Affine-permutation-matrix LDPC (APM-LDPC) code[1]
Description
LDPC code whose parity-check matrix matrix can be put into the form of a block matrix consisting of permutation sub-matrices representing the affine permutation group or the zero sub-matrix. Given a cyclic group \(\mathbb{Z}_r\), the affine permutation group is \(\mathbb{Z}_r \rtimes \mathbb{Z}_r^{\times}\), where \(\mathbb{Z}_r^{\times}\) is the multiplicative group of integers modulo \(r\). Such codes are often constructed by lifting certain protographs into such block matrices [2].Cousin
- Two-block group-algebra (2BGA) codes— APM-LDPC codes can be used to construct non-Abelian 2BGA codes based on the affine permutation group [3].
Member of code lists
Primary Hierarchy
Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Parents
Affine-permutation-matrix LDPC (APM-LDPC) code
References
- [1]
- S. Myung, K. Yang, and D. S. Park, “A Combining Method of Structured LDPC Codes from Affine Permutation Matrices”, 2006 IEEE International Symposium on Information Theory 674 (2006) DOI
- [2]
- I. E. Bocharova, F. Hug, R. Johannesson, B. D. Kudryashov, and R. V. Satyukov, “Searching for Voltage Graph-Based LDPC Tailbiting Codes With Large Girth”, IEEE Transactions on Information Theory 58, 2265 (2012) arXiv:1108.0840 DOI
- [3]
- K. Kasai, “Quantum Error Correction with Girth-16 Non-Binary LDPC Codes via Affine Permutation Construction”, (2025) arXiv:2504.17790
Page edit log
- Victor V. Albert (2025-09-15) — most recent
Cite as:
“Affine-permutation-matrix LDPC (APM-LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/apm_ldpc