Examples of minimal-memory, non-catastrophic quantum convolutional encoders
Examples of minimal-memory, non-catastrophic quantum convolutional encoders
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最小内存、非灾难性量子卷积编码器的示例
DOI：
10.1109/isit.2011.6034166
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Saied Hosseini
中科院分区：
文献类型：
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作者：
M. Wilde;M. Houshmand;Saied Hosseini
量子卷积编码理论中最重要的开放问题之一是为任意量子卷积码确定最小内存、非灾难性、多项式深度的卷积编码器。在这里，我们提出了一种技术，可以为几个示例量子卷积码找到具有如此理想特性的量子卷积编码器（对我们技术的全面通用性的阐述出现在其他地方）。我们首先展示如何使用仅利用一个内存量子位的编码器对经过充分研究的 Forney-Grassl-Guha (FGG) 代码进行编码（之前的 Grassl-Rötteler 编码器需要 15 个内存量子位）。然后，我们展示我们的技术如何找到与该编码器相对应的在线解码器，并且我们还详细介绍了我们的技术在量子卷积码的不同示例上的操作。最后，FGG 编码器内存的减少使得模拟使用它的量子 Turbo 码的性能变得可行，我们展示了此类模拟的结果。
One of the most important open questions in the theory of quantum convolutional coding is to determine a minimal-memory, non-catastrophic, polynomial-depth convolutional encoder for an arbitrary quantum convolutional code. Here, we present a technique that finds quantum convolutional encoders with such desirable properties for several example quantum convolutional codes (an exposition of our technique in full generality appears elsewhere). We first show how to encode the well-studied Forney-Grassl-Guha (FGG) code with an encoder that exploits just one memory qubit (the former Grassl-Rötteler encoder requires 15 memory qubits). We then show how our technique can find an online decoder corresponding to this encoder, and we also detail the operation of our technique on a different example of a quantum convolutional code. Finally, the reduction in memory for the FGG encoder makes it feasible to simulate the performance of a quantum turbo code employing it, and we present the results of such simulations.