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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. The fraction ''r'' = ''k''/''n'' is called the code rate. The fraction ''k’/k'', where ''k’'' denotes the number of symbols required for recovery, is called reception efficiency. The recovery algorithm expects that it is known which of the ''n'' symbols are lost. History Erasure coding was invented by Irving Reed and Gustave Solomon in 1960. There are many different erasure coding schemes. The most popular erasure codes are Reed-Solomon coding, Low-density parity-check code (LDPC codes), and Turbo codes. As of 2023, modern data storage systems can be designed to tolerate the complete failure of a few disks without data loss, using one of 3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Polynomial
In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data set of coordinate pairs (x_j, y_j) with 0 \leq j \leq k, the x_j are called ''nodes'' and the y_j are called ''values''. The Lagrange polynomial L(x) has degree \leq k and assumes each value at the corresponding node, L(x_j) = y_j. Although named after Joseph-Louis Lagrange, who published it in 1795, the method was first discovered in 1779 by Edward Waring. It is also an easy consequence of a formula published in 1783 by Leonhard Euler. Uses of Lagrange polynomials include the Newton–Cotes method of numerical integration, Shamir's secret sharing scheme in cryptography, and Reed–Solomon error correction in coding theory. For equispaced nodes, Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation. Definition Given a set of k + 1 nodes \, which must all be distinct, x_j \neq x_m for ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Online Codes
In computer science, online codes are an example of rateless erasure codes. These codes can encode a message into a number of symbols such that knowledge of any fraction of them allows one to recover the original message (with high probability). ''Rateless'' codes produce an arbitrarily large number of symbols which can be broadcast until the receivers have enough symbols. The online encoding algorithm consists of several phases. First the message is split into ''n'' fixed size message blocks. Then the ''outer encoding'' is an erasure code which produces auxiliary blocks that are appended to the message blocks to form a composite message. From this the inner encoding generates check blocks. Upon receiving a certain number of check blocks some fraction of the composite message can be recovered. Once enough has been recovered the outer decoding can be used to recover the original message. Detailed discussion Online codes are parameterised by the block size and two scalars, ''q'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low-density Parity-check Codes
Low-density parity-check (LDPC) codes are a class of error correction codes which (together with the closely-related turbo codes) have gained prominence in coding theory and information theory since the late 1990s. The codes today are widely used in applications ranging from wireless communications to flash-memory storage. Together with turbo codes, they sparked a revolution in coding theory, achieving order-of-magnitude improvements in performance compared to traditional error correction codes. Central to the performance of LDPC codes is their adaptability to the iterative belief propagation decoding algorithm. Under this algorithm, they can be designed to approach theoretical limits ( capacities) of many channels at low computation costs. Theoretically, analysis of LDPC codes focuses on sequences of codes of fixed code rate and increasing block length. These sequences are typically tailored to a set of channels. For appropriately designed sequences, the decoding error u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tornado Codes
In coding theory, Tornado codes are a class of erasure codes that support error correction. Tornado codes require a constant C more redundant blocks than the more data-efficient Reed–Solomon erasure codes, but are much faster to generate and can fix erasures faster. Software-based implementations of tornado codes are about 100 times faster on small lengths and about 10,000 times faster on larger lengths than Reed–Solomon erasure codes. Since the introduction of Tornado codes, many other similar erasure codes have emerged, most notably Online codes, LT codes and Raptor codes. Tornado codes use a layered approach. All layers except the last use an LDPC error correction code, which is fast but has a chance of failure. The final layer uses a Reed–Solomon correction code, which is slower but is optimal in terms of failure recovery. Tornado codes dictates how many levels, how many recovery blocks in each level, and the distribution used to generate blocks for the non-final laye ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HDFS
Apache Hadoop () is a collection of open-source software utilities for reliable, scalable, distributed computing. It provides a software framework for distributed storage and processing of big data using the MapReduce programming model. Hadoop was originally designed for computer clusters built from commodity hardware, which is still the common use. It has since also found use on clusters of higher-end hardware. All the modules in Hadoop are designed with a fundamental assumption that hardware failures are common occurrences and should be automatically handled by the framework. Overview The core of Apache Hadoop consists of a storage part, known as Hadoop Distributed File System (HDFS), and a processing part which is a MapReduce programming model. Hadoop splits files into large blocks and distributes them across nodes in a cluster. It then transfers packaged code into nodes to process the data in parallel. This approach takes advantage of data locality, where nodes manipulate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reed–Solomon Error Correction
In information theory and coding theory, Reed–Solomon codes are a group of error-correcting codes that were introduced by Irving S. Reed and Gustave Solomon in 1960. They have many applications, including consumer technologies such as MiniDiscs, CDs, DVDs, Blu-ray discs, QR codes, Data Matrix, data transmission technologies such as DSL and WiMAX, Broadcasting, broadcast systems such as satellite communications, Digital Video Broadcasting, DVB and ATSC Standards, ATSC, and storage systems such as RAID 6. Reed–Solomon codes operate on a block of data treated as a set of finite field, finite-field elements called symbols. Reed–Solomon codes are able to detect and correct multiple symbol errors. By adding check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to erroneous symbols, ''or'' locate and correct up to erroneous symbols at unknown locations. As an erasure code, it can correct up to erasures at locations that are known and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RAID-6
In computer storage, the standard RAID levels comprise a basic set of RAID ("redundant array of independent disks" or "redundant array of inexpensive disks") configurations that employ the techniques of striping, mirroring, or parity to create large reliable data stores from multiple general-purpose computer hard disk drives (HDDs). The most common types are RAID 0 (striping), RAID 1 (mirroring) and its variants, RAID 5 (distributed parity), and RAID 6 (dual parity). Multiple RAID levels can also be combined or ''nested'', for instance RAID 10 (striping of mirrors) or RAID 01 (mirroring stripe sets). RAID levels and their associated data formats are standardized by the Storage Networking Industry Association (SNIA) in the Common RAID Disk Drive Format (DDF) standard. The numerical values only serve as identifiers and do not signify performance, reliability, generation, hierarchy, or any other metric. While most RAID levels can provide good protection ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apache Hadoop
Apache Hadoop () is a collection of open-source software utilities for reliable, scalable, distributed computing. It provides a software framework for distributed storage and processing of big data using the MapReduce programming model. Hadoop was originally designed for computer clusters built from commodity hardware, which is still the common use. It has since also found use on clusters of higher-end hardware. All the modules in Hadoop are designed with a fundamental assumption that hardware failures are common occurrences and should be automatically handled by the framework. Overview The core of Apache Hadoop consists of a storage part, known as Hadoop Distributed File System (HDFS), and a processing part which is a MapReduce programming model. Hadoop splits files into large blocks and distributes them across nodes in a cluster. It then transfers packaged code into nodes to process the data in parallel. This approach takes advantage of data locality, where nodes manipulate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regenerating Code
Regeneration may refer to: Science and technology * Regeneration (biology), the ability to recreate lost or damaged cells, tissues, organs and limbs * Regeneration (ecology), the ability of ecosystems to regenerate biomass, using photosynthesis * Regeneration in humans, the ability of humans to recreate, or induce the regeneration of, lost tissue * Regenerative design, a process for resilient and sustainable development * Regenerative agriculture, a sub-category of organic agriculture History and politics * Regeneration (Colombia), La Regeneración, a 19th-century period and political movement in Colombia *Regeneration (Portugal), a 19th-century period in the history of Portugal * The ReGeneration, a cultural generation concerned with environmentalism * Viðreisn (Regeneration), a political party in Iceland founded in 2016 Music * ''Regeneration'' (Stanley Cowell album) (1976) * ''Regeneration'' (Roy Orbison album) (1977) * ''Regeneration'' (The Divine Comedy album) (2001) * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. The term ''fountain'' or ''rateless'' refers to the fact that these codes do not exhibit a fixed code rate. A fountain code is optimal if the original ''k'' source symbols can be recovered from any ''k'' successfully received encoding symbols (i.e., excluding those that were erased). Fountain codes are known that have efficient encoding and decoding algorithms and that allow the recovery of the original ''k'' source symbols from any ''k’'' of the encoding symbols with high probability, where ''k’'' is just slightly larger than ''k''. LT codes were the first practical realizat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Secret Sharing
Secret sharing (also called secret splitting) refers to methods for distributing a secrecy, secret among a group, in such a way that no individual holds any intelligible information about the secret, but when a sufficient number of individuals combine their 'shares', the secret may be reconstructed. Whereas ''insecure'' secret sharing allows an attacker to gain more information with each share, ''secure'' secret sharing is 'all or nothing' (where 'all' means the necessary number of shares). In one type of secret sharing scheme there is one ''dealer'' and ''n'' ''players''. The dealer gives a share of the secret to the players, but only when specific conditions are fulfilled will the players be able to reconstruct the secret from their shares. The dealer accomplishes this by giving each player a share in such a way that any group of ''t'' (for ''threshold'') or more players can together reconstruct the secret but no group of fewer than ''t'' players can. Such a system is called a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
