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LDPC codes have no limitations of minimum distance, that indirectly means that LDPC codes may be more efficient on relatively large code rates (e.g. 3/4, 5/6, 7/8) than turbo codes. However, LDPC codes are not the complete replacement: turbo codes are the best solution at the lower code rates (e.g. 1/6, 1/3, 1/2). See also People
This is a consequence of the fact that a parity check matrix of is a generator matrix of the dual code. G is a matrix, while H is a () matrix. Equivalent codes. Codes C 1 and C 2 are equivalent (denoted C 1 ~ C 2) if one code can be obtained from the other via the following two transformations: arbitrarily permute the components, and
The Reed–Muller RM(r, m) code of order r and length N = 2 m is the code generated by v 0 and the wedge products of up to r of the v i, 1 ≤ i ≤ m (where by convention a wedge product of fewer than one vector is the identity for the operation).
Default generator in R and the Python language starting from version 2.3. Xorshift: 2003 G. Marsaglia It is a very fast sub-type of LFSR generators. Marsaglia also suggested as an improvement the xorwow generator, in which the output of a xorshift generator is added with a Weyl sequence.
1.3.1 GPL pdoc: Andrew Gallant Text Python Any 2013 1.0.1 (2021) Unlicense (PD) perldoc: Larry Wall: Text Perl Any 1994 5.16.3 Artistic, GPL phpDocumentor: Joshua Eichorn Text PHP Any 2000 3.0.0 LGPL for 1.x, MIT for 2+ pydoc: Ka-Ping Yee: Text Python Any 2000 in Python core Python: RDoc: Dave Thomas Text C, C++, Ruby Any 2001/12/14 in Ruby ...
The BCH code with and higher has the generator polynomial. This code has minimal Hamming distance 15 and corrects 7 errors. It has 1 data bit and 14 checksum bits. It is also denoted as: (15, 1) BCH code. In fact, this code has only two codewords: 000000000000000 and 111111111111111 (a trivial repetition code ).
Systematic code. In coding theory, a systematic code is any error-correcting code in which the input data are embedded in the encoded output. Conversely, in a non-systematic code the output does not contain the input symbols. Systematic codes have the advantage that the parity data can simply be appended to the source block, and receivers do ...
Singleton bound. In coding theory, the Singleton bound, named after Richard Collom Singleton, is a relatively crude upper bound on the size of an arbitrary block code with block length , size and minimum distance . It is also known as the Joshibound. [1] proved by Joshi (1958) and even earlier by Komamiya (1953) .