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Error detection and correction

Index Error detection and correction

In information theory and coding theory with applications in computer science and telecommunication, error detection and correction or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. [1]

141 relations: Archive file, ARQ-E, ARQ-M, Automatic repeat request, Backchannel, Backward channel, Berger code, Binary erasure channel, Binary Golay code, Bit rate, Block (telecommunications), Block code, Broadcasting, Btrfs, Burst error, Burst error-correcting code, Cambridge University Press, Channel capacity, Check digit, Checksum, Claude Shannon, Code rate, Coding theory, Communication channel, Compact disc, Computer network, Computer science, Concatenated error correction code, Consultative Committee for Space Data Systems, Conventional PCI, Convolutional code, Cosmic ray, Cross-interleaved Reed–Solomon coding, Cyclic redundancy check, Damm algorithm, Data integrity, Data scrubbing, David J. C. MacKay, Decibel, Decoding methods, Delone set, Deterministic algorithm, Digital data, DIMM, Distributed data store, Dividend, Divisor, DVD, Dynamic random-access memory, Error correction code, ..., Ethernet, File format, Finite field, Forward error correction, Fountain code, Frame (networking), Gaussian function, Go-Back-N ARQ, Group coded recording, Hamming code, Hamming distance, Hard disk drive, Hash function, High-definition television, Hybrid automatic repeat request, Information theory, Internet protocol suite, IPv4, IPv6, Jupiter, Kernel.org, Latency (engineering), Linear code, Link adaptation, Link layer, Linux kernel, Linux Magazine, List of hash functions, Longitudinal redundancy check, Low-density parity-check code, Luhn algorithm, Magnetic tape data storage, Marcel J. E. Golay, Memory scrubbing, Message authentication code, Modular arithmetic, Modulation, Multidimensional parity-check code, Neptune, Network congestion, Network packet, Noise (electronics), Noisy-channel coding theorem, Numbers station, Ones' complement, Operating system, OSI model, Parchive, Parity bit, Phase-shift keying, Polynomial long division, Preimage attack, Prentice Hall, Protocol stack, Quadrature amplitude modulation, RAID, Random-access memory, Redundancy (information theory), Reed–Muller code, Reed–Solomon error correction, Reliability (computer networking), Remainder, Repetition code, Return channel, Richard Hamming, Routing, Saturn, Selective Repeat ARQ, Signal-to-noise ratio, Simplex communication, Single event upset, Soft error, Stop-and-wait ARQ, Systematic code, TCP congestion control, Telecommunication, Time complexity, Timeout (computing), Transmission Control Protocol, Transponder, Transverse redundancy check, Triple modular redundancy, Tsinghua University, Turbo code, Uranus, User Datagram Protocol, Verhoeff algorithm, Viterbi decoder, Voyager 1, Voyager 2, ZFS. Expand index (91 more) »

Archive file

An archive file is a file that is composed of one or more computer files along with metadata........

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ARQ-E

ARQ-E is a radio transmission method used to send data over short wave radio.

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ARQ-M

ARQ-M, short for Automatic Repeat reQuest, Multiplex, is a radio telegraphy protocol used to reliably forward telex messages over partially reliable radio links.

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Automatic repeat request

Automatic repeat request (ARQ), also known as automatic repeat query, is an error-control method for data transmission that uses acknowledgements (messages sent by the receiver indicating that it has correctly received a data frame or packet) and timeouts (specified periods of time allowed to elapse before an acknowledgment is to be received) to achieve reliable data transmission over an unreliable service.

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Backchannel

Backchannel is the practice of using networked computers to maintain a real-time online conversation alongside the primary group activity or live spoken remarks.

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Backward channel

In a data transmission circuit a backward channel is the channel that passes data in a direction opposite to that of its associated forward channel.

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Berger code

In telecommunication, a Berger code is a unidirectional error detecting code, named after its inventor, J. M. Berger.

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Binary erasure channel

disambiguation: Landauer's principle A binary erasure channel (or BEC) is a common communications channel model used in coding theory and information theory.

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Binary Golay code

In mathematics and electronics engineering, a binary Golay code is a type of linear error-correcting code used in digital communications.

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Bit rate

In telecommunications and computing, bit rate (bitrate or as a variable R) is the number of bits that are conveyed or processed per unit of time.

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Block (telecommunications)

In telecommunications a block is one of.

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Block code

In coding theory, a block code is any member of the large and important family of error-correcting codes that encode data in blocks.

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Broadcasting

Broadcasting is the distribution of audio or video content to a dispersed audience via any electronic mass communications medium, but typically one using the electromagnetic spectrum (radio waves), in a one-to-many model.

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Btrfs

Btrfs (pronounced as "butter fuss", "better F S", "butter F S", "b-tree F S", or simply by spelling it out) is a file system based on the copy-on-write (COW) principle, initially designed at Oracle Corporation for use in Linux.

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Burst error

In telecommunication, a burst error or error burst is a contiguous sequence of symbols, received over a communication channel, such that the first and last symbols are in error and there exists no contiguous subsequence of m correctly received symbols within the error burst.

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Burst error-correcting code

In coding theory, burst error-correcting codes employ methods of correcting burst errors, which are errors that occur in many consecutive bits rather than occurring in bits independently of each other.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Channel capacity

Channel capacity, in electrical engineering, computer science and information theory, is the tight upper bound on the rate at which information can be reliably transmitted over a communication channel.

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Check digit

A check digit is a form of redundancy check used for error detection on identification numbers, such as bank account numbers, which are used in an application where they will at least sometimes be input manually.

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Checksum

A checksum is a small-sized datum derived from a block of digital data for the purpose of detecting errors which may have been introduced during its transmission or storage.

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Claude Shannon

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as "the father of information theory".

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Code rate

In telecommunication and information theory, the code rate (or information rate) of a forward error correction code is the proportion of the data-stream that is useful (non-redundant).

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Coding theory

Coding theory is the study of the properties of codes and their respective fitness for specific applications.

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Communication channel

A communication channel or simply channel refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel in telecommunications and computer networking.

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Compact disc

Compact disc (CD) is a digital optical disc data storage format that was co-developed by Philips and Sony and released in 1982.

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Computer network

A computer network, or data network, is a digital telecommunications network which allows nodes to share resources.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Concatenated error correction code

In coding theory, concatenated codes form a class of error-correcting codes that are derived by combining an inner code and an outer code.

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Consultative Committee for Space Data Systems

The Consultative Committee for Space Data Systems (CCSDS) was founded in 1982 for governmental and quasi-governmental space agencies to discuss and develop standards for space data and information systems.

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Conventional PCI

Conventional PCI, often shortened to PCI, is a local computer bus for attaching hardware devices in a computer.

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Convolutional code

In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream.

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Cosmic ray

Cosmic rays are high-energy radiation, mainly originating outside the Solar System and even from distant galaxies.

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Cross-interleaved Reed–Solomon coding

In the compact disc system, cross-interleaved Reed–Solomon code (CIRC) provides error detection and error correction.

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Cyclic redundancy check

A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks and storage devices to detect accidental changes to raw data.

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Damm algorithm

In error detection, the Damm algorithm is a check digit algorithm that detects all single-digit errors and all adjacent transposition errors.

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Data integrity

Data integrity is the maintenance of, and the assurance of the accuracy and consistency of, data over its entire life-cycle, and is a critical aspect to the design, implementation and usage of any system which stores, processes, or retrieves data.

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Data scrubbing

Data scrubbing is an error correction technique that uses a background task to periodically inspect main memory or storage for errors, then correct detected errors using redundant data in the form of different checksums or copies of data.

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David J. C. MacKay

Sir David John Cameron MacKay (22 April 1967 – 14 April 2016) was a British physicist, mathematician, and academic.

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Decibel

The decibel (symbol: dB) is a unit of measurement used to express the ratio of one value of a physical property to another on a logarithmic scale.

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Decoding methods

In coding theory, decoding is the process of translating received messages into codewords of a given code.

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Delone set

In the mathematical theory of metric spaces, ε-nets, ε-packings, ε-coverings, uniformly discrete sets, relatively dense sets, and Delone sets (named after Boris Delone) are several closely related definitions of well-spaced sets of points, and the packing radius and covering radius of these sets measure how well-spaced they are.

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Deterministic algorithm

In computer science, a deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states.

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Digital data

Digital data, in information theory and information systems, is the discrete, discontinuous representation of information or works.

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DIMM

A DIMM or dual in-line memory module comprises a series of dynamic random-access memory integrated circuits.

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Distributed data store

A distributed data store is a computer network where information is stored on more than one node, often in a replicated fashion.

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Dividend

A dividend is a payment made by a corporation to its shareholders, usually as a distribution of profits.

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Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

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DVD

DVD (an abbreviation of "digital video disc" or "digital versatile disc") is a digital optical disc storage format invented and developed by Philips and Sony in 1995.

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Dynamic random-access memory

Dynamic random-access memory (DRAM) is a type of random access semiconductor memory that stores each bit of data in a separate tiny capacitor within an integrated circuit.

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Error correction code

In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels.

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Ethernet

Ethernet is a family of computer networking technologies commonly used in local area networks (LAN), metropolitan area networks (MAN) and wide area networks (WAN).

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File format

A file format is a standard way that information is encoded for storage in a computer file.

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Finite field

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.

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Forward error correction

In telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels.

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Fountain code

In coding theory, fountain codes (also known as rateless erasure codes) are a class of erasure codes with the property that a potentially limitless sequence of encoding symbols can be generated from a given set of source symbols such that the original source symbols can ideally be recovered from any subset of the encoding symbols of size equal to or only slightly larger than the number of source symbols.

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Frame (networking)

A frame is a digital data transmission unit in computer networking and telecommunication.

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Gaussian function

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the form: for arbitrary real constants, and.

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Go-Back-N ARQ

Go-Back-N ARQ is a specific instance of the automatic repeat request (ARQ) protocol, in which the sending process continues to send a number of frames specified by a window size even without receiving an acknowledgement (ACK) packet from the receiver.

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Group coded recording

In computer science, group coded recording or group code recording (GCR) refers to several distinct but related encoding methods for magnetic media.

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Hamming code

In telecommunication, Hamming codes are a family of linear error-correcting codes.

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Hamming distance

In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.

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Hard disk drive

A hard disk drive (HDD), hard disk, hard drive or fixed disk is an electromechanical data storage device that uses magnetic storage to store and retrieve digital information using one or more rigid rapidly rotating disks (platters) coated with magnetic material.

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Hash function

A hash function is any function that can be used to map data of arbitrary size to data of a fixed size.

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High-definition television

High-definition television (HDTV) is a television system providing an image resolution that is of substantially higher resolution than that of standard-definition television, either analog or digital.

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Hybrid automatic repeat request

Hybrid automatic repeat request (hybrid ARQ or HARQ) is a combination of high-rate forward error-correcting coding and ARQ error-control.

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Information theory

Information theory studies the quantification, storage, and communication of information.

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Internet protocol suite

The Internet protocol suite is the conceptual model and set of communications protocols used on the Internet and similar computer networks.

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IPv4

Internet Protocol version 4 (IPv4) is the fourth version of the Internet Protocol (IP).

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IPv6

Internet Protocol version 6 (IPv6) is the most recent version of the Internet Protocol (IP), the communications protocol that provides an identification and location system for computers on networks and routes traffic across the Internet.

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Jupiter

Jupiter is the fifth planet from the Sun and the largest in the Solar System.

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Kernel.org

kernel.org is the main distribution point of source code for the Linux kernel, which is the base of the Linux operating system.

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Latency (engineering)

Latency is a time interval between the stimulation and response, or, from a more general point of view, a time delay between the cause and the effect of some physical change in the system being observed.

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Linear code

In coding theory, a linear code is an error-correcting code for which any linear combination of codewords is also a codeword.

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Link adaptation

Link adaptation, or adaptive coding and modulation (ACM), is a term used in wireless communications to denote the matching of the modulation, coding and other signal and protocol parameters to the conditions on the radio link (e.g. the pathloss, the interference due to signals coming from other transmitters, the sensitivity of the receiver, the available transmitter power margin, etc.). For example, WiMAX uses a rate adaptation algorithm that adapts the modulation and coding scheme (MCS) according to the quality of the radio channel, and thus the bit rate and robustness of data transmission.

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Link layer

In computer networking, the link layer is the lowest layer in the Internet Protocol Suite, the networking architecture of the Internet.

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Linux kernel

The Linux kernel is an open-source monolithic Unix-like computer operating system kernel.

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Linux Magazine

Linux Magazine is an international magazine for Linux software enthusiasts and professionals.

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List of hash functions

This is a list of hash functions, including cyclic redundancy checks, checksum functions, and cryptographic hash functions.

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Longitudinal redundancy check

In telecommunication, a longitudinal redundancy check (LRC), or horizontal redundancy check, is a form of redundancy check that is applied independently to each of a parallel group of bit streams.

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Low-density parity-check code

In information theory, a low-density parity-check (LDPC) code is a linear error correcting code, a method of transmitting a message over a noisy transmission channel.

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Luhn algorithm

The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, National Provider Identifier numbers in the United States, Canadian Social Insurance Numbers, Israel ID Numbers and Greek Social Security Numbers (ΑΜΚΑ).

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Magnetic tape data storage

Magnetic tape data storage is a system for storing digital information on magnetic tape using digital recording.

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Marcel J. E. Golay

Marcel Jules Edouard Golay (May 3, 1902 – April 27, 1989) was a Swiss-born mathematician, physicist, and information theorist, who applied mathematics to real-world military and industrial problems.

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Memory scrubbing

Memory scrubbing consists of reading from each computer memory location, correcting bit errors (if any) with an error-correcting code (ECC), and writing the corrected data back to the same location.

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Message authentication code

In cryptography, a message authentication code (MAC), sometimes known as a tag, is a short piece of information used to authenticate a message—in other words, to confirm that the message came from the stated sender (its authenticity) and has not been changed.

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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Modulation

In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted.

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Multidimensional parity-check code

A multidimensional parity-check code (MDPC) is a simple type of error correcting code that operates by arranging the message into a multidimensional grid, and calculating a parity digit for each row and column.

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Neptune

Neptune is the eighth and farthest known planet from the Sun in the Solar System.

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Network congestion

Network congestion in data networking and queueing theory is the reduced quality of service that occurs when a network node or link is carrying more data than it can handle.

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Network packet

A network packet is a formatted unit of data carried by a packet-switched network.

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Noise (electronics)

In electronics, noise is an unwanted disturbance in an electrical signal.

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Noisy-channel coding theorem

In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.

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Numbers station

A numbers station is a shortwave radio station characterized by broadcasts of formatted numbers, which are believed to be addressed to intelligence officers operating in foreign countries.

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Ones' complement

The ones' complement of a binary number is defined as the value obtained by inverting all the bits in the binary representation of the number (swapping 0s for 1s and vice versa).

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Operating system

An operating system (OS) is system software that manages computer hardware and software resources and provides common services for computer programs.

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OSI model

The Open Systems Interconnection model (OSI model) is a conceptual model that characterizes and standardizes the communication functions of a telecommunication or computing system without regard to its underlying internal structure and technology.

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Parchive

Parchive (a portmanteau of parity archive, and formally known as Parity Volume Set Specification) is an erasure code system that produces par files for checksum verification of data integrity, with the capability to perform data recovery operations that can repair or regenerate corrupted or missing data.

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Parity bit

A parity bit, or check bit, is a bit added to a string of binary code to ensure that the total number of 1-bits in the string is even or odd.

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Phase-shift keying

Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave).

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Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.

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Preimage attack

In cryptography, a preimage attack on cryptographic hash functions tries to find a message that has a specific hash value.

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Prentice Hall

Prentice Hall is a major educational publisher owned by Pearson plc.

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Protocol stack

The protocol stack or network stack is an implementation of a computer networking protocol suite or protocol family.

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Quadrature amplitude modulation

Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information.

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RAID

RAID (Redundant Array of Independent Disks, originally Redundant Array of Inexpensive Disks) is a data storage virtualization technology that combines multiple physical disk drive components into one or more logical units for the purposes of data redundancy, performance improvement, or both.

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Random-access memory

Random-access memory (RAM) is a form of computer data storage that stores data and machine code currently being used.

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Redundancy (information theory)

In Information theory, redundancy measures the fractional difference between the entropy of an ensemble, and its maximum possible value \log(|\mathcal_X|).

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Reed–Muller code

Reed–Muller codes are a family of linear error-correcting codes used in communications.

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Reed–Solomon error correction

Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960.

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Reliability (computer networking)

In computer networking, a reliable protocol provides notifications to the sender as to the delivery of transmitted data, as opposed to an unreliable protocol, which does not provide assurance of the delivery of data to the intended recipient(s).

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Remainder

In mathematics, the remainder is the amount "left over" after performing some computation.

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Repetition code

In coding theory, the repetition code is one of the most basic error-correcting codes.

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Return channel

In communications systems, the return channel (also reverse channel or return link) is the transmission link from a user terminal to the central hub.

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Richard Hamming

Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was an American mathematician whose work had many implications for computer engineering and telecommunications.

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Routing

Routing is the process of selecting a path for traffic in a network, or between or across multiple networks.

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Saturn

Saturn is the sixth planet from the Sun and the second-largest in the Solar System, after Jupiter.

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Selective Repeat ARQ

Selective Repeat ARQ / Selective Reject ARQ is a specific instance of the Automatic Repeat-Request (ARQ) protocol used to solve sequence number dilemma in communications.

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Signal-to-noise ratio

Signal-to-noise ratio (abbreviated SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise.

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Simplex communication

Simplex communication is a communication channel that sends information in one direction only.

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Single event upset

A single event upset (SEU) is a change of state caused by one single ionizing particle (ions, electrons, photons...) striking a sensitive node in a micro-electronic device, such as in a microprocessor, semiconductor memory, or power transistors.

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Soft error

In electronics and computing, a soft error is a type of error where a signal or datum is wrong.

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Stop-and-wait ARQ

Stop-and-wait ARQ, also referred to as alternating bit protocol, is a method in telecommunications to send information between two connected devices.

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Systematic code

In coding theory, a systematic code is any error-correcting code in which the input data is embedded in the encoded output.

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TCP congestion control

Transmission Control Protocol (TCP) uses a network congestion-avoidance algorithm that includes various aspects of an additive increase/multiplicative decrease (AIMD) scheme, with other schemes such as slow-start and congestion window to achieve congestion avoidance.

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Telecommunication

Telecommunication is the transmission of signs, signals, messages, words, writings, images and sounds or information of any nature by wire, radio, optical or other electromagnetic systems.

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Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

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Timeout (computing)

In telecommunications and related engineering (including computer networking and programming), the term timeout or time-out has several meanings, including.

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Transmission Control Protocol

The Transmission Control Protocol (TCP) is one of the main protocols of the Internet protocol suite.

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Transponder

In telecommunication, a transponder can be one of two types of devices.

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Transverse redundancy check

In telecommunications, a transverse redundancy check (TRC) or vertical redundancy check is a redundancy check for synchronized parallel bits applied once per bit time, across the bit streams.

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Triple modular redundancy

In computing, triple modular redundancy, sometimes called triple-mode redundancy, (TMR) is a fault-tolerant form of N-modular redundancy, in which three systems perform a process and that result is processed by a majority-voting system to produce a single output.

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Tsinghua University

Tsinghua University (abbreviated THU;; also romanized as Qinghua) is a major research university in Beijing, China and a member of the elite C9 League of Chinese universities.

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Turbo code

In information theory, turbo codes (originally in French Turbocodes) are a class of high-performance forward error correction (FEC) codes developed around 1990–91 (but first published in 1993), which were the first practical codes to closely approach the channel capacity, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level.

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Uranus

Uranus is the seventh planet from the Sun.

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User Datagram Protocol

In computer networking, the User Datagram Protocol (UDP) is one of the core members of the Internet protocol suite.

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Verhoeff algorithm

The Verhoeff algorithm is a checksum formula for error detection developed by the Dutch mathematician Jacobus Verhoeff and was first published in 1969.

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Viterbi decoder

A Viterbi decoder uses the Viterbi algorithm for decoding a bitstream that has been encoded using convolutional code or trellis code.

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Voyager 1

Voyager 1 is a space probe launched by NASA on September 5, 1977.

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Voyager 2

Voyager 2 is a space probe launched by NASA on August 20, 1977, to study the outer planets.

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ZFS

ZFS is a combined file system and logical volume manager designed by Sun Microsystems and now owned by Oracle Corporation.

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References

[1] https://en.wikipedia.org/wiki/Error_detection_and_correction

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