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