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Information about Exponential Golomb Coding

An Exponential-Golomb code (or just Exp-Golomb code) of order is a type of universal code, parameterized by a whole number . To encode a nonnegative integer in an order- exp-Golomb code, one can use the following method:
  1. Take the number in binary except for the last digits and add 1 to it (arithmetically). Write this down.
  2. Count the bits written, subtract one, and write that number of starting zero bits preceding the previous bit string.
  3. Write the last bits in binary.


For the code begins: 0 => 1 => 1 1 => 10 => 010 2 => 11 => 011 3 => 100 => 00100 4 => 101 => 00101 5 => 110 => 00110 6 => 111 => 00111 7 => 1000 => 0001000 8 => 1001 => 0001001 ...

Exp-Golomb coding for is used in the H.264/MPEG-4 AVC video compression standard, in which there is also a variation for the coding of signed numbers by assigning the value 0 to the binary codeword '0' and assigning subsequent codewords to input values of increasing magnitude and alternating sign.

Exp-Golomb coding is also used in the Dirac video codec.

The exp-Golomb code is identical to the Elias gamma code of the same number plus one. Thus it can encode zero, whereas Elias gamma can only encode numbers greater than zero.

Despite the similar name, exp-Golomb is only somewhat similar to Golomb coding, which is a type of entropy coding but not a universal code.

See also:

Data compression methods
 •  • [ e]
Lossless compression methods
Theory
Entropy Complexity Redundancy		Entropy encoding
Huffman Adaptive Huffman Arithmetic (Shannon-Fano Range) Golomb Exp-Golomb Universal (Elias Fibonacci)		Dictionary
LZ77/78 LZW LZO DEFLATE LZMA LZX		Others
RLE BWT PPM DMC
Audio compression methods
Theory
Convolution Sampling Nyquist–Shannon theorem		Audio codecs parts
LPC (LAR LSP) WLPC CELP ACELP A-law μ-law MDCT Fourier transform Psychoacoustic model		Others
Dynamic range compression Speech compression Sub-band coding
Image compression methods
Terms
Color space Pixel Chroma subsampling Compression artifact		Methods
RLE Fractal Wavelet SPIHT DCT KLT		Others
Bit rate Test images PSNR quality measure Quantization
Video compression
Terms
Video Characteristics Frame Frame types Video quality		Video codec parts
Motion compensation DCT Quantization		Others
Video codecs Rate distortion theory (CBR ABR VBR)
Timeline of information theory, data compression, and error-correcting codes
(See for formats and for codecs)
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.
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The term whole number is used differently by different authors. It may mean:
  • Natural number, an element of the counting numbers, sometimes including zero
  • Integer, an element in the set containing all natural numbers, their negatives, and zero

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H.264 is a standard for video compression. It is also known as MPEG-4 Part 10, or AVC (for Advanced Video Coding). It was written by the ITU-T Video Coding Experts Group (VCEG) together with the ISO/IEC Moving Picture Experts Group (MPEG) as
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Dirac is a prototype algorithm for the encoding and decoding of raw video. It was presented by the BBC in January 2004 as the basis of a new codec for the transmission of video over the Internet.
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Elias gamma code is a universal code encoding positive integers. It is used most commonly when coding integers whose upper-bound cannot be determined beforehand.

To code a number:
  1. Write it in binary.

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The introduction to this article provides insufficient context for those unfamiliar with the subject matter.
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Elias gamma code is a universal code encoding positive integers. It is used most commonly when coding integers whose upper-bound cannot be determined beforehand.

To code a number:
  1. Write it in binary.

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Elias delta code is a universal code encoding the positive integers. To code a number:
  1. Write it in binary.
  2. Count the bits and write down that number of bits in binary (X).

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Elias omega coding is a universal code encoding the positive integers. Like Elias gamma coding and Elias delta coding, it works by prefixing the integer with a representation of its order of magnitude in a universal code.
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Universal Code can refer to:
  • Universal code (data compression)
  • Universal Code (biology)
  • An alternate term for a Universal law
  • Universal code (ethics)
  • Universal Product Code
  • Universal code (typography)
  • Universal code (cartography)

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data compression or source coding is the process of encoding information using fewer bits (or other information-bearing units) than an un-encoded representation would use through use of specific encoding schemes.
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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
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Information theory is a branch of applied mathematics and engineering involving the quantification of information to find fundamental limits on compressing and reliably communicating data.
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Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable.

Shannon entropy quantifies the information contained in a piece of data: it is the minimum average message length, in bits (if using base-2 logarithms), that must
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In computer science, the Kolmogorov complexity (also known as descriptive complexity, Kolmogorov-Chaitin complexity, stochastic complexity, algorithmic entropy, or program-size complexity
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Redundancy in information theory is the number of bits used to transmit a message minus the number of bits of actual information in the message. Informally, it is the amount of wasted "space" used to transmit certain data.
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In information theory an entropy encoding is a lossless data compression scheme that is independent of the media’s specific characteristics.

One of the main types of entropy coding assigns codes to symbols so as to match code lengths with the probabilities of the
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Huffman coding is an entropy encoding algorithm used for lossless data compression. The term refers to the use of a variable-length code table for encoding a source symbol (such as a character in a file) where the variable-length code table has been derived in a particular way
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Adaptive Huffman coding (also called Dynamic Huffman coding) is an adaptive coding technique based on Huffman coding, building the code as the symbols are being transmitted, having no initial knowledge of source distribution, that allows one-pass encoding and adaptation to
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Arithmetic coding is a method for lossless data compression. Normally, a string of characters such as the words "hello there" is represented using a fixed number of bits per character, as in the ASCII code.
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Range encoding is a form of arithmetic coding, a data compression method, that is believed to be free from arithmetic coding related patents. It is on this basis that interest in range encoding has arisen, particularly in the open source community.
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The introduction to this article provides insufficient context for those unfamiliar with the subject matter.
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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.
..... Click the link for more information.
Elias gamma code is a universal code encoding positive integers. It is used most commonly when coding integers whose upper-bound cannot be determined beforehand.

To code a number:
  1. Write it in binary.

..... Click the link for more information.
Fibonacci coding is a universal code which encodes positive integers into binary code words. All tokens end with "11" and have no "11" before the end.

The formula used to generate Fibonacci codes is:


where F(i) is the i-th Fibonacci number.
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A dictionary coder, also sometimes known as a substitution coder, is any of a number 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')
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LZ77 and LZ78 are the names for the two lossless data compression algorithms published in papers by Abraham Lempel and Jacob Ziv in 1977 and 1978. They are also known as LZ1 and LZ2 respectively [1] .
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Lempel-Ziv-Welch (LZW) is a universal lossless data compression algorithm created by Abraham Lempel, Jacob Ziv, and Terry Welch. It was published by Welch in 1984 as an improved implementation of the LZ78 algorithm published by Lempel and Ziv in 1978.
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Lempel-Ziv-Oberhumer (LZO) is a data compression algorithm that is focused on decompression speed. The algorithm is lossless and the reference implementation is thread safe.

A free software tool which implements it is lzop.
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DEFLATE is a lossless data compression algorithm that uses a combination of the LZ77 algorithm and Huffman coding. It was originally defined by Phil Katz for version 2 of his PKZIP archiving tool, and was later specified in RFC 1951.
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