Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices

• URL: http://arxiv.org/abs/2212.10245v2
• Date: Tue, 21 Mar 2023 10:33:54 GMT
• Title: Neural Belief Propagation Decoding of Quantum LDPC Codes Using Overcomplete Check Matrices
• Authors: Sisi Miao, Alexander Schnerring, Haizheng Li, and Laurent Schmalen
• Abstract summary: We propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency.
• Score: 60.02503434201552
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The recent success in constructing asymptotically good quantum low-density parity-check (QLDPC) codes makes this family of codes a promising candidate for error-correcting schemes in quantum computing. However, conventional belief propagation (BP) decoding of QLDPC codes does not yield satisfying performance due to the presence of unavoidable short cycles in their Tanner graph and the special degeneracy phenomenon. In this work, we propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix. This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency. Furthermore, we propose a novel neural belief propagation decoder based on the quaternary BP decoder of QLDPC codes which leads to further decoding performance improvements.

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