Codes whose parity-check matrix is constructed non-deterministically via the MacKay-Neal prescription. The parity-check matrix of an \((l,r,g\))-MN-LDPC code 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 \(g\) .
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 .
Free-energy minimization and a BP decoder .
- D. J. C. MacKay and R. M. Neal, “Good codes based on very sparse matrices”, Cryptography and Coding 100 (1995) DOI
- D. J. C. MacKay, “Good error-correcting codes based on very sparse matrices”, IEEE Transactions on Information Theory 45, 399 (1999) DOI
- 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
- Henry D. Pfister, private communication, 2022
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- Victor V. Albert (2023-05-04) — most recent
“MacKay-Neal LDPC (MN-LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/mn_ldpc