Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check Matrices
Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this work, we first propose to decode QLDPC codes with a belief propa...
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IEEE
2025-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10876114/ |
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| author | Sisi Miao Alexander Schnerring Haizheng Li Laurent Schmalen |
| author_facet | Sisi Miao Alexander Schnerring Haizheng Li Laurent Schmalen |
| author_sort | Sisi Miao |
| collection | DOAJ |
| description | Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this work, we first propose to decode QLDPC codes with a belief propagation (BP) decoder operating on overcomplete check matrices. Then, we extend the neural BP (NBP) decoder, which was originally studied for suboptimal binary BP decoding of QLPDC codes, to quaternary BP decoders. Numerical simulation results demonstrate that both approaches as well as their combination yield a low-latency, high-performance decoder for several short to moderate length QLDPC codes. |
| format | Article |
| id | doaj-art-dd09af6778664d6f83c2009fa003ce26 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-dd09af6778664d6f83c2009fa003ce262025-02-12T00:02:43ZengIEEEIEEE Access2169-35362025-01-0113256372564910.1109/ACCESS.2025.353947510876114Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check MatricesSisi Miao0https://orcid.org/0000-0002-3483-7891Alexander Schnerring1Haizheng Li2Laurent Schmalen3https://orcid.org/0000-0002-1459-9128Communications Engineering Laboratory (CEL), Karlsruhe Institute of Technology (KIT), Karlsruhe, GermanyInstitute of Solar Research, German Aerospace Center (DLR), Almería, SpainCommunications Engineering Laboratory (CEL), Karlsruhe Institute of Technology (KIT), Karlsruhe, GermanyCommunications Engineering Laboratory (CEL), Karlsruhe Institute of Technology (KIT), Karlsruhe, GermanyQuantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this work, we first propose to decode QLDPC codes with a belief propagation (BP) decoder operating on overcomplete check matrices. Then, we extend the neural BP (NBP) decoder, which was originally studied for suboptimal binary BP decoding of QLPDC codes, to quaternary BP decoders. Numerical simulation results demonstrate that both approaches as well as their combination yield a low-latency, high-performance decoder for several short to moderate length QLDPC codes.https://ieeexplore.ieee.org/document/10876114/Quantum error correctionquantum low-density parity-check codesneural networkschannel codingdecoding algorithms |
| spellingShingle | Sisi Miao Alexander Schnerring Haizheng Li Laurent Schmalen Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check Matrices IEEE Access Quantum error correction quantum low-density parity-check codes neural networks channel coding decoding algorithms |
| title | Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check Matrices |
| title_full | Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check Matrices |
| title_fullStr | Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check Matrices |
| title_full_unstemmed | Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check Matrices |
| title_short | Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes With Overcomplete Check Matrices |
| title_sort | quaternary neural belief propagation decoding of quantum ldpc codes with overcomplete check matrices |
| topic | Quantum error correction quantum low-density parity-check codes neural networks channel coding decoding algorithms |
| url | https://ieeexplore.ieee.org/document/10876114/ |
| work_keys_str_mv | AT sisimiao quaternaryneuralbeliefpropagationdecodingofquantumldpccodeswithovercompletecheckmatrices AT alexanderschnerring quaternaryneuralbeliefpropagationdecodingofquantumldpccodeswithovercompletecheckmatrices AT haizhengli quaternaryneuralbeliefpropagationdecodingofquantumldpccodeswithovercompletecheckmatrices AT laurentschmalen quaternaryneuralbeliefpropagationdecodingofquantumldpccodeswithovercompletecheckmatrices |