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287:, which in mathematics, denotes a difference), but the term is typically only used if both versions are meaningful outside compression and decompression. For example, while the process of compressing the error in the above-mentioned lossless audio compression scheme could be described as delta encoding from the approximated sound wave to the original sound wave, the approximated version of the sound wave is not meaningful in any other context.
249:, but there are other techniques that do not work for typical text that are useful for some images (particularly simple bitmaps), and other techniques that take advantage of the specific characteristics of images (such as the common phenomenon of contiguous 2-D areas of similar tones, and the fact that color images usually have a preponderance of a limited range of colors out of those representable in the color space).
737:) are the latest generation of lossless algorithms that compress data (typically sequences of nucleotides) using both conventional compression algorithms and specific algorithms adapted to genetic data. In 2012, a team of scientists from Johns Hopkins University published the first genetic compression algorithm that does not rely on external genetic databases for compression. HAPZIPPER was tailored for
792:, so winners in these benchmarks may be unsuitable for everyday use due to the slow speed of the top performers. Another drawback of some benchmarks is that their data files are known, so some program writers may optimize their programs for best performance on a particular data set. The winners on these benchmarks often come from the class of
1079:; for example, a compression application may consider files whose names end in ".zip", ".arj" or ".lha" uncompressible without any more sophisticated detection. A common way of handling this situation is quoting input, or uncompressible parts of the input in the output, minimizing the compression overhead. For example, the
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1019: − 1 bits, these kinds of claims can be safely discarded without even looking at any further details regarding the purported compression scheme. Such an algorithm contradicts fundamental laws of mathematics because, if it existed, it could be applied repeatedly to losslessly reduce any file to length 1.
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Most practical compression algorithms provide an "escape" facility that can turn off the normal coding for files that would become longer by being encoded. In theory, only a single additional bit is required to tell the decoder that the normal coding has been turned off for the entire input; however,
883:
Lossless data compression algorithms cannot guarantee compression for all input data sets. In other words, for any lossless data compression algorithm, there will be an input data set that does not get smaller when processed by the algorithm, and for any lossless data compression algorithm that makes
842:
Sami Runsas (the author of NanoZip) maintained
Compression Ratings, a benchmark similar to Maximum Compression multiple file test, but with minimum speed requirements. It offered the calculator that allowed the user to weight the importance of speed and compression ratio. The top programs were fairly
167:
model, the data is analyzed and a model is constructed, then this model is stored with the compressed data. This approach is simple and modular, but has the disadvantage that the model itself can be expensive to store, and also that it forces using a single model for all data being compressed, and so
1074:
Real compression algorithm designers accept that streams of high information entropy cannot be compressed, and accordingly, include facilities for detecting and handling this condition. An obvious way of detection is applying a raw compression algorithm and testing if its output is smaller than its
874:
The
Compression Analysis Tool is a Windows application that enables end users to benchmark the performance characteristics of streaming implementations of LZF4, Deflate, ZLIB, GZIP, BZIP2 and LZMA using their own data. It produces measurements and charts with which users can compare the compression
172:
models dynamically update the model as the data is compressed. Both the encoder and decoder begin with a trivial model, yielding poor compression of initial data, but as they learn more about the data, performance improves. Most popular types of compression used in practice now use adaptive coders.
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than N. So if we know nothing about the properties of the data we are compressing, we might as well not compress it at all. A lossless compression algorithm is useful only when we are more likely to compress certain types of files than others; then the algorithm could be designed to compress those
205:
additionally uses data points from other pairs and multiplication factors to mix them into the difference. These factors must be integers, so that the result is an integer under all circumstances. So the values are increased, increasing file size, but hopefully the distribution of values is more
1091:
Mark Nelson, in response to claims of "magic" compression algorithms appearing in comp.compression, has constructed a 415,241 byte binary file of highly entropic content, and issued a public challenge of $ 100 to anyone to write a program that, together with its input, would be smaller than his
193:
These techniques take advantage of the specific characteristics of images such as the common phenomenon of contiguous 2-D areas of similar tones. Every pixel but the first is replaced by the difference to its left neighbor. This leads to small values having a much higher probability than large
1022:
On the other hand, it has also been proven that there is no algorithm to determine whether a file is incompressible in the sense of
Kolmogorov complexity. Hence it is possible that any particular file, even if it appears random, may be significantly compressed, even including the size of the
991:
that the algorithm is designed to remove, and thus belong to the subset of files that that algorithm can make shorter, whereas other files would not get compressed or even get bigger. Algorithms are generally quite specifically tuned to a particular type of file: for example, lossless audio
180:
meaning that they can accept any bitstring) can be used on any type of data, many are unable to achieve significant compression on data that are not of the form for which they were designed to compress. Many of the lossless compression techniques used for text also work reasonably well for
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194:
values. This is often also applied to sound files, and can compress files that contain mostly low frequencies and low volumes. For images, this step can be repeated by taking the difference to the top pixel, and then in videos, the difference to the pixel in the next frame can be taken.
103:
Lossless compression is used in cases where it is important that the original and the decompressed data be identical, or where deviations from the original data would be unfavourable. Common examples are executable programs, text documents, and source code. Some image file formats, like
209:
The adaptive encoding uses the probabilities from the previous sample in sound encoding, from the left and upper pixel in image encoding, and additionally from the previous frame in video encoding. In the wavelet transformation, the probabilities are also passed through the hierarchy.
722:. However, many ordinary lossless compression algorithms produce headers, wrappers, tables, or other predictable output that might instead make cryptanalysis easier. Thus, cryptosystems must utilize compression algorithms whose output does not contain these predictable patterns.
969:
In fact, if we consider files of length N, if all files were equally probable, then for any lossless compression that reduces the size of some file, the expected length of a compressed file (averaged over all possible files of length N) must necessarily be
986:
The "trick" that allows lossless compression algorithms, used on the type of data they were designed for, to consistently compress such files to a shorter form is that the files the algorithms are designed to act on all have some form of easily modeled
2102:
862:
The
Monster of Compression benchmark by Nania Francesco Antonio tested compression on 1Gb of public data with a 40-minute time limit. In December 2009, the top ranked archiver was NanoZip 0.07a and the top ranked single file compressor was
895:
Suppose that there is a compression algorithm that transforms every file into an output file that is no longer than the original file, and that at least one file will be compressed into an output file that is shorter than the original
953:
that is simultaneously the output of the compression function on two different inputs. That file cannot be decompressed reliably (which of the two originals should that yield?), which contradicts the assumption that the algorithm was
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of all files that will become usefully shorter. This is the theoretical reason why we need to have different compression algorithms for different kinds of files: there cannot be any algorithm that is good for all kinds of data.
744:
Genomic sequence compression algorithms, also known as DNA sequence compressors, explore the fact that DNA sequences have characteristic properties, such as inverted repeats. The most successful compressors are XM and GeCo. For
313:. For this reason, many different algorithms exist that are designed either with a specific type of input data in mind or with specific assumptions about what kinds of redundancy the uncompressed data are likely to contain.
2112:, "n "Frequency-Time Based Data Compression Method" supporting the compression, encryption, decompression, and decryption and persistence of many binary digits through frequencies where each frequency represents many bits."
1010:
It is provably impossible to create an algorithm that can losslessly compress any data. While there have been many claims through the years of companies achieving "perfect compression" where an arbitrary number
1049:
on sequences (normally of octets). Compression is successful if the resulting sequence is shorter than the original sequence (and the instructions for the decompression map). For a compression algorithm to be
763:
Self-extracting executables contain a compressed application and a decompressor. When executed, the decompressor transparently decompresses and runs the original application. This is especially often used in
140:
for the input data, and the second step uses this model to map input data to bit sequences in such a way that "probable" (i.e. frequently encountered) data will produce shorter output than "improbable" data.
814:
dating back to 1987 is no longer widely used due to its small size. Matt
Mahoney maintained the Calgary Compression Challenge, created and maintained from May 21, 1996, through May 21, 2016, by Leonid A.
252:
As mentioned previously, lossless sound compression is a somewhat specialized area. Lossless sound compression algorithms can take advantage of the repeating patterns shown by the wave-like nature of the
77:. Different algorithms exist that are designed either with a specific type of input data in mind or with specific assumptions about what kinds of redundancy the uncompressed data are likely to contain.
268:
models to predict the "next" value and encoding the (hopefully small) difference between the expected value and the actual data. If the difference between the predicted and the actual data (called the
197:
A hierarchical version of this technique takes neighboring pairs of data points, stores their difference and sum, and on a higher level with lower resolution continues with the sums. This is called
875:
speed, decompression speed and compression ratio of the different compression methods and to examine how the compression level, buffer size and flushing operations affect the results.
176:
Lossless compression methods may be categorized according to the type of data they are designed to compress. While, in principle, any general-purpose lossless compression algorithm (
226:
compression, and in particular licensing practices by patent holder Unisys that many developers considered abusive, some open source proponents encouraged people to avoid using the
741:
data and achieves over 20-fold compression (95% reduction in file size), providing 2- to 4-fold better compression much faster than leading general-purpose compression utilities.
1381:; Mandyam, Giridhar D.; Magotra, Neeraj (April 17, 1995). Rodriguez, Arturo A.; Safranek, Robert J.; Delp, Edward J. (eds.). "DCT-based scheme for lossless image compression".
272:) tends to be small, then certain difference values (like 0, +1, −1 etc. on sample values) become very frequent, which can be exploited by encoding them in few output bits.
978:
Thus, the main lesson from the argument is not that one risks big losses, but merely that one cannot always win. To choose an algorithm always means implicitly to select a
884:
at least one file smaller, there will be at least one file that it makes larger. This is easily proven with elementary mathematics using a counting argument called the
1819:
1029:, which appear random but can be generated by a very small program. However, even though it cannot be determined whether a particular file is incompressible, a
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848:
218:
Many of these methods are implemented in open-source and proprietary tools, particularly LZW and its variants. Some algorithms are patented in the
128:
files are typically used on portable players and in other cases where storage space is limited or exact replication of the audio is unnecessary.
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provided binary data yet be able to reconstitute it without error. A similar challenge, with $ 5,000 as reward, was issued by Mike
Goldman.
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from "plain" to "compressed" bit sequences. The pigeonhole principle prohibits a bijection between the collection of sequences of length
160:, whereas Huffman compression is simpler and faster but produces poor results for models that deal with symbol probabilities close to 1.
852:
66:, no lossless compression algorithm can shrink the size of all possible data: Some data will get longer by at least one symbol or bit.
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shows that over 99% of files of any given length cannot be compressed by more than one byte (including the size of the decompressor).
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383:
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XM is slightly better in compression ratio, though for sequences larger than 100 MB its computational requirements are impractical.
156:. Arithmetic coding achieves compression rates close to the best possible for a particular statistical model, which is given by the
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We must therefore conclude that our original hypothesis (that the compression function makes no file longer) is necessarily untrue.
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Proceedings of the 1998 IEEE International
Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181)
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data cannot be consistently compressed by any conceivable lossless data compression algorithm; indeed, this result is used to
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data format specifies the 'compression method' of 'Stored' for input files that have been copied into the archive verbatim.
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1988:
1964:
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125:
1066:−1. Therefore, it is not possible to produce a lossless algorithm that reduces the size of every possible input sequence.
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and other countries and their legal usage requires licensing by the patent holder. Because of patents on certain kinds of
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772:. This type of compression is not strictly limited to binary executables, but can also be applied to scripts, such as
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Compression algorithms are usually effective for human- and machine-readable documents and cannot shrink the size of
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most encoding algorithms use at least one full byte (and typically more than one) for this purpose. For example,
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with a selection of domain-specific prediction filters. However, the patents on LZW expired on June 20, 2003.
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The
Generic Compression Benchmark, maintained by Matt Mahoney, tests compression of data generated by random
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121:
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The
Compression Ratings website published a chart summary of the "frontier" in compression ratio and time.
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Pratas, D.; Pinho, A. J.; Ferreira, P. J. S. G. (2016). "Efficient compression of genomic sequences".
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that allows the original data to be perfectly reconstructed from the compressed data with no loss of
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436:(RLE) – Simple scheme that provides good compression of data containing many runs of the same value
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It is sometimes beneficial to compress only the differences between two versions of a file (or, in
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17:
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different due to the speed requirement. In
January 2010, the top program was NanoZip followed by
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93:
92:. It is also often used as a component within lossy data compression technologies (e.g. lossless
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Lossless compression algorithms and their implementations are routinely tested in head-to-head
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8th International Conference on Informatics in Schools: Situation, Evolution, and Perspectives
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1004:
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But 2 is smaller than 2+1, so by the pigeonhole principle there must be some file of length
788:. There are a number of better-known compression benchmarks. Some benchmarks cover only the
714:
encryption for added security. When properly implemented, compression greatly increases the
362:(LZ77 and LZ78) – Dictionary-based algorithm that forms the basis for many other algorithms
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Most lossless compression programs do two things in sequence: the first step generates a
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Many of the lossless compression techniques used for text also work reasonably well for
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Lossless data compression is used in many applications. For example, it is used in the
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1984:
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1252:"General characteristics and design considerations for temporal subband video coding"
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594:
593:– (includes lossless compression method via Le Gall–Tabatabai 5/3 reversible integer
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81:
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compressed files never need to grow by more than 5 bytes per 65,535 bytes of input.
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coding, where competitions are held for demos with strict size limits, as small as
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keeps its size during compression. There are 2 such files possible. Together with
892:
Assume that each file is represented as a string of bits of some arbitrary length.
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1956:
1955:. The Morgan Kaufmann Series in Multimedia Information and Systems (5 ed.).
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124:
formats are most often used for archiving or production purposes, while smaller
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1980:
1469:
Alfred J. Menezes; Paul C. van Oorschot; Scott A. Vanstone (October 16, 1996).
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27:
Data compression approach allowing perfect reconstruction of the original data
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2006:
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No lossless compression algorithm can efficiently compress all possible data
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942:, this makes 2+1 files that all compress into one of the 2 files of length
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707:
470:
1236:
564:– High Efficiency Image File Format (lossless or lossy compression, using
316:
Some of the most common lossless compression algorithms are listed below.
3233:
3111:
2907:
2783:
2733:
1977:
Lossless Compression Handbook (Communications, Networking and Multimedia)
1513:
43:. Lossless compression is possible because most real-world data exhibits
40:
347:
reversible transform for making textual data more compressible, used by
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2728:
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773:
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515:
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428:
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compression programs do not work well on text files, and vice versa.
823:
590:
504:
333:
1023:
decompressor. An example is the digits of the mathematical constant
163:
There are two primary ways of constructing statistical models: in a
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1051:
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415:
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202:
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The primary encoding algorithms used to produce bit sequences are
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2396:
1687:(September 28 – October 1, 2015). "Surprising Computer Science".
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606:
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51:
permits reconstruction only of an approximation of the original
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1495:
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400:
70:
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1777:
An Introduction to Kolmogorov Complexity and its Applications
1256:
856:
829:
584:
575:
348:
329:
2477:
2331:
2316:
2306:
2049:
1738:"Lossless Compression - an overview | ScienceDirect Topics"
1389:. International Society for Optics and Photonics: 474–478.
1383:
Digital Video Compression: Algorithms and Technologies 1995
1185:"Unit 4 Lab 4: Data Representation and Compression, Page 6"
671:
571:
555:
387:
373:
113:
89:
52:
644:– Portable Document Format (lossless or lossy compression)
279:, of successive images within a sequence). This is called
168:
performs poorly on files that contain heterogeneous data.
2452:
2418:
1284:"Mathematical properties of the JPEG2000 wavelet filters"
826:
635:
410:
368:– Combines LZ77 compression with Huffman coding, used by
109:
105:
97:
85:
1062:
and any subset of the collection of sequences of length
674:– (lossless or lossy compression of RGB and RGBA images)
2089:
1498:"HapZipper: sharing HapMap populations just got easier"
1025:
668:– Tag Image File Format (lossless or lossy compression)
1798:
1691:. Lecture Notes in Computer Science. Vol. 9378.
1086:
915:
be the length (in bits) of the compressed version of
818:
The Large Text Compression Benchmark and the similar
1755:
1662:
356:– Entropy encoding, pairs well with other algorithms
230:(GIF) for compressing still image files in favor of
1544:
1377:
1211:"Lossless Streaming – the future of high res audio"
802:, in his February 2010 edition of the free booklet
587:– (lossless or lossy compression of B&W images)
112:, use only lossless compression, while others like
1813:
3336:
2069:
1070:Points of application in real compression theory
911:bits that compresses to something shorter. Let
603:– (lossless/near-lossless compression standard)
1912:"The Million Random Digit Challenge Revisited"
1832:
903:be the least number such that there is a file
386:(LZMA) – Very high compression ratio, used by
2133:
1679:
1677:
1423:
2147:
2071:"Lossless and lossy audio formats for music"
1578:
1496:Chanda, P.; Elhaik, E.; Bader, J.S. (2012).
1462:
687:– Lossless compression of 3D triangle meshes
1031:simple theorem about incompressible strings
1015:of random bits can always be compressed to
718:by removing patterns that might facilitate
2140:
2126:
1674:
1564:: CS1 maint: location missing publisher (
1036:
213:
120:may use either lossless or lossy methods.
100:encoders and other lossy audio encoders).
1975:Sayood, Khalid, ed. (December 18, 2002).
1773:
1683:
1521:
1432:. Vol. 3. pp. 1769–1772 vol.3.
1281:
1249:
1075:input. Sometimes, detection is made by
725:
623:, includes a lossless compression method
297:Category:Lossless compression algorithms
2097:from the original on February 10, 2013.
1350:The Essential Guide to Video Processing
301:List of lossless compression algorithms
55:, though usually with greatly improved
14:
3337:
1974:
1950:
1909:
1761:
1668:
1538:
1426:"Reversible discrete cosine transform"
1250:Sullivan, Gary (December 8–12, 2003).
710:often compress data (the "plaintext")
2121:
1346:
1291:IEEE Transactions on Image Processing
1208:
59:(and therefore reduced media sizes).
1275:
1148:Lossless Transform Audio Compression
806:, additionally lists the following:
1951:Sayood, Khalid (October 27, 2017).
1780:. New York: Springer. p. 102.
1636:. September 1, 2016. Archived from
1424:Komatsu, K.; Sezaki, Kaoru (1998).
1054:, the compression map must form an
455:(ALAC – Apple Lossless Audio Codec)
24:
2024:
1944:
1927:"The $ 5000 Compression Challenge"
1598:"Large Text Compression Benchmark"
1087:The Million Random Digit Challenge
543:
447:Adaptive Transform Acoustic Coding
427:(PPM) – Optimized for compressing
319:
25:
3361:
1999:
1924:
1164:Universal code (data compression)
609:– (lossless or lossy compression)
384:Lempel–Ziv–Markov chain algorithm
3314:
3313:
3304:
3303:
1953:Introduction to Data Compression
1893:".ZIP File Format Specification"
1774:Li, Ming; Vitányi, Paul (1993).
1472:Handbook of Applied Cryptography
308:
3350:Lossless compression algorithms
1918:
1903:
1885:
1826:
1767:
1730:
1644:
1626:
1616:"Generic Compression Benchmark"
1608:
1590:
1572:
1489:
731:Genetics compression algorithms
702:
574:– (lossless RLE compression of
1910:Nelson, Mark (June 20, 2006).
1808:
1802:
1417:
1371:
1340:
1243:
1221:
1202:
1177:
878:
752:
678:
425:Prediction by partial matching
13:
1:
2091:"Image Compression Benchmark"
1209:Price, Andy (March 3, 2022).
1170:
1003:the concept of randomness in
779:
698:list of lossless video codecs
403:in tandem with Huffman coding
188:
131:
2027:"Theory of Data Compression"
1581:"Data Compression Explained"
1118:Entropy (information theory)
1103:Comparison of file archivers
558:– Free Lossless Image Format
328:– Entropy encoding, used by
7:
2055:Hydrogenaudio Knowledgebase
1854:10.1007/978-3-319-16250-8_3
1701:10.1007/978-3-319-25396-1_1
1652:"Compression Analysis Tool"
1548:Data Compression Conference
1282:Unser, M.; Blu, T. (2003).
1095:
656:– Portable Network Graphics
397:Lempel–Ziv–Storer–Szymanski
306:
228:Graphics Interchange Format
10:
3366:
3195:Compressed data structures
2517:RLE + BWT + MTF + Huffman
2185:Asymmetric numeral systems
1838:"The Pigeonhole Principle"
1438:10.1109/ICASSP.1998.681802
1262:Video Coding Experts Group
804:Data Compression Explained
756:
461:(also known as MPEG-4 ALS)
294:
290:
234:(PNG), which combines the
199:discrete wavelet transform
3299:
3283:
3267:
3185:
3110:
3042:
3033:
2956:
2890:
2881:
2782:
2699:
2690:
2606:
2554:Discrete cosine transform
2544:
2535:
2484:LZ77 + Huffman + context
2437:
2347:
2277:
2165:
2156:
2108:February 2, 2017, at the
1821:is not partial recursive.
1792:Theorem 2.6 The function
1215:Audio Media International
733:(not to be confused with
631:Discrete Cosine Transform
527:TTA (True Audio Lossless)
487:Meridian Lossless Packing
481:Free Lossless Audio Codec
345:Burrows–Wheeler transform
232:Portable Network Graphics
3259:Smallest grammar problem
2007:"LZF compression format"
1235:. Unisys. Archived from
1229:"LZW Patent Information"
995:In particular, files of
691:
539:(Windows Media Lossless)
440:
3200:Compressed suffix array
2749:Nyquist–Shannon theorem
1347:Bovik, Alan C. (2009).
1311:10.1109/TIP.2003.812329
1037:Mathematical background
650:– Quite OK Image Format
552:– AV1 Image File Format
283:(from the Greek letter
214:Historical legal issues
84:file format and in the
1815:
1658:. Noemax Technologies.
975:types of data better.
796:compression software.
790:data compression ratio
759:Executable compression
510:Original Sound Quality
501:(also known as HD-AAC)
465:Direct Stream Transfer
360:Lempel-Ziv compression
45:statistical redundancy
3229:Kolmogorov complexity
3097:Video characteristics
2474:LZ77 + Huffman + ANS
2051:"Lossless comparison"
1899:chapter V, section J.
1816:
1742:www.sciencedirect.com
1640:on September 1, 2016.
1579:Matt Mahoney (2010).
1138:Kolmogorov complexity
1043:compression algorithm
1005:Kolmogorov complexity
726:Genetics and genomics
459:Audio Lossless Coding
94:mid/side joint stereo
73:data that contain no
3319:Compression software
2913:Compression artifact
2869:Psychoacoustic model
2103:US patent #7,096,360
1814:{\displaystyle C(x)}
1796:
1336:on October 13, 2019.
886:pigeonhole principle
518:(RealAudio Lossless)
495:(Monkey's Audio APE)
64:pigeonhole principle
62:By operation of the
33:Lossless compression
3309:Compression formats
2948:Texture compression
2943:Standard test image
2759:Silence compression
1395:1995SPIE.2419..474M
1303:2003ITIP...12.1080U
1045:can be viewed as a
822:both use a trimmed
476:DTS-HD Master Audio
434:Run-length encoding
158:information entropy
3217:Information theory
3072:Display resolution
2898:Chroma subsampling
2287:Byte pair encoding
2232:Shannon–Fano–Elias
2077:. November 6, 2003
1836:(March 18, 2015).
1811:
1723:See in particular
1514:10.1093/nar/gks709
1133:Information theory
1123:Grammar-based code
735:genetic algorithms
638:– PiCture eXchange
533:(WavPack lossless)
413:images and Unix's
341:– Entropy encoding
309:§ Limitations
264:essentially using
148:(also used by the
3332:
3331:
3181:
3180:
3131:Deblocking filter
3029:
3028:
2877:
2876:
2686:
2685:
2531:
2530:
2057:. January 5, 2015
1863:978-3-319-16250-8
1710:978-3-319-25396-1
1695:. pp. 1–11.
1554:. Snowbird, Utah.
1502:Nucleic Acids Res
1482:978-1-4398-2191-6
1403:10.1117/12.206386
1154:Lossy compression
595:wavelet transform
399:(LZSS) – Used by
339:Arithmetic coding
311:for more on this)
277:video compression
240:deflate algorithm
154:arithmetic coding
150:deflate algorithm
138:statistical model
96:preprocessing by
57:compression rates
49:lossy compression
16:(Redirected from
3357:
3345:Data compression
3317:
3316:
3307:
3306:
3136:Lapped transform
3040:
3039:
2918:Image resolution
2903:Coding tree unit
2888:
2887:
2697:
2696:
2542:
2541:
2163:
2162:
2149:Data compression
2142:
2135:
2128:
2119:
2118:
2098:
2086:
2084:
2082:
2075:Bobulous Central
2066:
2064:
2062:
2046:
2044:
2042:
2033:. Archived from
2031:Data Compression
2021:
2019:
2017:
1994:
1990:978-0-12390754-7
1970:
1966:978-0-12809474-7
1938:
1937:
1935:
1933:
1925:Craig, Patrick.
1922:
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1335:
1329:. Archived from
1297:(9): 1080–1090.
1288:
1279:
1273:
1272:
1270:
1268:
1247:
1241:
1240:
1239:on June 2, 2009.
1225:
1219:
1218:
1206:
1200:
1199:
1197:
1195:
1181:
1113:David A. Huffman
1108:Data compression
716:unicity distance
662:– Truevision TGA
418:
409:(LZW) – Used by
407:Lempel–Ziv–Welch
312:
263:
262:
258:
47:. By contrast,
37:data compression
21:
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3358:
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3335:
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3333:
3328:
3295:
3279:
3263:
3244:Rate–distortion
3177:
3106:
3025:
2952:
2873:
2778:
2774:Sub-band coding
2682:
2607:Predictive type
2602:
2527:
2494:LZSS + Huffman
2444:LZ77 + Huffman
2433:
2343:
2279:Dictionary type
2273:
2175:Adaptive coding
2152:
2146:
2110:Wayback Machine
2080:
2078:
2060:
2058:
2040:
2038:
2015:
2013:
2005:
2002:
1991:
1967:
1957:Morgan Kaufmann
1947:
1945:Further reading
1942:
1941:
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1627:
1620:mattmahoney.net
1614:
1613:
1609:
1602:mattmahoney.net
1596:
1595:
1591:
1586:. pp. 3–5.
1583:
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1357:. p. 355.
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934:file of length
881:
837:Turing machines
782:
761:
755:
728:
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681:
546:
544:Raster graphics
443:
414:
322:
320:General purpose
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178:general-purpose
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2678:Psychoacoustic
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2087:
2067:
2047:
2037:on May 8, 2016
2022:
2001:
2000:External links
1998:
1997:
1996:
1989:
1981:Academic Press
1979:(1 ed.).
1972:
1965:
1946:
1943:
1940:
1939:
1917:
1902:
1884:
1862:
1848:. p. 21.
1842:Proof Patterns
1834:Joshi, Mark S.
1825:
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1355:Academic Press
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1145:
1143:List of codecs
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1120:
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1041:Abstractly, a
1038:
1035:
959:
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947:
920:
897:
893:
888:, as follows:
880:
877:
869:
868:
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812:Calgary Corpus
794:context-mixing
781:
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757:Main article:
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354:Huffman coding
351:
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281:delta encoding
266:autoregressive
247:indexed images
215:
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187:
183:indexed images
146:Huffman coding
133:
130:
122:Lossless audio
35:is a class of
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2764:Sound quality
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2025:Phamdo, Nam.
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2012:
2008:
2004:
2003:
1992:
1986:
1982:
1978:
1973:
1968:
1962:
1958:
1954:
1949:
1948:
1928:
1921:
1913:
1906:
1898:
1894:
1888:
1873:
1869:
1865:
1859:
1855:
1851:
1847:
1843:
1839:
1835:
1829:
1822:
1805:
1799:
1789:
1787:0-387-94053-7
1783:
1779:
1778:
1770:
1764:, p. 38.
1763:
1758:
1743:
1739:
1733:
1726:
1720:
1716:
1712:
1706:
1702:
1698:
1694:
1690:
1686:
1680:
1678:
1671:, p. 41.
1670:
1665:
1657:
1653:
1647:
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1621:
1617:
1611:
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1599:
1593:
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1575:
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1499:
1492:
1484:
1478:
1475:. CRC Press.
1474:
1473:
1465:
1457:
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1449:
1447:0-7803-4428-6
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1364:9780080922508
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1324:
1320:
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1267:September 13,
1263:
1259:
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1234:
1230:
1224:
1216:
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1159:Normal number
1157:
1155:
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834:
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797:
795:
791:
787:
777:
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771:
767:
760:
750:
748:
742:
740:
736:
732:
723:
721:
720:cryptanalysis
717:
713:
709:
708:Cryptosystems
700:
699:
686:
683:
682:
673:
670:
667:
664:
661:
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628:
625:
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583:
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389:
385:
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371:
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346:
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288:
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273:
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220:United States
211:
207:
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161:
159:
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147:
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119:
115:
111:
107:
101:
99:
95:
91:
87:
83:
78:
76:
72:
67:
65:
60:
58:
54:
50:
46:
42:
38:
34:
30:
19:
3275:Hutter Prize
3239:Quantization
3144:Compensation
2938:Quantization
2661:Compensation
2227:Shannon–Fano
2167:Entropy type
2157:
2099:overview of
2079:. Retrieved
2074:
2059:. Retrieved
2054:
2039:. Retrieved
2035:the original
2030:
2014:. Retrieved
2010:
1976:
1952:
1930:. Retrieved
1920:
1905:
1897:PKWARE, Inc.
1887:
1875:. Retrieved
1841:
1828:
1791:
1776:
1769:
1757:
1745:. Retrieved
1741:
1732:
1688:
1664:
1655:
1646:
1638:the original
1628:
1619:
1610:
1601:
1592:
1574:
1547:
1540:
1505:
1501:
1491:
1471:
1464:
1429:
1419:
1386:
1382:
1379:Ahmed, Nasir
1373:
1349:
1342:
1331:the original
1294:
1290:
1277:
1265:. Retrieved
1255:
1245:
1237:the original
1233:About Unisys
1232:
1223:
1214:
1204:
1192:. Retrieved
1188:
1179:
1128:Hutter Prize
1090:
1073:
1063:
1059:
1040:
1024:
1021:
1016:
1012:
1009:
1000:
994:
985:
979:
977:
971:
968:
960:
950:
943:
939:
935:
931:
927:
923:
916:
912:
908:
907:with length
904:
900:
882:
873:
870:
820:Hutter Prize
803:
800:Matt Mahoney
798:
783:
762:
743:
729:
711:
706:
703:Cryptography
695:
620:
616:
537:WMA Lossless
471:Dolby TrueHD
315:
304:
274:
269:
251:
244:
217:
208:
196:
192:
177:
175:
169:
164:
162:
143:
137:
135:
102:
79:
68:
61:
32:
31:
29:
3234:Prefix code
3087:Frame types
2908:Color space
2734:Convolution
2464:LZ77 + ANS
2375:Incremental
2348:Other types
2267:Levenshtein
2081:October 17,
2061:October 17,
2041:October 17,
2016:October 17,
1995:(488 pages)
1971:(790 pages)
1762:Sayood 2002
1747:October 30,
1669:Sayood 2002
1508:(20): 1–7.
1189:bjc.edc.org
879:Limitations
753:Executables
679:3D Graphics
629:– Lossless
615:– formerly
126:lossy audio
41:information
3339:Categories
3291:Mark Adler
3249:Redundancy
3166:Daubechies
3149:Estimation
3082:Frame rate
3004:Daubechies
2964:Chain code
2923:Macroblock
2729:Companding
2666:Estimation
2586:Daubechies
2292:Lempel–Ziv
2252:Exp-Golomb
2180:Arithmetic
1877:August 24,
1656:Free Tools
1171:References
1077:heuristics
989:redundancy
786:benchmarks
780:Benchmarks
774:JavaScript
747:eukaryotes
516:RealPlayer
499:MPEG-4 SLS
429:plain text
295:See also:
206:peaked.
189:Multimedia
132:Techniques
75:redundancy
3268:Community
3092:Interlace
2478:Zstandard
2257:Fibonacci
2247:Universal
2205:Canonical
1872:116983697
1685:Bell, Tim
1634:"Summary"
1560:cite book
1056:injection
954:lossless.
832:data set.
824:Knowledge
815:Broukhis.
591:JPEG 2000
505:OptimFROG
334:Zstandard
3254:Symmetry
3222:Timeline
3205:FM-index
3050:Bit rate
3043:Concepts
2891:Concepts
2754:Sampling
2707:Bit rate
2700:Concepts
2402:Sequitur
2237:Tunstall
2210:Modified
2200:Adaptive
2158:Lossless
2106:Archived
2095:Archived
1846:Springer
1719:26313283
1693:Springer
1532:22844100
1456:17045923
1411:13894279
1319:18237979
1194:April 9,
1096:See also
1052:lossless
1047:function
922:Because
853:flashzip
621:HD Photo
416:compress
203:JPEG2000
170:Adaptive
18:Lossless
3212:Entropy
3161:Wavelet
3140:Motion
2999:Wavelet
2979:Fractal
2974:Deflate
2957:Methods
2744:Latency
2657:Motion
2581:Wavelet
2498:LHA/LZH
2448:Deflate
2397:Re-Pair
2392:Grammar
2222:Shannon
2195:Huffman
2151:methods
1932:June 8,
1725:pp. 8–9
1523:3488212
1391:Bibcode
1327:2765169
1299:Bibcode
972:greater
964:deflate
845:FreeArc
685:OpenCTM
617:WMPhoto
613:JPEG XR
607:JPEG XL
601:JPEG-LS
581:images)
531:WavPack
522:Shorten
449:(ATRAC)
419:utility
366:Deflate
291:Methods
261:
257:
238:-based
3323:codecs
3284:People
3187:Theory
3154:Vector
2671:Vector
2488:Brotli
2438:Hybrid
2337:Snappy
2190:Golomb
2011:github
1987:
1963:
1870:
1860:
1784:
1717:
1707:
1530:
1520:
1479:
1454:
1444:
1409:
1361:
1325:
1317:
1150:(LTAC)
1001:define
997:random
980:subset
867:1.30c.
855:, and
739:HapMap
712:before
483:(FLAC)
401:WinRAR
380:images
376:, and
165:static
152:) and
71:random
3114:parts
3112:Codec
3077:Frame
3035:Video
3019:SPIHT
2928:Pixel
2883:Image
2837:ACELP
2808:ADPCM
2798:μ-law
2793:A-law
2786:parts
2784:Codec
2692:Audio
2631:ACELP
2619:ADPCM
2596:SPIHT
2537:Lossy
2521:bzip2
2512:LZHAM
2468:LZFSE
2370:Delta
2262:Gamma
2242:Unary
2217:Range
1868:S2CID
1715:S2CID
1584:(PDF)
1552:(PDF)
1452:S2CID
1407:S2CID
1334:(PDF)
1323:S2CID
1287:(PDF)
1257:ITU-T
932:every
896:file.
857:7-Zip
830:UTF-8
692:Video
585:JBIG2
576:Amiga
524:(SHN)
512:(OSQ)
489:(MLP)
467:(DST)
441:Audio
349:bzip2
330:LZFSE
307:(see
270:error
88:tool
3126:DPCM
2933:PSNR
2864:MDCT
2857:WLPC
2842:CELP
2803:DPCM
2651:WLPC
2636:CELP
2614:DPCM
2564:MDCT
2508:LZMA
2409:LDCT
2387:DPCM
2332:LZWL
2322:LZSS
2317:LZRW
2307:LZJB
2083:2017
2063:2017
2043:2017
2018:2017
1985:ISBN
1961:ISBN
1934:2009
1879:2021
1858:ISBN
1782:ISBN
1749:2022
1705:ISBN
1566:link
1528:PMID
1477:ISBN
1442:ISBN
1387:2419
1359:ISBN
1315:PMID
1269:2019
1196:2022
926:<
899:Let
865:ccmx
810:The
766:demo
696:See
672:WebP
666:TIFF
627:LDCT
619:and
572:ILBM
566:HEVC
562:HEIF
556:FLIF
550:AVIF
390:and
388:7zip
374:gzip
332:and
299:and
255:data
236:LZ77
116:and
114:TIFF
90:gzip
53:data
3171:DWT
3121:DCT
3065:VBR
3060:CBR
3055:ABR
3014:EZW
3009:DWT
2994:RLE
2984:KLT
2969:DCT
2852:LSP
2847:LAR
2832:LPC
2825:FFT
2722:VBR
2717:CBR
2712:ABR
2646:LSP
2641:LAR
2626:LPC
2591:DWT
2576:FFT
2571:DST
2559:DCT
2458:LZS
2453:LZX
2429:RLE
2424:PPM
2419:PAQ
2414:MTF
2382:DMC
2360:CTW
2355:BWT
2327:LZW
2312:LZO
2302:LZ4
2297:842
1850:doi
1697:doi
1518:PMC
1510:doi
1434:doi
1399:doi
1307:doi
1081:zip
849:CCM
827:XML
660:TGA
654:PNG
648:QOI
642:PDF
636:PCX
579:IFF
411:GIF
378:PNG
370:ZIP
326:ANS
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118:MNG
110:GIF
108:or
106:PNG
98:MP3
86:GNU
82:ZIP
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285:Δ
259:—
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