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Line Spectral Pairs
Line spectral pairs (LSP) or line spectral frequencies (LSF) are used to represent linear prediction coefficients (LPC) for transmission over a channel.[1] LSPs have several properties (e.g. smaller sensitivity to quantization noise) that make them superior to direct quantization of LPCs. For this reason, LSPs are very useful in speech coding
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Linear Predictive Coding
Linear predictive coding (LPC) is a tool used mostly in audio signal processing and speech processing for representing the spectral envelope of a digital signal of speech in compressed form, using the information of a linear predictive model.[1] It is one of the most powerful speech analysis techniques, and one of the most useful methods for encoding good quality speech at a low bit rate and provides extremely accurate estimates of speech parameters.Contents1 Overview 2 Early history of LPC 3 LPC coefficient representations 4 Applications 5 See also 6 Notes 7 References 8 Further reading 9 External linksOverview[edit] Main article: source–filter model of speech production LPC starts with the assumption that a speech signal is produced by a buzzer at the end of a tube (voiced sounds), with occasional added hissing and popping sounds (sibilants and plosive sounds)
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LZFSE
LZFSE ( Lempel–Ziv Finite State Entropy) is an open source lossless data compression algorithm created by Apple Inc.[1]Contents1 Overview 2 Implementation 3 See also 4 References 5 External linksOverview[edit] The name is an acronym for Lempel–Ziv + Finite State Entropy[2] (implementation of asymmetric numeral systems). LZFSE was introduced by Apple at its Worldwide Developer Conference (WWDC) 2015. It shipped with that year's iOS 9 and OS X 10.11
OS X 10.11
releases. Apple claims that LZFSE compresses with a ratio comparable to that of zlib (DEFLATE) and decompresses 2–3x faster while using fewer resources, therefore offering higher energy efficiency
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Universal Code (data Compression)
In data compression, a universal code for integers is a prefix code that maps the positive integers onto binary codewords, with the additional property that whatever the true probability distribution on integers, as long as the distribution is monotonic (i.e., p(i) ≥ p(i + 1) for all positive i), the expected lengths of the codewords are within a constant factor of the expected lengths that the optimal code for that probability distribution would have assigned. A universal code is asymptotically optimal if the ratio between actual and optimal expected lengths is bounded by a function of the information entropy of the code that, in addition to being bounded, approaches 1 as entropy approaches infinity. In general, most prefix codes for integers assign longer codewords to larger integers
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Fibonacci Coding
In mathematics and computing, Fibonacci coding
Fibonacci coding
is a universal code[citation needed] which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end. The Fibonacci code is closely related to the Zeckendorf representation, a positional numeral system that uses Zeckendorf's theorem and has the property that no number has a representation with consecutive 1s
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Elias Gamma Coding
Elias gamma code is a universal code encoding positive integers developed by Peter Elias.[1]:197, 199 It is used most commonly when coding integers whose upper-bound cannot be determined beforehand.Contents1 Encoding 2 Decoding 3 Uses 4 Generalizations 5 References 6 See alsoEncoding[edit] To code a number x≥1:Let N=⌊log2 x⌋ be the highest power of 2 it contains, so 2N ≤ x < 2N+1. Write out N zero bits, then Append the binary form of x, an N+1-bit binary number.An equivalent way to express the same process:Encode N in unary; that is, as N zeroes followed by a one. Append the remaining N binary digits of x to this representation of N.To represent a number x displaystyle x , Elias gamma uses 2 ⌊ log 2 ⁡ ( x ) ⌋ + 1 displaystyle 2lfloor log _ 2 (x)r
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Levenshtein Coding
Levenstein coding, or Levenshtein coding, is a universal code encoding the non-negative integers developed by Vladimir Levenshtein.[1][2]Contents1 Encoding 2 Example code2.1 Encoding 2.2 Decoding3 See also 4 ReferencesEncoding[edit] The code of zero is "0"; to code a positive number:Initialize the step count variable C to 1. Write the binary representation of the number without the leading "1" to the beginning of the code. Let M be the number of bits written in step 2. If M is not 0, increment C, repeat from step 2 with M as the new number. Write C "1" bits and a "0" to the beginning of the code.The code begins:Number Encoding Implied probability0 0 1/21 10 1/42 110 0 1/163 110 1 1/164 1110 0 00 1/1285 1110 0 01 1/1286 1110 0 10 1/1287 1110 0 11 1/1288 1110 1 000 1/2569 1110 1 001 1/25610 1110 1 010 1/25611 1110 1 011 1/25612 1110 1 100 1/25
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Dictionary Coder
A dictionary coder, also sometimes known as a substitution coder, is a class of lossless data compression algorithms which operate by searching for matches between the text to be compressed and a set of strings contained in a data structure (called the 'dictionary') maintained by the encoder. When the encoder finds such a match, it substitutes a reference to the string's position in the data structure. Methods and applications[edit] Some dictionary coders use a 'static dictionary', one whose full set of strings is determined before coding begins and does not change during the coding process. This approach is most often used when the message or set of messages to be encoded is fixed and large; for instance, an application that stores the contents of a book in the limited storage space of a PDA generally builds a static dictionary from a concordance of the text and then uses that dictionary to compress the verses
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Byte Pair Encoding
Byte
Byte
pair encoding[1] or digram coding[2] is a simple form of data compression in which the most common pair of consecutive bytes of data is replaced with a byte that does not occur within that data. A table of the replacements is required to rebuild the original data. The algorithm was first described publicly by Philip Gage in a February 1994 article "A New Algorithm for Data Compression" in the C Users Journal. Byte
Byte
pair encoding example[edit] Suppose we wanted to encode the dataaaabdaaabacThe byte pair "aa" occurs most often, so it will be replaced by a byte that is not used in the data, "Z". Now we have the following data and replacement table:ZabdZabac Z=aaThen we repeat the process with byte pair "ab", replacing it with Y:ZYdZYac Y=ab Z=aaWe could stop here, as the only literal byte pair left occurs only once
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DEFLATE
In computing, Deflate is a lossless data compression algorithm and associated file format that uses a combination of the LZ77 algorithm and Huffman coding. It was originally defined by Phil Katz for version 2 of his PKZIP
PKZIP
archiving tool. The file format was later specified in RFC 1951.[1] The original algorithm as designed by Katz was patented as U.S
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Snappy (compression)
Snappy (previously known as Zippy) is a fast data compression and decompression library written in C++
C++
by Google
Google
based on ideas from LZ77 and open-sourced in 2011.[2][3] It does not aim for maximum compression, or compatibility with any other compression library; instead, it aims for very high speeds and reasonable compression. Compression speed is 250 MB/s and decompression speed is 500 MB/s using a single core of a Core i7[which?] processor running in 64-bit mode. The compression ratio is 20–100% lower than gzip.[4] Snappy is widely used in Google
Google
projects like Bigtable, MapReduce and in compression data in Google's internal RPC systems. It can be used in open-source projects like MariaDB ColumnStore,[5] Cassandra, Hadoop, LevelDB, MongoDB, RocksDB, Lucene.[6] Decompression is tested to detect any errors in the compressed stream
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LZ77 And LZ78
LZ77 and LZ78 are the two lossless data compression algorithms published in papers by Abraham Lempel
Abraham Lempel
and Jacob Ziv
Jacob Ziv
in 1977[1] and 1978.[2] They are also known as LZ1 and LZ2 respectively.[3] These two algorithms form the basis for many variations including LZW, LZSS, LZMA and others. Besides their academic influence, these algorithms formed the basis of several ubiquitous compression schemes, including GIF
GIF
and the DEFLATE algorithm used in PNG and ZIP. They are both theoretically dictionary coders. LZ77 maintains a sliding window during compression
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LZJB
LZJB is a lossless data compression algorithm invented by Jeff Bonwick to compress crash dumps and data in ZFS. The software is CDDL license licensed. It includes a number of improvements to the LZRW1 algorithm, a member of the Lempel–Ziv family of compression algorithms.[1]. The name LZJB is derived from its parent algorithm and its creator—Lempel Ziv Jeff Bonwick. Bonwick is also one of two architects of ZFS, and the creator of the Slab Allocator. References[edit]^ Y. Rathore, M. Ahirwar, R. Pandey (2013). "A Brief Study of Data Compression Algorithms". 11 (10). Journal of Computer Science IJCSIS: 90. CS1 maint: Multiple names: authors list (link)External links[edit]""compress" source code". Archived from the original on 8 June 2012.  " LZJB source code"
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Shannon–Fano–Elias Coding
In information theory, Shannon–Fano–Elias coding is a precursor to arithmetic coding, in which probabilities are used to determine codewords.[1]Contents1 Algorithm description1.1 Example2 Algorithm analysis2.1 Prefix code 2.2 Code length3 ReferencesAlgorithm description[edit] Given a discrete random variable X of ordered values to be encoded, let p ( x ) displaystyle p(x) be the probability for any x in X
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Lempel–Ziv–Markov Chain Algorithm
The Lempel–Ziv–Markov chain algorithm (LZMA) is an algorithm used to perform lossless data compression. It has been under development either since 1996 or 1998[1] and was first used in the 7z format of the 7-Zip
7-Zip
archiver. This algorithm uses a dictionary compression scheme somewhat similar to the LZ77 algorithm published by Abraham Lempel and Jacob Ziv
Jacob Ziv
in 1977 and features a high compression ratio (generally higher than bzip2)[2][3] and a variable compression-dictionary size (up to 4 GB),[4] while still maintaining decompression speed similar to other commonly used compression algorithms.[5] LZMA2 is a simple container format that can include both uncompressed data and LZMA data, possibly with multiple different LZMA encoding parameters
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