Rapid development of supercomputers and the prospect of quantum computers are posing increasingly serious threats to the security of communication. Using the principles of quantum mechanics, quantum communication offers provable security of communication and is a promising solution to counter such threats. Quantum secure direct communication (QSDC) is one important branch of quantum communication. In contrast to other branches of quantum communication, it transmits secret information directly. Recently, remarkable progress has been made in proof-of-principle experimental demonstrations of QSDC. However, it remains a technical feat to bring QSDC into a practical application. Here, we report the implementation of a practical quantum secure communication system. The security is analyzed in the Wyner wiretap channel theory. The system uses a coding scheme of concatenation of low-density parity-check (LDPC) codes and works in a regime with a realistic environment of high noise and high loss. The present system operates with a repetition rate of 1 MHz at a distance of 1.5 kilometers. The secure communication rate is 50 bps, sufficient to effectively send text messages and reasonably sized files of images and sounds.
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descendant codes are developed, including the characterizations of the roots of the generator polynomial of a cyclic descendant code. The second part of the paper shows that cyclic and quasi-cyclic descendant LDPC codes can be derived from cyclic finite geometry LDPC codes using the results developed in first part of the paper.This enlarges the repertoire of cyclic LDPC codes. The third part of the paper analyzes the trapping sets of regular LDPC codes whose parity-check matrices satisfy a certain constraint on their rows and columns. Several classes of finite geometry and finite field cyclic and quasi-cyclic LDPC codes with large minimum weights are shown to have no harmful trapping sets with size smaller than their minimum weights. Consequently, their performance error-floors are dominated by their minimum weights.
In order to achieve high spectral efficiency and low access delay, this paper introduces cyclical non-orthogonal multiple access (NOMA) into unmanned aerial vehicle (UAV)-enabled wireless network. It allows the UAV to communicate with multiple ground users in the same time-frequency resources, cyclically. The minimum throughput over all ground users is maximized by jointly optimizing multiuser communication scheduling with cyclical NOMA and UAV trajectory. It turns out that the maximization of minimum throughput is a mixed integer non-linear non-convex optimization problem. In this paper, this problem is decoupled into two blocks, i.e., the optimization of multiuser communication scheduling with cyclical NOMA and the optimization of UAV trajectory. Then, a joint optimization algorithm is proposed based on the block coordinate descent method. The simulation results demonstrate that the proposed joint optimization method can double the minimum throughput, compared with cyclical TDMA. In addition, it reduces users' average access delay and UAV's flying range under the same minimum throughput. INDEX TERMS Cyclical NOMA, minimum throughput optimization, multiuser communication scheduling, UAV-enabled wireless network, UAV trajectory.
The encoding complexity of a general (en,ek) quasicyclic code is O(e 2 (n − k)k). This paper presents a novel lowcomplexity encoding algorithm for quasi-cyclic (QC) codes based on matrix transformation. First, a message vector is encoded into a transformed codeword in the transform domain. Then, the transmitted codeword is obtained from the transformed codeword by the inverse Galois Fourier transform. For binary QC codes, a simple and fast mapping is required to post-process the transformed codeword such that the transmitted codeword is binary as well. The complexity of our proposed encoding algorithm is O(e(n−k)k) symbol operations for non-binary codes and O(e(n − k)k log 2 e) bit operations for binary codes. These complexities are much lower than their traditional counterpart O(e 2 (n−k)k). For example, our complexity of encoding a 64-ary (4095,2160) QC code is only 1.59% of that of traditional encoding, and our complexities of encoding the binary (4095, 2160) and (8176, 7154) QC codes are respectively 9.52% and 1.77% of those of traditional encoding. We also study the application of our low-complexity encoding algorithm to one of the most important subclasses of QC codes, namely QC-LDPC codes, especially when their parity-check matrices are rank deficient.
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