parity-check matrix
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Parity-check matrix — In coding theory, a parity check matrix of a linear block code C is a generator matrix of the dual code. As such, a codeword c is in C if and only if the matrix vector product Hc=0. The rows of a parity check matrix are parity checks on the… … Wikipedia
Low-density parity-check code — In information theory, a low density parity check code (LDPC code) is an error correcting code, a method of transmitting a message over a noisy transmission channel. [David J.C. MacKay (2003) Information theory, inference and learning algorithms … Wikipedia
Low-Density-Parity-Check-Code — Low Density Parity Check Codes, auch als LDPC oder Gallager Codes bezeichnet, sind lineare Blockcodes zur Fehlerkorrektur. Sie wurden 1962 von Robert Gray Gallager im Rahmen seiner Dissertation am MIT entwickelt [1] [2]. Low Density Parity Check… … Deutsch Wikipedia
Generator matrix — In coding theory, a generator matrix is a basis for a linear code, generating all its possible codewords.If the matrix is G and the linear code is C , : w =cGwhere w is a unique codeword of the linear code C , c is a unique row vector, and a… … Wikipedia
Distributed source coding — (DSC) is an important problem in information theory and communication. DSC problems regard the compression of multiple correlated information sources that do not communicate with each other.[1] By modeling the correlation between multiple sources … Wikipedia
Hamming code — In telecommunication, a Hamming code is a linear error correcting code named after its inventor, Richard Hamming. Hamming codes can detect and correct single bit errors. In other words, the Hamming distance between the transmitted and received… … Wikipedia
Linear code — In mathematics and information theory, a linear code is an important type of block code used in error correction and detection schemes. Linear codes allow for more efficient encoding and decoding algorithms than other codes (cf. syndrome… … Wikipedia
List of mathematics articles (P) — NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… … Wikipedia
Niederreiter cryptosystem — In cryptography, the Niederreiter cryptosystem is a variation of the McEliece Cryptosystem developed in 1986 by Harald Niederreiter [1]. It applies the same idea to the parity check matrix H of a linear code. Niederreiter is equivalent to… … Wikipedia
Decoding methods — In communication theory and coding theory, decoding is the process of translating received messages into codewords of a given code. There has been many common methods of mapping messages to codewords. These are often used to recover messages sent … Wikipedia
Ternary Golay code — There are two closely related error correcting codes known as ternary Golay codes. The code generally known simply as the ternary Golay code is a perfect (11, 6, 5) ternary linear code; the extended ternary Golay code is a (12, 6, 6) linear code… … Wikipedia