Description
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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Cousins
- Low-density generator-matrix (LDGM) code — LDPC and LDGM codes are dual to each other.
- Quantum low-density parity-check (QLDPC) code
- Tornado code — Tornado codes are similar to LDPC codes, but they use a highly irregular weight distribution for the underlying graphs [17].
References
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- R. Gallagher, Low-density parity check codes. 1963. PhD thesis, MIT Cambridge, MA.
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- Venkatesan Guruswami, “Iterative Decoding of Low-Density Parity Check Codes (A Survey)”. cs/0610022
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- Shrinivas Kudekar, Tom Richardson, and Ruediger Urbanke, “Spatially Coupled Ensembles Universally Achieve Capacity under Belief Propagation”. 1201.2999
- [6]
- Jonathan Mosheiff et al., “LDPC Codes Achieve List Decoding Capacity”. 1909.06430
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- T. J. Richardson and R. L. Urbanke, “Efficient encoding of low-density parity-check codes”, IEEE Transactions on Information Theory 47, 638 (2001). DOI
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- S. Lin and D. J. Costello, Error Control Coding, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2004.
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- LDPC coding for OFDMA PHY. 802.16REVe Sponsor Ballot Recirculation comment, July 2004. IEEE C802.16e04/141r2
- [12]
- R. Purnamasari, H. Wijanto, and I. Hidayat, “Design and implementation of LDPC(Low Density Parity Check) coding technique on FPGA (Field Programmable Gate Array) for DVB-S2 (Digital Video Broadcasting-Satellite)”, 2014 IEEE International Conference on Aerospace Electronics and Remote Sensing Technology (2014). DOI
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- Michael Helmling, Stefan Scholl, Florian Gensheimer, Tobias Dietz, Kira Kraft, Stefan Ruzika, and Norbert Wehn. Database of Channel Codes and ML Simulation Results. URL, 2022.
- [14]
- G. Liva, F. Steiner. “pretty-good-codes.org: Online library of good channel codes”, URL: http://pretty-good-codes.org/
- [15]
- A. Shokrollahi, “LDPC Codes: An Introduction”, Coding, Cryptography and Combinatorics 85 (2004). DOI
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- A. Cassagne et al., “AFF3CT: A Fast Forward Error Correction Toolbox!”, SoftwareX 10, 100345 (2019). DOI
- [17]
- A. Shokrollahi, “Raptor codes”, IEEE Transactions on Information Theory 52, 2551 (2006). DOI
Zoo code information
Cite as:
“Low-density parity-check (LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/ldpc
Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/properties/ldpc.yml.