Belief-Propagation with Quantum Messages for Polar Codes on Classical-Quantum Channels
Belief-Propagation with Quantum Messages for Polar Codes on Classical-Quantum Channels
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DOI：
10.1109/isit54713.2023.10206723
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
Avijit Mandal;S. Brandsen;H. Pfister
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文献类型：
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作者：
Avijit Mandal;S. Brandsen;H. Pfister
本文考虑了通用经典量子（CQ）通道的极地代码的设计和解码。它重点是通过量子消息（BPQM）来解码，尤其是配对测量BPQM（PM-BPQM）解码的想法。由于PM-BPQM解码器接受经典的密度演化（DE）分析，因此可以使用DE来设计任何CQ通道的极性代码，然后有效地计算代码速率和错误概率之间的权衡。我们还针对极地代码实施并测试了PM-BPQM解码器的经典模拟。虽然可以在量子计算机上有效地实现解码器，但在古典计算机上模拟解码器实际上具有指数复杂性。因此，解码器的仿真结果受到限制，主要是为了验证我们的理论结果。
This paper considers the design and decoding of polar codes for general classical-quantum (CQ) channels. It focuses on decoding via belief-propagation with quantum messages (BPQM) and, in particular, the idea of paired-measurement BPQM (PM-BPQM) decoding. Since the PM-BPQM decoder admits a classical density evolution (DE) analysis, one can use DE to design a polar code for any CQ channel and then efficiently compute the trade-off between code rate and error probability. We have also implemented and tested a classical simulation of our PM-BPQM decoder for polar codes. While the decoder can be implemented efficiently on a quantum computer, simulating the decoder on a classical computer actually has exponential complexity. Thus, simulation results for the decoder are somewhat limited and are included primarily to validate our theoretical results.