Description
A code whose parity-check matrix is constructed non-deterministically via the MacKay-Neal prescription.
An \((l,r,g)\)-MN-LDPC code is a non-systematic two-edge-type LDPC code whose parity-check matrix is of the form \((H_1~H_2)\), where \(H_1\) is a random binary matrix of column weight \(l\) and row weight \(r\), and \(H_2\) is a random binary matrix of column and row weight \(g\); the bits corresponding to \(H_1\) are punctured [3].
Rate
Certain sequences of optimally decoded codes can nearly achieve the Shannon capacity [1,2]. A sequence of codes achieves the capacity of memoryless binary-input symmetric-output channels under MAP decoding [3]. Standard MN-LDPC codes have no BP threshold, while bounded-density spatially coupled MN-LDPC codes have BEC BP thresholds close to the Shannon limit [3].Decoding
Free-energy minimization and a BP decoder [1].Cousins
- Low-density generator-matrix (LDGM) code— \((l,r,1\))-MN-LDPC codes are LDGM [3].
- Irregular repeat-accumulate (IRA) code— MN-LDPC and IRA codes intersect for certain parameters [4].
- Hsu-Anastasopoulos LDPC (HA-LDPC) code— HA-LDPC and MN-LDPC codes are dual to each other [3].
- Spatially coupled LDPC (SC-LDPC) code— Spatial coupling of MN-LDPC protographs yields bounded-density SC-MN codes with BEC BP thresholds close to the Shannon limit [3].
Primary Hierarchy
Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Parents
MN-LDPC codes re-invigorated the study of LDPC codes about 30 years after their discovery.
Multi-edge LDPC code\(q\)-ary LDPC Tanner Linear \(q\)-ary Linear code over \(\mathbb{Z}_q\) LRC Distributed-storage ECC
MN-LDPC codes can be formulated as multi-edge LDPC codes [3].
MacKay-Neal LDPC (MN-LDPC) code
References
- [1]
- D. J. C. MacKay and R. M. Neal, “Good codes based on very sparse matrices”, Lecture Notes in Computer Science 100 (1995) DOI
- [2]
- D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices”, IEEE Transactions on Information Theory 45, 399 (1999) DOI
- [3]
- K. KASAI and K. SAKANIWA, “Spatially-Coupled MacKay-Neal Codes and Hsu-Anastasopoulos Codes”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A, 2161 (2011) arXiv:1102.4612 DOI
- [4]
- H. D. Pfister, private communication, 2022
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2023-05-04)
Cite as:
“MacKay-Neal LDPC (MN-LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/mn_ldpc, arXiv:2606.11484