Belief propagation with guided decimation, enhanced with damping and adjusted initial log-likelihood ratios, performs competitively on erasure channels for several quantum LDPC codes, approaching the vertical-horizontal decoder's performance.
Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices
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abstract
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.
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Erasure Decoding for Quantum LDPC Codes via Belief Propagation with Guided Decimation
Belief propagation with guided decimation, enhanced with damping and adjusted initial log-likelihood ratios, performs competitively on erasure channels for several quantum LDPC codes, approaching the vertical-horizontal decoder's performance.