Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology (CICAEET), Jiangsu Engineering Center of Network Monitoring, School of Computer and Software, Nanjing University of Information Science & Technology, Nanjing 210044, China.
Anhui Meteorological Observatory, Hefei 230031, China.
Sensors (Basel). 2019 Nov 20;19(23):5071. doi: 10.3390/s19235071.
Today's sensor networks need robustness, security and efficiency with a high level of assurance. Error correction is an effective communicational technique that plays a critical role in maintaining robustness in informational transmission. The general way to tackle this problem is by using forward error correction (FEC) between two communication parties. However, by applying zero-error coding one can assure information fidelity while signals are transmitted in sensor networks. In this study, we investigate zero-error coding via both classical and quantum channels, which consist of n obfuscated symbols such as Shannon's zero-error communication. As a contrast to the standard classical zero-error coding, which has a computational complexity of , a general approach is proposed herein to find zero-error codewords in the case of quantum channel. This method is based on a n-symbol obfuscation model and the matrix's linear transformation, whose complexity dramatically decreases to . According to a comparison with classical zero-error coding, the quantum zero-error capacity of the proposed method has obvious advantages over its classical counterpart, as the zero-error capacity equals the rank of the quantum coefficient matrix. In particular, the channel capacity can reach n when the rank of coefficient matrix is full in the n-symbol multilateral obfuscation quantum channel, which cannot be reached in the classical case. Considering previous methods such as low density parity check code (LDPC), our work can provide a means of error-free communication through some typical channels. Especially in the quantum case, zero-error coding can reach both a high coding efficiency and large channel capacity, which can improve the robustness of communication in sensor networks.
当今的传感器网络需要具有高度保证的鲁棒性、安全性和效率。纠错是一种有效的通信技术，在保持信息传输的鲁棒性方面起着至关重要的作用。解决这个问题的一般方法是在两个通信方之间使用前向纠错（FEC）。然而，通过应用零误差编码，可以在传感器网络中传输信号时确保信息保真度。在本研究中，我们通过经典和量子通道研究零误差编码，这些通道由 n 个混淆符号组成，例如香农的零误差通信。与标准的经典零误差编码的计算复杂度为 相比，我们提出了一种一般方法来找到量子通道中的零误差码字。该方法基于 n 个符号混淆模型和矩阵的线性变换，其复杂度急剧降低到 。与经典零误差编码相比，该方法的量子零误差容量具有明显的优势，因为零误差容量等于量子系数矩阵的秩。特别是在 n 个符号多边混淆量子信道中，当系数矩阵的秩满时，信道容量可以达到 n，这在经典情况下是无法达到的。与低密度奇偶校验码（LDPC）等先前的方法相比，我们的工作可以通过一些典型的信道提供无错误通信的手段。特别是在量子情况下，零误差编码可以达到高编码效率和大信道容量，从而提高传感器网络中通信的鲁棒性。
