Lossless data compression

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Lossless data compression is a class of data compression algorithms that allows the exact original data to be reconstructed from the compressed data. This can be contrasted to lossy data compression, which does not allow the exact original data to be reconstructed from the compressed data.

Lossless data compression is used in software compression tools such as the highly popular ZIP file format, used by PKZIP, WinZip and Mac OS 10.3, and the Unix programs bzip2, gzip and compress. Other popular formats include Stuffit, RAR and 7z.

Lossless compression is used when it is important that the original and the decompressed data be identical, or when no assumption can be made on whether certain deviation is uncritical. Typical examples are executable programs and source code. Some image file formats, notably PNG, use only lossless compression, while others like TIFF and MNG may use either lossless or lossy methods. GIF uses a lossless compression method, but most GIF implementations are incapable of representing full color, so they quantize the image (often with dithering) to 256 or fewer colors before encoding as GIF. Color quantization is a lossy process, but reconstructing the color image and then re-quantizing it produces no additional loss. (Some rare GIF implementations make multiple passes over an image, adding 255 new colors on each pass.)

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Lossless compression techniques

Lossless compression methods may be categorized according to the type of data they are designed to compress. The three main types of targets for compression algorithms are text, images, and sound. Whilst, in principle, any general-purpose lossless compression algorithm (general-purpose means that they can handle all binary input) can be used on any type of data, many are unable to achieve significant compression on data that is not of the form that they are designed to deal with. Sound data, for instance, cannot be compressed well with conventional text compression algorithms.

Most lossless compression programs use two different kinds of algorithms: one which generates a statistical model for the input data, and another which maps the input data to bit strings using this model in such a way that "probable" (e.g. frequently encountered) data will produce shorter output than "improbable" data. Often, only the former algorithm is named, while the second is implied (through common use, standardization etc.) or unspecified.

Statistical modelling algorithms for text (or text-like binary data such as executables) include:

Encoding algorithms to produce bit sequences are:

Many of these methods are implemented in open-source and proprietary tools, particularly LZW and its variants. Some algorithms are patented in the USA and other countries and their legal usage requires licensing by the patent holder. Because of patents on certain kinds of LZW compression, and in particular licensing practices by patent holder Unisys that many developers considered abusive, some open source activists encouraged people to avoid using the Graphics Interchange Format (GIF) for compressing image files in favor of Portable Network Graphics PNG, which combines the LZ77-based deflate algorithm with a selection of domain-specific prediction filters.

Many of the lossless compression techniques used for text also work reasonably well for indexed images, 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 colour images usually have a preponderance to a limited range of colours out of those representable in the colour space).

As mentioned previously, lossless sound compression is a somewhat specialised area. Lossless sound compression algorithms can take advantage of the repeating patterns shown by the wave-like nature of the data - essentially using 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 "error") 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.

It is sometimes beneficial to compress only the differences between two versions of a file (or, in video compression, of an image). This is called delta compression (from the Greek letter Δ which is commonly used in mathematics to denote 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 compression from the approximated sound wave to the original sound wave, the approximated version of the sound wave is not meaningful in any other context.

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Lossless compression methods

For a complete list, see Category:Lossless compression algorithms

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Audio compression

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Graphic compression

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Video compression

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Lossless data compression must always make some files longer

Lossless data compression algorithms cannot guarantee to compress (that is make smaller) 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. This is easily proven with elementary mathematics using a counting argument, as follows:

  • Assume that each file is represented as a string of bits of some arbitrary length.
  • Suppose that there is a compression algorithm that transforms every file into a distinct file which is no longer than the original file, and that at least one file will be compressed into something that is shorter than itself.
  • Let M be the least number such that there is a file F with length M bits that compresses to something shorter. Let N be the length of the compressed version of F.
  • Because N<M, every file of length N keeps its size during compression. There are 2N such files. Together with F, this makes 2N+1 files which all compress into one of the 2N files of length N.
  • But 2N is smaller than 2N+1, so there must be some file of length N which 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 lossless.
  • We must conclude that our original hypothesis (that the compression function makes no file longer) must be untrue.

Any lossless compression algorithm that makes some files shorter must necessarily make some files longer, but it is not necessary that those files become very much longer. Most practical compression algorithms provide an "escape" facility that can turn off the normal coding for files that would become longer by being encoded. Then the only increase in size is a few bits to tell the decoder that the normal coding has been turned off for the entire input. For example, deflate compressed files never need to grow by more than 5 bytes per 65,535 bytes of input.

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 to implicitly select a subset 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.

The most common class of real-world data files that fail to become shorter on compression are cases when a file containing data compressed by one algorithm are fed to another algorithm (for instance, when already-compressed audio or image files are added to a zip or gzip compressed archive).

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See also

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External links

de:Verlustfreie Datenkompression es:Algoritmo de compresión sin pérdida it:Compressione dati lossless ja:可逆圧縮 pl:Kompresja bezstratna sv:Icke-förstörande komprimering ru:Lossless

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