\(q\)-ary LDPC code[1] 

Also known as Non-binary LDPC (NBDPC) code.

Description

A \(q\)-ary linear code with a sparse parity-check matrix. Alternatively, a member of an infinite family of \([n,k,d]_q\) codes for which the number of nonzero entries in each row and column of the parity-check matrix are both bounded above by a constant as \(n\to\infty\).

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 a nonzero field element (error). Despite the fact that there is more than one nonzero outcome, \(q>2g\)-ary linear codes with sparse parity-check matrices are also called LDPC codes.

Parent

  • Tanner code — \(q\)-ary LDPC codes are \(q\)-ary Tanner codes on sparse bipartite graphs whose constraint nodes represent \(q\)-ary parity-check codes.

Children

Cousin

  • \(q\)-ary LDGM code — The dual of a \(q\)-ary LDPC code has a sparse generator matrix and is called a \(q\)-ary LDGM code.

References

[1]
M. C. Davey and D. J. C. MacKay, “Low density parity check codes over GF(q)”, 1998 Information Theory Workshop (Cat. No.98EX131) DOI
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Zoo Code ID: q-ary_ldpc

Cite as:
“\(q\)-ary LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/q-ary_ldpc
BibTeX:
@incollection{eczoo_q-ary_ldpc,
  title={\(q\)-ary LDPC code},
  booktitle={The Error Correction Zoo},
  year={2023},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/q-ary_ldpc}
}
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Permanent link:
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Cite as:

“\(q\)-ary LDPC code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/q-ary_ldpc

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/q-ary_digits/tanner/q-ary_ldpc.yml.