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تسجيل مستخدم جديدPolar Codes for Quantum Reading
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نشر من قبل
Francisco Revson Fernandes Pereira
تاريخ النشر
2020
مجال البحث
الهندسة المعلوماتية
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English
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Quantum reading provides a general framework where to formulate the statistical discrimination of quantum channels. Several paths have been taken for such a problem. However, there is much to be done in the avenue of optimizing channel discrimination using classical codes. At least two open questions can be pointed to: how to construct low complexity encoding schemes that are interesting for channel discrimination and, more importantly, how to develop capacity-achieving protocols. The aim of this paper is to present a solution to these questions using polar codes. Firstly, we characterize the rate and reliability of the channels under polar encoding. We also show that the error probability of the scheme proposed decays exponentially with respect to the code length. Lastly, an analysis of the optimal quantum states to be used as probes is given.
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Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while satisfying broadcas
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underlying polar codes can employ any decoding scheme such as the successive cancellation (SC) decoding (PCM-SC), the belief propagation (BP) decoding (PCM-BP), and the successive cancellation list (SCL) decoding (PCM-SCL). The analysis shows that the packet error rate (PER) of PCM decreases to the order of PER squared while maintaining the same complexity as the underlying polar codes. Simulation results indicate that for PCM-SC, the PER is comparable to (less than 0.3 dB) the stand-alone SCL decoding with two lists for the block length $N=256$. The PER of PCM-SCL with $L$ lists can match that of the stand-alone SCL decoding with $2L$ lists. Two hardware decoders for PCM are also implemented: the in-serial (IS) decoder and the low-latency interleaved (LLI) decoder. For $N=256$, synthesis results show that in the worst case, the latency of the PCM LLI decoder is only $16.1%$ of the adaptive SCL decoder with $L=2$, while the throughput is improved by 13 times compared to it.
In this paper, we propose textit{selectively precoded polar (SPP) code}, built on top of Arikans capacity achieving polar codes. We provide the encoding and decoding scheme for SPP code. Simulation results show that for a target frame erasure rate (F
ER) of $mathbf{10^{-5}}$, a (128, 64) SPP code is just 0.23 dB away from the information theoretic limit at this blocklength. Further, it is also shown that such codes possess better distance properties compared to other contemporary polar code variants.
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