Code Self-synchronization
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Code Self-synchronization
In coding theory, especially in telecommunications, a self-synchronizing code is a uniquely decodable code in which the symbol stream formed by a portion of one code word, or by the overlapped portion of any two adjacent code words, is not a valid code word. Put another way, a set of strings (called "code words") over an alphabet is called a self-synchronizing code if for each string obtained by concatenating two code words, the substring starting at the second symbol and ending at the second-last symbol does not contain any code word as substring. Every self-synchronizing code is a prefix code, but not all prefix codes are self-synchronizing. Other terms for self-synchronizing code are synchronized code or, ambiguously, comma-free code. A self-synchronizing code permits the proper framing of transmitted code words provided that no uncorrected errors occur in the symbol stream; external synchronization is not required. Self-synchronizing codes also allow recovery from uncorr ...
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Coding Theory
Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data storage. Codes are studied by various scientific disciplines—such as information theory, electrical engineering, mathematics, linguistics, and computer science—for the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. There are four types of coding: # Data compression (or ''source coding'') # Error detection and correction, Error control (or ''channel coding'') # Cryptography, Cryptographic coding # Line code, Line coding Data compression attempts to remove unwanted redundancy from the data from a source in order to transmit it more efficiently. For example, DEFLATE data compression makes files small ...
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Kleene Star
In mathematical logic and theoretical computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation on a Set (mathematics), set to generate a set of all finite-length strings that are composed of zero or more repetitions of members from . It was named after American mathematician Stephen Cole Kleene, who first introduced and widely used it to characterize Automata theory, automata for regular expressions. In mathematics, it is more commonly known as the free monoid construction. Definition Given a set V, define :V^=\ (the set consists only of the empty string), :V^=V, and define recursively the set :V^=\ for each i>0. V^i is called the i-th power of V, it is a shorthand for the Concatenation#Concatenation of sets of strings, concatenation of V by itself i times. That is, ''V^i'' can be understood to be the set of all strings that can be represented as the concatenation of i members from V. The definition of Kleene star on V is : V^*=\bigcup_V^i ...
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General Services Administration
The General Services Administration (GSA) is an Independent agencies of the United States government, independent agency of the United States government established in 1949 to help manage and support the basic functioning of federal agencies. GSA supplies products and communications for U.S. government offices, provides transportation and office space to federal employees, and develops government-wide cost-minimizing policies and other management tasks. GSA employs about 12,000 federal workers. It has an annual operating budget of roughly $33 billion and oversees $66 billion of procurement annually. It contributes to the management of about $500 billion in U.S. federal property, divided chiefly among 8,397 owned and leased buildings (with a total of 363 million square feet of space) as well as a 215,000-vehicle fleet vehicle, motor pool. Among the real estate assets it manages are the Ronald Reagan Building, Ronald Reagan Building and International Trade Center in Washingto ...
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Cambridge University Press
Cambridge University Press was the university press of the University of Cambridge. Granted a letters patent by King Henry VIII in 1534, it was the oldest university press in the world. Cambridge University Press merged with Cambridge Assessment to form Cambridge University Press and Assessment under Queen Elizabeth II's approval in August 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it published over 50,000 titles by authors from over 100 countries. Its publications include more than 420 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also published Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. It also served as the King's Printer. Cambridge University Press, as part of the University of Cambridge, was a ...
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Academic Press
Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal completed the next year, after a regulatory review. Thus, Academic Press is now an imprint of Elsevier. Academic Press publishes reference books, serials and online products in the subject areas of: * Communications engineering * Economics * Environmental science * Finance * Food science and nutrition * Geophysics * Life sciences * Mathematics and statistics * Neuroscience * Physical sciences * Psychology Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feel ... Well-known products include the '' Methods in Enzymology'' series and encyclopedias such ...
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Self-synchronizing Block Code
A comma-free code is block code in which no concatenation of two code words contains a valid code word that overlaps both. Comma-free codes are also known as ''self-synchronizing block codes'' because no synchronization is required to find the beginning of a code word. See also * Self-synchronizing code * UTF-8 UTF-8 is a character encoding standard used for electronic communication. Defined by the Unicode Standard, the name is derived from ''Unicode Transformation Format 8-bit''. Almost every webpage is transmitted as UTF-8. UTF-8 supports all 1,112,0 ..., a comma-free character encoding References External links * Coding theory {{applied-math-stub ...
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Self-clocking Signal
In telecommunications and electronics, a self-clocking signal is one that can be decoded without the need for a separate clock signal or other source of Synchronization (computer science), synchronization. This is usually done by including embedded synchronization information within the signal, and adding constraints on the coding of the data payload such that false synchronization can easily be detected. Most line codes are designed to be self-clocking. Isochronicity and anisochronicity If a clock signal is embedded in the data transmission, there are two possibilities: the clock signals are sent at the same time as the data (isochronous), or at a different time (anisochronous). Isochronous self-clocking signals If the embedded clock signal is isochronous, it gets sent simultaneously with the data. Below is an example signal, in this case using the Manchester code self-clocking signal. The data and clock cycles can be thought of as "adding up" to a combination, where both the c ...
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Pollard's Lambda Method
In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known Pollard's rho algorithm for solving the same problem. Although Pollard described the application of his algorithm to the discrete logarithm problem in the multiplicative group of units modulo a prime ''p'', it is in fact a generic discrete logarithm algorithm—it will work in any finite cyclic group. Algorithm Suppose G is a finite cyclic group of order n which is generated by the element \alpha, and we seek to find the discrete logarithm x of the element \beta to the base \alpha. In other words, one seeks x \in Z_n such that \alpha^x = \beta. The lambda algorithm allows one to search for x in some interval ,\ldots,bsubset Z_n. One may search the entire range of poss ...
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Overlapping Instructions
In computer programming, machine code is computer code consisting of machine language instructions, which are used to control a computer's central processing unit (CPU). For conventional binary computers, machine code is the binaryOn nonbinary machines it is, e.g., a decimal representation. representation of a computer program that is actually read and interpreted by the computer. A program in machine code consists of a sequence of machine instructions (possibly interspersed with data). Each machine code instruction causes the CPU to perform a specific task. Examples of such tasks include: # Load a word from memory to a CPU register # Execute an arithmetic logic unit (ALU) operation on one or more registers or memory locations # Jump or skip to an instruction that is not the next one In general, each architecture family (e.g., x86, ARM) has its own instruction set architecture (ISA), and hence its own specific machine code language. There are exceptions, such as the ...
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Kruskal's Principle
The Kruskal count (also known as Kruskal's principle, Dynkin–Kruskal count, Dynkin's counting trick, Dynkin's card trick, coupling card trick or shift coupling) is a probabilistic concept originally demonstrated by the Russian mathematician Evgenii Borisovich Dynkin in the 1950s or 1960s discussing coupling (probability), coupling effects and rediscovered as a card trick by the American mathematician Martin David Kruskal in the early 1970s as a side-product while working on another problem. It was published by Kruskal's friend Martin Gardner and magician Karl Fulves in 1975. This is related to a similar trick published by magician Alexander F. Kraus in 1957 as ''Sum total'' and later called ''Kraus principle''. Besides uses as a card trick, the underlying phenomenon has applications in cryptography, code breaking, software tamper protection, code self-synchronization, control-flow resynchronization, design of variable-length codes and variable-length instruction sets, web navi ...
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