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DOI: 10.4230/LIPIcs.TQC.2013.157

Towards Efficient Decoding of Classical-Quantum Polar Codes

Authors: Mark M. Wilde, Olivier Landon-Cardinal, and Patrick Hayden

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

Abstract

Known strategies for sending bits at the capacity rate over a general channel with classical input and quantum output (a cq channel) require the decoder to implement impractically complicated collective measurements. Here, we show that a fully collective strategy is not necessary in order to recover all of the information bits. In fact, when coding for a large number N uses of a cq channel W, N*I(W_{acc}) of the bits can be recovered by a non-collective strategy which amounts to coherent quantum processing of the results of product measurements, where I(W_{acc}) is the accessible information of the channel W. In order to decode the other N(I(W)-I(W_{acc})) bits, where I(W) is the Holevo rate, our conclusion is that the receiver should employ collective measurements. We also present two other results: 1) collective Fuchs-Caves measurements (quantum likelihood ratio measurements) can be used at the receiver to achieve the Holevo rate and 2) we give an explicit form of the Helstrom measurements used in small-size polar codes. The main approach used to demonstrate these results is a quantum extension of Arikan's polar codes.

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Mark M. Wilde, Olivier Landon-Cardinal, and Patrick Hayden. Towards Efficient Decoding of Classical-Quantum Polar Codes. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 157-177, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{wilde_et_al:LIPIcs.TQC.2013.157,
  author =	{Wilde, Mark M. and Landon-Cardinal, Olivier and Hayden, Patrick},
  title =	{{Towards Efficient Decoding of Classical-Quantum Polar Codes}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{157--177},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.157},
  URN =		{urn:nbn:de:0030-drops-43141},
  doi =		{10.4230/LIPIcs.TQC.2013.157},
  annote =	{Keywords: classical-quantum channel, classical-quantum polar codes, quantum likelihood ratio, quantum successive cancellation decoder}
}

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Towards Efficient Decoding of Classical-Quantum Polar Codes

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