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Generator matrix. In coding theory, a generator matrix is a matrix whose rows form a basis for a linear code. The codewords are all of the linear combinations of the rows of this matrix, that is, the linear code is the row space of its generator matrix.
LDPC codes are also known as Gallager codes, in honor of Robert G. Gallager, who developed the LDPC concept in his doctoral dissertation at the Massachusetts Institute of Technology in 1960. [4] [5] However, LDPC codes require computationally expensive iterative decoding, so they went unused for decades. In 1993 the newly invented turbo codes demonstrated that codes with iterative decoding ...
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. It can be used to decide whether a particular vector is a codeword and is also used in decoding algorithms.
A generator matrix for the dual code is the parity-check matrix for the original code and vice versa. The dual of the dual code is always the original code.
Free Fire is a free-to-play battle royale game developed and published by Garena for Android and iOS. [4] It was released on 8 December 2017. It became the most downloaded mobile game globally in 2019 and has over 1 billion downloads on Google Play Store. In the first quarter of 2021 it was the highest grossing mobile game in the US. [5] In November 2019, it surpassed $1 billion in lifetime ...
The parity-check matrix of a Hamming code is constructed by listing all columns of length r that are non-zero, which means that the dual code of the Hamming code is the shortened Hadamard code, also known as a Simplex code. The parity-check matrix has the property that any two columns are pairwise linearly independent .
11 queer musicians tell Harper's Bazaar about the albums that shaped their identities and artistry.
Infinitesimal generator (stochastic processes) In mathematics — specifically, in stochastic analysis — the infinitesimal generator of a Feller process (i.e. a continuous-time Markov process satisfying certain regularity conditions) is a Fourier multiplier operator [1] that encodes a great deal of information about the process.