Polar Codes for CQ Channels: Decoding via Belief-Propagation with Quantum Messages
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917567353847808 |
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| author | Mandal, Avijit Brandsen, S. Pfister, Henry D. |
| author_facet | Mandal, Avijit Brandsen, S. Pfister, Henry D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07167 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polar Codes for CQ Channels: Decoding via Belief-Propagation with Quantum Messages Mandal, Avijit Brandsen, S. Pfister, Henry D. Information Theory 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. |
| title | Polar Codes for CQ Channels: Decoding via Belief-Propagation with Quantum Messages |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.07167 |