122 research outputs found
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.Comment: 21 pages, 2 figures, submission to the 8th Conference on the Theory
of Quantum Computation, Communication, and Cryptograph
Using a visual structured criterion for the analysis of alternating-treatment designs
Although visual inspection remains common in the analysis of single-case designs, the lack of
agreement between raters is an issue that may seriously compromise its validity. Thus, the
purpose of our study was to develop and examine the properties of a simple structured criterion
to supplement the visual analysis of alternating-treatment designs. To this end, we generated
simulated datasets with varying number of points, number of conditions, effect sizes and
autocorrelations, and then measured Type I error rates and power produced by the visual
structured criterion (VSC) and permutation analyses. We also validated the results for Type I
error rates using nonsimulated data. Overall, our results indicate that using the VSC as a
supplement for the analysis of systematically alternating-treatment designs with at least five
points per condition generally provides adequate control over Type I error rates and sufficient
power to detect most behavior changes
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