Refined Belief Propagation Decoding of Sparse-Graph Quantum Codes
arXiv:2002.06502 · doi:10.1109/JSAIT.2020.3011758
Abstract
Quantum stabilizer codes constructed from sparse matrices have good performance and can be efficiently decoded by belief propagation (BP). A conventional BP decoding algorithm treats binary stabilizer codes as additive codes over GF(4). This algorithm has a relatively complex process of handling check-node messages, which incurs higher decoding complexity. Moreover, BP decoding of a stabilizer code usually suffers a performance loss due to the many short cycles in the underlying Tanner graph. In this paper, we propose a refined BP decoding algorithm for quantum codes with complexity roughly the same as binary BP. For a given error syndrome, this algorithm decodes to the same output as the conventional quaternary BP but the passed node-to-node messages are single-valued, unlike the quaternary BP, where multivalued node-to-node messages are required. Furthermore, the techniques of message strength normalization can naturally be applied to these single-valued messages to improve the performance. Another observation is that the message-update schedule affects the performance of BP decoding against short cycles. We show that running BP with message strength normalization according to a serial schedule (or other schedules) may significantly improve the decoding performance and error floor in computer simulation.
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- Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound
- Log-domain decoding of quantum LDPC codes over binary finite fields
- Decoding of Quantum Data-Syndrome Codes via Belief Propagation
- Improved Belief Propagation Decoding Algorithms for Surface Codes
- Graph Neural Networks for Enhanced Decoding of Quantum LDPC Codes
- Comparison of 2D topological codes and their decoding performances
- Refined Belief-Propagation Decoding of Quantum Codes with Scalar Messages
- Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices
- On Belief Propagation Decoding of Quantum Codes with Quaternary Reliability Statistics
- Degenerate quantum erasure decoding
- Generalized quantum data-syndrome codes and belief propagation decoding for phenomenological noise
- Syndrome decoding by quantum approximate optimization
- Union-Intersection Union-Find for Decoding Depolarizing Errors in Topological Codes
- Decoding Correlated Errors in Quantum LDPC Codes
- Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory
- Informed Dynamic Scheduling for QLDPC Codes