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Array-based LDPC (AB-LDPC) code[1,2]

Description

QC-LDPC code constructed deterministically from a disk array code known as a B-code. Its parity-check matrix admits a compact representation [3] and is related to RS codes.

Realizations

Certain AB-LDPC codes have been proposed to be used for DSL transmission [4].

Cousin

  • B-code— AB-LDPC codes are constructed from certain classes of B-codes. B-codes can be viewed as binary codes by mapping their ring elements to permutation matrices (cf. lifting). The resulting codes turn out to be LDPC [2].

Member of code lists

Primary Hierarchy

Classical Domain
Binary Kingdom
Binary codeECC
Binary group-orbit codeECC
Linear binary codeLinear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC
Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Multi-edge LDPC code
Protograph LDPC code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Quasi-cyclic LDPC (QC-LDPC) codeECC
Parents
Quasi-cyclic LDPC (QC-LDPC) code
Algebraic LDPC code\(q\)-ary LDPC Tanner Linear \(q\)-ary Linear code over \(\mathbb{Z}_q\) LRC Distributed-storage ECC
Array-based LDPC (AB-LDPC) code
Children
Tanner-Sridhara-Fuja (TSF) code

References

[1]
Fan, John L. "Array codes as low-density parity-check codes." Proc. 2nd Int. Symp. on Turbo Codes & Related Topics, Brest, France, Sept. 2000.
[2]
J. L. Fan, “Array Codes as LDPC Codes”, Constrained Coding and Soft Iterative Decoding 195 (2001) DOI
[3]
T. Mittelholzer, “Efficient encoding and minimum distance bounds of Reed-Solomon-type array codes”, Proceedings IEEE International Symposium on Information Theory, 282 DOI
[4]
E. Eleftheriou and S. Olcer, “Low-density parity-check codes for digital subscriber lines”, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333) 3, 1752 DOI
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Zoo Code ID: array_ldpc

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

“Array-based LDPC (AB-LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/array_ldpc

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/tanner/qc/array_ldpc.yml.