Hsu-Anastasopoulos LDPC (HA-LDPC) code[1]
Description
A regular LDPC code obtained from a concatenation of a certain random regular LDPC code and a certain random LDGM code. Using rate-one LDGM codes eliminates high-weight codewords while admitting an amount of low-weight codewords that asymptotically vanishes, allowing code families to achieve the GV bound with high probability.Rate
HA-LDPC codes achieve capacity on the BEC channel under BP decoding [1] and the memoryless binary-input output-symmetric (MBIOS) channels under ML decoding [1] and under MAP decoding [2]. They also achieve the GV bound with asymptotically high probability when the concatenation is with a rate-one LDGM code [1].Cousins
- Low-density generator-matrix (LDGM) code— HA-LDPC codes are a concatenation of an LDPC and an LDGM code.
- Concatenated code— HA-LDPC codes are a concatenation of an LDPC and an LDGM code.
- MacKay-Neal LDPC (MN-LDPC) code— HA-LDPC and MN-LDPC codes are dual to each other [2].
- Dual linear code— HA-LDPC and MN-LDPC codes are dual to each other [2].
Primary Hierarchy
Low-density parity-check (LDPC) code\(q\)-ary LDPC Tanner Linear \(q\)-ary LRC Distributed-storage ECC
Parents
Multi-edge LDPC code\(q\)-ary LDPC Tanner Linear \(q\)-ary Linear code over \(\mathbb{Z}_q\) LRC Distributed-storage ECC
HA-LDPC codes can be formulated as multi-edge LDPC codes [2].
Hsu-Anastasopoulos LDPC (HA-LDPC) code
References
- [1]
- C.-H. Hsu and A. Anastasopoulos, “Capacity-Achieving Codes with Bounded Graphical Complexity on Noisy Channels”, (2005) arXiv:cs/0509062
- [2]
- 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
Page edit log
- Victor V. Albert (2023-05-04) — most recent
Cite as:
“Hsu-Anastasopoulos LDPC (HA-LDPC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/ha_ldpc