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Exponential-Golomb Coding
An exponential-Golomb code (or just Exp-Golomb code) is a type of universal code. To encode any nonnegative integer ''x'' using the exp-Golomb code: # Write down ''x''+1 in binary # Count the bits written, subtract one, and write that number of starting zero bits preceding the previous bit string. The first few values of the code are: 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 ... In the above examples, consider the case 3. For 3, x+1 = 3 + 1 = 4. 4 in binary is '100'. '100' has 3 bits, and 3-1 = 2. Hence add 2 zeros before '100', which is '00100' Similarly, consider 8. '8 + 1' in binary is '1001'. '1001' has 4 bits, and 4-1 is 3. Hence add 3 zeros before 1001, which is '0001001'. This is identical to the Elias gamma code of ''x''+1, allowing it to encode 0. Extension to negative numbers Exp-Golomb coding is used in the H.2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. Such a code can be used to efficiently communicate a message drawn from a set of possible messages, by simply ordering the set of messages b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonnegative Integer
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''cardinal numbers'', and numbers used for ordering are called ''ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports jersey numbers). Some definitions, including the standard ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural numbers form a set. Many other number sets are built by success ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elias Gamma Code
Elias γ code or Elias gamma code is a universal code encoding positive integers developed by Peter Elias. It is used most commonly when coding integers whose upper-bound cannot be determined beforehand. Encoding To code a number ''x'' ≥ 1: # Let N = \lfloor \log_2 x \rfloor be the highest power of 2 it contains, so 2''N'' ≤ ''x'' < 2''N''+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, Elias gamma (γ) uses 2 \lfloor \log_2(x) \rfloor + 1 bits. The code begins (the implied probability distribution for the code is added for clarity): Decoding To decode an Elias gamma-coded integer: #Read and count 0s from the stream until you reach the first 1. Call this count of zeroes ''N''. #Consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High Efficiency Video Coding
High Efficiency Video Coding (HEVC), also known as H.265 and MPEG-H Part 2, is a video compression standard designed as part of the MPEG-H project as a successor to the widely used Advanced Video Coding (AVC, H.264, or MPEG-4 Part 10). In comparison to AVC, HEVC offers from 25% to 50% better data compression at the same level of video quality, or substantially improved video quality at the same bit rate. It supports resolutions up to 8192×4320, including 8K UHD, and unlike the primarily 8-bit AVC, HEVC's higher fidelity Main 10 profile has been incorporated into nearly all supporting hardware. While AVC uses the integer discrete cosine transform (DCT) with 4×4 and 8×8 block sizes, HEVC uses integer DCT and DST transforms with varied block sizes between 4×4 and 32×32. The High Efficiency Image Format (HEIF) is based on HEVC. , HEVC is used by 43% of video developers, and is the second most widely used video coding format after AVC. Concept In most ways, HEVC is an extensi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac (video Compression Format)
Dirac is an open and royalty-free video compression format, specification and system developed by BBC Research & Development. Schrödinger and dirac-research (formerly just called "Dirac") are open and royalty-free software implementations (video codecs) of Dirac. Dirac format aims to provide high-quality video compression for Ultra High Definition Television, Ultra HDTV and beyond, and as such competes with existing formats such as H.264 and VC-1. The specification was finalised in January 2008, and further developments are only bug fixes and constraints. In September of that year, version 1.0.0 of an I-frame only subset known as ''Dirac Pro'' was released and has since been standardised by the Society of Motion Picture and Television Engineers, SMPTE as ''VC-2''. Version 2.2.3 of the full Dirac specification, including motion compensation and inter-frame coding, was issued a few days later. Dirac Pro was used internally by the BBC to transmit HDTV pictures at the 2008 Summer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elias Gamma Coding
Elias γ code or Elias gamma code is a universal code encoding positive integers developed by Peter Elias. It is used most commonly when coding integers whose upper-bound cannot be determined beforehand. Encoding To code a number ''x'' ≥ 1: # Let N = \lfloor \log_2 x \rfloor be the highest power of 2 it contains, so 2''N'' ≤ ''x'' < 2''N''+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, Elias gamma (γ) uses 2 \lfloor \log_2(x) \rfloor + 1 bits. The code begins (the implied probability distribution for the code is added for clarity): Decoding To decode an Elias gamma-coded integer: #Read and count 0s from the stream until you reach the first 1. Call this count of zeroes ''N''. #Consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elias Delta Coding
Elias δ code or Elias delta code is a universal code encoding the positive integers developed by Peter Elias. Encoding To code a number ''X'' ≥ 1: # Let ''N'' = ⌊log2 ''X''⌋; be the highest power of 2 in ''X'', so 2''N'' ≤ ''X'' < 2''N''+1. # Let ''L'' = ⌊log2 ''N''+1⌋ be the highest power of 2 in ''N''+1, so 2''L'' ≤ ''N''+1 < 2''L''+1. # Write ''L'' zeros, followed by # the ''L''+1-bit binary representation of ''N''+1, followed by # all but the leading bit (i.e. the last ''N'' bits) of ''X''. An equivalent way to express the same process: #Separate ''X'' into the highest power of 2 it contains (2''N'') and the remaining ''N'' binary digits. #Encode ''N''+1 with . #Append the remaining ''N'' binary digits to this representation of ''N''+1. To re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elias Omega Coding
Elias ω coding or Elias omega coding is a universal code encoding the positive integers developed by Peter Elias. Like Elias gamma coding and Elias delta coding, it works by prefixing the positive integer with a representation of its order of magnitude in a universal code. Unlike those other two codes, however, Elias omega recursively encodes that prefix; thus, they are sometimes known as recursive Elias codes. Omega coding is used in applications where the largest encoded value is not known ahead of time, or to compress data in which small values are much more frequent than large values. To encode a positive integer ''N'': #Place a "0" at the end of the code. #If ''N'' = 1, stop; encoding is complete. #Prepend the binary representation of ''N'' to the beginning of the code. This will be at least two bits, the first bit of which is a 1. #Let ''N'' equal the number of bits just prepended, minus one. #Return to Step 2 to prepend the encoding of the new ''N''. To decode an E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numeral Systems
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number ''eleven'' in the decimal numeral system (used in common life), the number ''three'' in the binary numeral system (used in computers), and the number ''two'' in the unary numeral system (e.g. used in tallying scores). The number the numeral represents is called its value. Not all number systems can represent all numbers that are considered in the modern days; for example, Roman numerals have no zero. Ideally, a numeral system will: *Represent a useful set of numbers (e.g. all integers, or rational numbers) *Give every number represented a unique representation (or at least a standard representation) *Reflect the algebraic and arithme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
