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Refined Belief Propagation Decoding of Sparse-Graph Quantum Codes
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<span title="2020-07-22">2020</span>
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arXiv
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<span class="release-stage" >pre-print</span>
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<span title="2020-02-16">2020</span>
<span class="release-stage" >pre-print</span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.06502v1">arXiv:2002.06502v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w24d2dmo2zdunj567x3qthf26e">fatcat:w24d2dmo2zdunj567x3qthf26e</a> </span>
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.06502v1">arXiv:2002.06502v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w24d2dmo2zdunj567x3qthf26e">fatcat:w24d2dmo2zdunj567x3qthf26e</a> </span>
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.
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<a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.06502v2">arXiv:2002.06502v2</a>
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... 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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