Array-based LDPC (AB-LDPC) code

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].

Parents

Child

Tanner-Sridhara-Fuja (TSF) code

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].

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, 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) DOI

Page edit log

Victor V. Albert (2023-05-04) — most recent

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.