PAQ архивінің қағидалары және тиімділігі

PAQ is a series of lossless data compression archivers that have gone through collaborative development to top rankings on several benchmarks measuring compression ratio (although at the expense of speed and memory usage). Specialized versions of PAQ have won the Hutter Prize and the Calgary Challenge. PAQ is free software distributed under the GNU General Public License.

A string s is compressed to the shortest byte string representing a base 256 big endian number x in the range [0, 1] such that P(r < s) ≤ x < P(r ≤ s), where P(r < s) is the probability that a random string r with the same length as s will be lexicographically less than s. It is always possible to find an x such that the length of x is at most one byte longer than the Shannon limit, −log2P(r = s) bits. The length of s is stored in the archive header. The arithmetic coder in PAQ is implemented by maintaining for each prediction a lower and upper bound on x, initially [0, 1]. After each prediction, the current range is split into two parts in proportion to P(0) and P(1), the probability that the next bit of s will be a 0 or 1 respectively, given the previous bits of s. The next bit is then encoded by selecting the corresponding subrange to be the new range. The number x is decompressed back to string s by making an identical series of bit predictions (since the previous bits of s are known). The range is split as with compression. The portion containing x becomes the new range, and the corresponding bit is appended to s.

In PAQ, the lower and upper bounds of the range are represented in 3 parts. The most significant base 256 digits are identical, so they can be written as the leading bytes of x. The next 4 bytes are kept in memory, such that the leading byte is different. The trailing bits are assumed to be all zeros for the lower bound and all ones for the upper bound. Compression is terminated by writing one more byte from the lower bound.

Some versions of PAQ, in particular PAsQDa, PAQAR (both PAQ6 derivatives), and PAQ8HP1 through PAQ8HP8 (PAQ8 derivatives and Hutter prize recipients) preprocess text files by looking up words in an external dictionary and replacing them with 1 to 3 byte codes. In addition, uppercase letters are encoded with a special character followed by the lowercase letter. In the PAQ8HP series, the dictionary is organized by grouping syntactically and semantically related words together. This allows models to use just the most significant bits of the dictionary codes as context.

The following table is a sample from the Large Text Compression Benchmark by Matt Mahoney that consists of a file consisting of 109 bytes (1 GB, or 0.931 GiB) of English Wikipedia text. Program Compressed size (bytes) % of original size Compression time (ns/B) Memory (MiB) PAQ8HP8 133,423,109 64 639 1849 PPMd 183,976,014 880 256 bzip2 254,007,875 379 8 InfoZIP 322,649,703 104 0.1

See Lossless compression benchmarks for a list of file compression benchmarks.

The following lists the major enhancements to the PAQ algorithm. In addition, there have been a large number of incremental improvements, which are omitted. PAQ1 was released on January 6, 2002 by Matt Mahoney. It used fixed weights and did not include an analog or sparse model. PAQ1SSE/PAQ2 was released on May 11, 2003 by Serge Osnach. It significantly improved compression by adding a Secondary Symbol Estimation (SSE) stage between the predictor and encoder. SSE inputs a short context and the current prediction and outputs a new prediction from a table. The table entry is then adjusted to reflect the actual bit value. PAQ3N, released October 9, 2003 added a sparse model. PAQ4, released November 15, 2003 by Matt Mahoney used adaptive weighting. PAQ5 (December 18, 2003) and PAQ6 (December 30, 2003) were minor improvements, including a new analog model. At this point, PAQ was competitive with the best PPM compressors and attracted the attention of the data compression community, which resulted in a large number of incremental improvements through April 2004. Berto Destasio tuned the models and adjusted the bit count discounting schedule. Johan de Bock made improvements to the user interface. David A. Scott made improvements to the arithmetic coder. Fabio Buffoni made speed improvements. During the period May 20, 2004 through July 27, 2004, Alexander Ratushnyak released seven versions of PAQAR, which made significant compression improvements by adding many new models, multiple mixers with weights selected by context, adding an SSE stage to each mixer output, and adding a preprocessor to improve the compression of Intel executable files. PAQAR stood as the top ranked compressor through the end of 2004 but was significantly slower than prior PAQ versions. During the period January 18, 2005 through February 7, 2005, Przemyslaw Skibinski released four versions of PASqDa, based on PAQ6 and PAQAR with the addition of an English dictionary preprocessor. It achieved the top ranking on the Calgary corpus but not on most other benchmarks. A modified version of PAQ6 won the Calgary Challenge on January 10, 2004 by Matt Mahoney. This was bettered by ten subsequent versions of PAQAR by Alexander Ratushnyak. The most recent was submitted on June 5, 2006, consisting of compressed data and program source code totaling 589,862 bytes. PAQ7 was released December 2005 by Matt Mahoney. PAQ7 is a complete rewrite of PAQ6 and variants (PAQAR, PAsQDa). Compression ratio was similar to PAQAR but 3 times faster. However it lacked x86 and a dictionary, so it did not compress Windows executables and English text files as well as PAsQDa. It does include models for color BMP, TIFF and JPEG files, so compresses these files better. The primary difference from PAQ6 is it uses a neural network to combine models rather than a gradient descent mixer. Another feature is PAQ7's ability to compress embedded jpeg and bitmap images in Excel , Word and pdf files. PAQ8A was released on January 27, 2006, PAQ8C on February 13, 2006. These were experimental pre release of anticipated PAQ8. It fixed several issues in PAQ7 (poor compression in some cases). PAQ8A also included model for compressing (x86) executables. PAQ8F was released on February 28, 2006. PAQ8F had 3 improvements over PAQ8A: a more memory efficient context model, a new indirect context model to improve compression, and a new user interface to support drag and drop in Windows. It does not use an English dictionary like the PAQ8B/C/D/E variants. PAQ8G was released March 3, 2006 by Przemyslaw Skibinski. PAQ8G is PAQ8F with dictionaries added and some other improvements as a redesigned TextFilter (which does not decrease compression performance on non textual files)
PAQ8H was released on March 22, 2006 by Alexander Ratushnyak and updated on March 24, 2006. PAQ8H is based on PAQ8G with some improvements to the model. PAQ8I was released on August 18, 2006 by Pavel L. Holoborodko, with bug fixes on August 24, September 4, and September 13. It added a grayscale image model for PGM files. PAQ8J was released on November 13, 2006 by Bill Pettis. It was based on PAQ8F with some text model improvements taken from PAQ8HP5. Thus, it did not include the text dictionaries from PAQ8G or PGM model from PAQ8I. Serge Osnach released a series of modeling improvements: PAQ8JA on November 16, 2006, PAQ8JB on November 21, and PAQ8JC on November 28. PAQ8JD was released on December 30, 2006 by Bill Pettis. This version has since been ported to 32 bit Windows for several processors, and 32 and 64 bit Linux. PAQ8K was released on February 13, 2007 by Bill Pettis. It includes additional models for binary files. PAQ8L was released on March 8, 2007 by Matt Mahoney. It is based on PAQ8JD and adds a DMC model. PAQ8O was released on August 24, 2007 by Andreas Morphis. Contains improved BMP and JPEG models over PAQ8L. Can be optionally compiled with SSE2 support and for 64 bit Linux. The algorithm has notable performance benefits under 64 bit OS. PAQ8P was released on August 25, 2008 by Andreas Morphis. Contains improved BMP model and adds a WAV model. PAQ8PX was released on April 25, 2009 by Jan Ondrus. It contains various improvements like better WAV compression and EXE compression. PAQ8KX was released on July 15, 2009 by Jan Ondrus. It is a combination of PAQ8K with PAQ8PX. PAQ8PF was released on September 9, 2009 by LovePimple without source code (which the GPL license requires). It compresses 7% worse, but is 7 times faster compared to PAQ8PX v66 (measured with 1 MB English text)
PAQ9A was released on December 31, 2007 by Matt Mahoney. A new experimental version. It does not include models for specific file types, has an LZP preprocessor and supports files over 2 GB. ZPAQ was released on March 12, 2009 by Matt Mahoney. It uses a new archive format designed so that the current ZPAQ program will be able to decompress archives created by future ZPAQ versions (the various PAQ variants listed above are not forward compatible in this fashion). It achieves this by specifying the decompression algorithm in a bytecode program that is stored in each created archive file.

The series PAQ8HP1 through PAQ8HP8 were released by Alexander Ratushnyak from August 21, 2006 through January 18, 2007 as Hutter Prize submissions. The Hutter Prize is a text compression contest using a 100 MB English and XML data set derived from Wikipedia's source. The PAQ8HP series was forked from PAQ8H. The programs include text preprocessing dictionaries and models tuned specifically to the benchmark. All non text models were removed. The dictionaries were organized to group syntactically and semantically related words and to group words by common suffix. The former strategy improves compression because related words (which are likely to appear in similar context) can be modeled on the high order bits of their dictionary codes. The latter strategy makes the dictionary easier to compress. The size of the decompression program and compressed dictionary is included in the contest ranking. On October 27, 2006, it was announced that PAQ8HP5 won a Hutter Prize for Lossless Compression of Human Knowledge of €3,416. On June 30, 2007, Ratushnyak's PAQ8HP12 was awarded a second Hutter prize of €1732, improving upon his previous record by 3.46%.