Towards Efficient Decoding of Classical-Quantum Polar Codes
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.
classical-quantum channel
classical-quantum polar codes
quantum likelihood ratio
quantum successive cancellation decoder
157-177
Regular Paper
Mark M.
Wilde
Mark M. Wilde
Olivier
Landon-Cardinal
Olivier Landon-Cardinal
Patrick
Hayden
Patrick Hayden
10.4230/LIPIcs.TQC.2013.157
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode