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Erasure code

Index Erasure code

In coding theory, an erasure code is a forward error correction (FEC) code under the assumption of bit erasures (rather than bit errors), which transforms a message of k symbols into a longer message (code word) with n symbols such that the original message can be recovered from a subset of the n symbols. [1]

22 relations: Alice and Bob, Code rate, Coding theory, Finite field, Forward error correction, Fountain code, Lagrange polynomial, Low-density parity-check code, Luby transform code, Online codes, Parchive, Parity bit, Polynomial interpolation, Processor register, RAID, Raptor code, Reed–Solomon error correction, Secret sharing, Spelling alphabet, Tahoe-LAFS, Tornado code, Vandermonde matrix.

Alice and Bob

Alice and Bob are fictional characters commonly used as placeholder names in cryptology, as well as science and engineering literature.

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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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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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Lagrange polynomial

In numerical analysis, Lagrange polynomials are used for polynomial interpolation.

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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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Luby transform code

In computer science, Luby transform codes (LT codes) are the first class of practical fountain codes that are near-optimal erasure correcting codes.

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Online codes

In computer science, online codes are an example of rateless erasure codes.

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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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Polynomial interpolation

In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset.

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Processor register

In computer architecture, a processor register is a quickly accessible location available to a computer's central processing unit (CPU).

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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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Raptor code

In computer science, raptor codes (rapid tornado; see Tornado codes) are the first known class of fountain codes with linear time encoding and decoding.

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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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Secret sharing

Secret sharing (also called secret splitting) refers to methods for distributing a secret amongst a group of participants, each of whom is allocated a share of the secret.

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Spelling alphabet

A spelling alphabet, word-spelling alphabet, voice procedure alphabet, radio alphabet, or telephone alphabet is a set of words used to stand for the letters of an alphabet in oral communication.

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Tahoe-LAFS (Tahoe Least-Authority File Store) is a free and open, secure, decentralized, fault-tolerant, distributed data store and distributed file system.

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Tornado code

In computer science, Tornado codes are a class of erasure codes that support error correction.

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Vandermonde matrix

In linear algebra, a Vandermonde matrix, named after Alexandre-Théophile Vandermonde, is a matrix with the terms of a geometric progression in each row, i.e., an m × n matrix 1 & \alpha_1 & \alpha_1^2 & \dots & \alpha_1^\\ 1 & \alpha_2 & \alpha_2^2 & \dots & \alpha_2^\\ 1 & \alpha_3 & \alpha_3^2 & \dots & \alpha_3^\\ \vdots & \vdots & \vdots & \ddots &\vdots \\ 1 & \alpha_m & \alpha_m^2 & \dots & \alpha_m^ \end, or for all indices i and j. (Some authors use the transpose of the above matrix.) The determinant of a square Vandermonde matrix (where m.

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Redirects here:

Deletion code, Erasure codes, Erasure coding, Erasure correcting code, Optimal erasure codes with arbitrary parameters.


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

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