
	www.cs.utsa.edu /~wagner/laws/huffman.html (2369 words)

	ITU Telecommunication Standardization Sector (ITU-T) - Extensions to JPEG-1 (T.85x Series)
		The Huffman coding method is required in the T.81 baseline.
		For all other encoding processes (extended sequential, progressive, hierarchical, and lossless), the use of all defined entropy coders is allowed.
		Since the Q15-coder resolves the carry in the decoder instead of in the encoder, it has a low latency compared to the QM-coder arithmetic coder incorporated in T.81, which has a potential latency of the rest of the entire entropy-coded segment.
	www.itu.int /ITU-T/studygroups/com16/jpeg1x/about.html (267 words)

	Method and apparatus for carry-over control in arithmetic entropy coding (US4973961)
		The so-called "infinite" output register is emulated by employing a counter and a finite register.
		To this end, a count is accumulated of sets, i.e., bytes, of consecutive prescribed logical signals of a first kind, i.e., logical 1's, being generated by an arithmetic coding register and possibly modified by a carry indication.
		The accumulated count is then employed to supply as an output a like number of sets including logical signals of a second kind, i.e., logical 0's, or logical signals of the first kind, i.e., logical 1's, depending on whether or not a carry would propagate through the stages of the so-called "infinite" register being emulated.
	www.delphion.com /details?pn=US04973961__ (532 words)

	Some Compression Techniques
		In entropy coding, a characteristic called redundancy is used to decrease the size of the file.
		In Run-Length Encoding, which is a special kind of entropy coding, repetitive symbols/characters are collected and the pixels/positions where they are repeated are written down into the coded file.
		This type of coding is an example of variable length encoding (VLE), in which different symbols have codes that aren't of the same length.
	www.pha.jhu.edu /~sundar/intermediate/tech.html (932 words)

	EDN Access — 01.18.96 JPEG parameters determine compression-system performance
		JPEG uses a Huffman code to represent the magnitude category M. It then appends M bits after the Huffman code to identify a particular member of the category.
		The compressor uses a Huffman code to represent the run-length byte and appends bits to identify the member of the magnitude category.
		Assign short codes to the most common ones with the code length roughly in proportion to the negative log of the frequency of occurrence.
	www.edn.com /archives/1996/011896/02df6.htm (3793 words)

	Department of Computer Science - UWO
		Instead of coding one coefficient at one time, embedded coding actually encode the coefficients from most to least significant bit based on their binary representations.
		For video coding, it is designed to take advantages of the neighboring coefficients in the previous frame and next frame.
		The predictive audio coding uses linear prediction to predict the data values and error feedback will be used to adjust the prediction errors.
	www.csd.uwo.ca /Talks/PhDJan25_130_02.shtml (833 words)

	Apparatus and method for performing m-ary finite state machine entropy coding (US5912636)
		an entropy encoding table coupled to receive state information from the channel state storage device and encode n bits of the input data at a time in response to the state information, where n is greater than or equal to two.
		Method and means for arithmetic coding utilizing a reduced number of operations
		Arithmetic coding data compression/de-compression by selectively employed, diverse arithmetic coding encoders and decoders
	www.delphion.com /details?pn=US05912636__ (324 words)

	Arithmetic coding - Wikipedia, the free encyclopedia
		It is a form of entropy encoding, but where other entropy encoding techniques separate the input message into its component symbols and replace each symbol with a code word, arithmetic coding encodes the entire message into a single number, a fraction n where (0.0 ≤ n < 1.0).
		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.
		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 (1980 words)

	Efficient Source Coding (Site not responding. Last check: 2007-11-03)
		The entropy of this source is 1.75 bits, which means it might be possible to use a code that required fewer bits, on the average, per transmission.
		In the example, the alphabet's entropy and the average number of bits/letter are equal: The Huffman code achieves the entropy limit.
		Note that Huffman's code is a variable length code, but that it has the prefix property: No codeword occurs at the beginning of another codeword.
	www.owlnet.rice.edu /~engi202/entropy.html (563 words)

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