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Low-density parity-check code

Index 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. [1]

76 relations: Amin Shokrollahi, BCH code, BCJR algorithm, Belief propagation, Binary erasure channel, Binary symmetric channel, Bipartite graph, Bit error rate, C (programming language), C++11, China Multimedia Mobile Broadcasting, Circulant matrix, Claude Shannon, Cliff effect, Code rate, Communications satellite, David J. C. MacKay, Decoding methods, Digital television, Digital Terrestrial Multimedia Broadcast, DOCSIS, DVB-C, DVB-S2, DVB-T2, Elementary matrix, Error floor, EXIT chart, Expander code, Factor graph, Finite geometry, Forward error correction, Fountain code, G.hn, Generator matrix, GF(2), Graph theory, Hamming code, IEEE 802.11ac, IEEE 802.11n-2009, Information theory, Institute of Electrical and Electronics Engineers, Irving S. Reed, ITU-T, Likelihood-ratio test, Linear code, Lookup table, Luby transform code, Massachusetts Institute of Technology, MATLAB, Maximum a posteriori estimation, ..., Modular arithmetic, NASA Deep Space Network, Noise (electronics), NP-completeness, Online codes, Orthogonal frequency-division multiplexing, Parity-check matrix, Polar code (coding theory), Python (programming language), Raptor code, Real number, Reed–Solomon error correction, Repeat-accumulate code, Richard Hamming, Robert G. Gallager, Serial concatenated convolutional codes, Shannon–Hartley theorem, Soft output Viterbi algorithm, Soft-in soft-out decoder, Sparse graph code, Sparse matrix, Tornado code, Turbo code, Wi-Fi, WiMAX, 10 Gigabit Ethernet. Expand index (26 more) »

Amin Shokrollahi

Amin Shokrollahi (born 1964) is an Iranian mathematician who has worked on a variety of topics including coding theory and algebraic complexity theory.

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BCH code

In coding theory, the BCH codes or Bose–Chaudhuri–Hocquenghem codes form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called Galois field).

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BCJR algorithm

The BCJR algorithm is an algorithm for maximum a posteriori decoding of error correcting codes defined on trellises (principally convolutional codes).

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Belief propagation

Belief propagation, also known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields.

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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 symmetric channel

A binary symmetric channel (or BSC) is a common communications channel model used in coding theory and information theory.

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Bipartite graph

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.

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Bit error rate

In digital transmission, the number of bit errors is the number of received bits of a data stream over a communication channel that have been altered due to noise, interference, distortion or bit synchronization errors.

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C (programming language)

C (as in the letter ''c'') is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations.

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C++11

C++11 is a version of the standard for the programming language C++.

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China Multimedia Mobile Broadcasting

China Mobile Multimedia Broadcasting (CMMB) is a mobile television and multimedia standard developed and specified in China by the State Administration of Radio, Film, and Television (SARFT).

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Circulant matrix

In linear algebra, a circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element to the right relative to the preceding row vector.

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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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Cliff effect

In telecommunications, the (digital) cliff effect or brickwall effect is a sudden loss of digital signal reception.

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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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Communications satellite

A communications satellite is an artificial satellite that relays and amplifies radio telecommunications signals via a transponder; it creates a communication channel between a source transmitter and a receiver at different locations on Earth.

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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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Decoding methods

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

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Digital television

Digital television (DTV) is the transmission of television signals, including the sound channel, using digital encoding, in contrast to the earlier television technology, analog television, in which the video and audio are carried by analog signals.

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Digital Terrestrial Multimedia Broadcast

DTMB (Digital Terrestrial Multimedia Broadcast) is the TV standard for mobile and fixed terminals used in the People's Republic of China, Cuba, Hong Kong, and Macau.

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DOCSIS

Data Over Cable Service Interface Specification (DOCSIS) is an international telecommunications standard that permits the addition of high-bandwidth data transfer to an existing cable TV (CATV) system.

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DVB-C

DVB-C stands for "Digital Video Broadcasting - Cable" and it is the DVB European consortium standard for the broadcast transmission of digital television over cable.

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DVB-S2

Digital Video Broadcasting - Satellite - Second Generation (DVB-S2) is a digital television broadcast standard that has been designed as a successor for the popular DVB-S system.

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DVB-T2

DVB-T2 is an abbreviation for "Digital Video Broadcasting — Second Generation Terrestrial"; it is the extension of the television standard DVB-T, issued by the consortium DVB, devised for the broadcast transmission of digital terrestrial television.

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Elementary matrix

In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation.

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Error floor

The error floor is a phenomenon encountered in modern iterated sparse graph-based error correcting codes like LDPC codes and turbo codes.

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EXIT chart

An extrinsic information transfer chart, commonly called an EXIT chart, is a technique to aid the construction of good iteratively-decoded error-correcting codes (in particular low-density parity-check (LDPC) codes and Turbo codes).

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Expander code

In coding theory, expander codes form a class of error-correcting codes that are constructed from bipartite expander graphs.

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Factor graph

A factor graph is a bipartite graph representing the factorization of a function.

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Finite geometry

A finite geometry is any geometric system that has only a finite number of points.

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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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G.hn

G.hn is a specification for home networking with data rates up to 2 Gbit/s and operation over four types of legacy wires: telephone wiring, coaxial cables, power lines and plastic optical fiber.

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Generator matrix

In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code.

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GF(2)

GF(2) (also F2, Z/2Z or Z2) is the '''G'''alois '''f'''ield of two elements.

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Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

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Hamming code

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

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IEEE 802.11ac

IEEE 802.11ac is a wireless networking standard in the 802.11 family (which is marketed under the brand name Wi-Fi), developed in the IEEE Standards Association, providing high-throughput wireless local area networks (WLANs) on the 5 GHz band.

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IEEE 802.11n-2009

IEEE 802.11n-2009, commonly shortened to 802.11n, is a wireless-networking standard that uses multiple antennas to increase data rates.

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Information theory

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

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Institute of Electrical and Electronics Engineers

The Institute of Electrical and Electronics Engineers (IEEE) is a professional association with its corporate office in New York City and its operations center in Piscataway, New Jersey.

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Irving S. Reed

Irving Stoy Reed (November 12, 1923 – September 11, 2012) was a mathematician and engineer.

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ITU-T

The ITU Telecommunication Standardization Sector (ITU-T) is one of the three sectors (divisions or units) of the International Telecommunication Union (ITU); it coordinates standards for telecommunications.

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Likelihood-ratio test

In statistics, a likelihood ratio test (LR test) is a statistical test used for comparing the goodness of fit of two statistical models — a null model against an alternative model.

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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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Lookup table

In computer science, a lookup table is an array that replaces runtime computation with a simpler array indexing operation.

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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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Massachusetts Institute of Technology

The Massachusetts Institute of Technology (MIT) is a private research university located in Cambridge, Massachusetts, United States.

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MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.

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Maximum a posteriori estimation

In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution.

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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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NASA Deep Space Network

The NASA Deep Space Network (DSN) is a worldwide network of US spacecraft communication facilities, located in the United States (California), Spain (Madrid), and Australia (Canberra), that supports NASA's interplanetary spacecraft missions.

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Noise (electronics)

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

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NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

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Online codes

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

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Orthogonal frequency-division multiplexing

In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies.

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Parity-check matrix

In coding theory, a parity-check matrix of a linear block code C is a matrix which describes the linear relations that the components of a codeword must satisfy.

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Polar code (coding theory)

In information theory, a polar code is a linear block error correcting code.

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Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

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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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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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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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Repeat-accumulate code

In computer science, repeat-accumulate codes (RA codes) are a low complexity class of error-correcting codes.

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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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Robert G. Gallager

Robert Gray Gallager (born May 29, 1931) is an American electrical engineer known for his work on information theory and communications networks.

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Serial concatenated convolutional codes

Serial concatenated convolutional codes (SCCC) are a class of forward error correction (FEC) codes highly suitable for turbo (iterative) decoding.

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Shannon–Hartley theorem

In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise.

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Soft output Viterbi algorithm

The soft output Viterbi algorithm (SOVA) is a variant of the classical Viterbi algorithm.

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Soft-in soft-out decoder

A soft-in soft-out (SISO) decoder is a type of soft-decision decoder used with error correcting codes.

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Sparse graph code

A Sparse graph code is a code which is represented by a sparse graph.

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Sparse matrix

In numerical analysis and computer science, a sparse matrix or sparse array is a matrix in which most of the elements are zero.

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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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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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Wi-Fi

Wi-Fi or WiFi is technology for radio wireless local area networking of devices based on the IEEE 802.11 standards.

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WiMAX

WiMAX (Worldwide Interoperability for Microwave Access) is a family of wireless communication standards based on the IEEE 802.16 set of standards, which provide multiple physical layer (PHY) and Media Access Control (MAC) options.

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10 Gigabit Ethernet

10 Gigabit Ethernet (10GE, 10GbE, or 10 GigE) is a group of computer networking technologies for transmitting Ethernet frames at a rate of 10 gigabits per second.

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Gallager code, Gallager codes, LDPC, LDPC code, LDPC codes, Ldpc, Ldpc code, Ldpc codes, Low Density Parity Check Codes, Low density parity check code, Low-density parity-check codes, Parity check code.

References

[1] https://en.wikipedia.org/wiki/Low-density_parity-check_code

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