Also known as Gallager codes. Binary or \(q\)-ary linear code with a sparse parity-check matrix. More precisely, a member of an infinite family of \([n,k,d]\) codes for which the number of nonzero entries in each row and column of the parity-check matrix are both bounded by a constant as \(n\to\infty\). An LDPC code is \((j,k)\)-regular if the parity-check matrix has a fixed number of \(j\) nonzero entries in each row and \(k\) entries in each column; otherwise, the LDPC code is irregular. The dual of an LDPC code has a sparse generator matrix and is called an LDGM code.
A parity check is performed by taking the inner product of a row of the parity-check matrix with a codeword that has been affected by a noise channel. A parity check yields either zero (no error) or one (error) for binary codes, while yielding zero (no error) or a nonzero field element (error) for \(q\)-ary codes. Despite the fact that there is more than one nonzero outcome, \(q\)-ary linear codes with sparse parity-check matrices are also called LDPC codes.
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Zoo code information
“Low-density parity-check (LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/ldpc