Achieving Secrecy Capacity of the Gaussian Wiretap Channel with Polar Lattices

In this work, an explicit wiretap coding scheme based on polar lattices is proposed to achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel. Firstly, polar lattices are used to construct secrecy-good lattices for the mod-$\Lambda_s$ Gaussian wiretap channel. Then we propose an explicit shaping scheme to remove this mod-$\Lambda_s$ front end and extend polar lattices to the genuine Gaussian wiretap channel. The shaping technique is based on the lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. By employing the asymmetric polar coding technique, we construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. As a result, the encoding complexity for the sender and the decoding complexity for the legitimate receiver are both O(N logN log(logN)). The proposed scheme is proven to be semantically secure.Comment: Submitted to IEEE Trans. Information Theory, revised. This is the authors' own version of the pape

Construction of lattices for communications and security

In this thesis, we propose a new class of lattices based on polar codes, namely polar lattices. Polar lattices enjoy explicit construction and provable goodness for the additive white Gaussian noise (AWGN) channel, \textit{i.e.}, they are \emph{AWGN-good} lattices, in the sense that the error probability (for infinite lattice coding) vanishes for any fixed volume-to-noise ratio (VNR) greater than $2\pi e$. Our construction is based on the multilevel approach of Forney \textit{et al.}, where on each level we construct a capacity-achieving polar code. We show the component polar codes are naturally nested, thereby fulfilling the requirement of the multilevel lattice construction. We present a more precise analysis of the VNR of the resultant lattice, which is upper-bounded in terms of the flatness factor and the capacity losses of the component codes. The proposed polar lattices are efficiently decodable by using multi-stage decoding. Design examples are presented to demonstrate the superior performance of polar lattices. However, there is no infinite lattice coding in the practical applications. We need to apply the power constraint on the polar lattices which generates the polar lattice codes. We prove polar lattice codes can achieve the capacity \frac{1}{2}\log(1+\SNR) of the power-constrained AWGN channel with a novel shaping scheme. The main idea is that by implementing the lattice Gaussian distribution over the AWGN-good polar lattices, the maximum error-free transmission rate of the resultant coding scheme can be arbitrarily close to the capacity \frac{1}{2}\log(1+\SNR). The shaping technique is based on discrete lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. Then it is straightforward to employ multilevel asymmetric polar codes which is a combination of polar lossless source coding and polar channel coding. The construction of polar codes for an asymmetric channel can be converted to that for a related symmetric channel, and it turns out that this symmetric channel is equivalent to an minimum mean-square error (MMSE) scaled $\Lambda/\Lambda'$ channel in lattice coding in terms of polarization, which eventually simplifies our coding design. Finally, we investigate the application of polar lattices in physical layer security. Polar lattice codes are proved to be able to achieve the strong secrecy capacity of the Mod-$\Lambda$ AWGN wiretap channel. The Mod-$\Lambda$ assumption was due to the fact that a practical shaping scheme aiming to achieve the optimum shaping gain was missing. In this thesis, we use our shaping scheme and extend polar lattice coding to the Gaussian wiretap channel. By employing the polar coding technique for asymmetric channels, we manage to construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. Then we prove the resultant wiretap coding scheme can achieve the strong secrecy capacity for the Gaussian wiretap channel.Open Acces

Construction of Capacity-Achieving Lattice Codes: Polar Lattices

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity \frac{1}{2}\log(1+\SNR) of the additive white Gaussian-noise (AWGN) channel. Our construction follows the multilevel approach of Forney \textit{et al.}, where we construct a capacity-achieving polar code on each level. The component polar codes are shown to be naturally nested, thereby fulfilling the requirement of the multilevel lattice construction. We prove that polar lattices are \emph{AWGN-good}. Furthermore, using the technique of source polarization, we propose discrete Gaussian shaping over the polar lattice to satisfy the power constraint. Both the construction and shaping are explicit, and the overall complexity of encoding and decoding is $O(N\log N)$ for any fixed target error probability.Comment: full version of the paper to appear in IEEE Trans. Communication

A nodule on the forearm

Glomus tumors are benign tumors of the skin. Clinically, these tumors can present as solid, painful subcutaneous nodules, frequently seen on the hand (particularly subungual region). Glomangiomyomas are the least common histological type of glomus tumor. In the literature, there are only a few glomangiomyoma cases of the forearm location. We report a patient with a painful nodule, diagnosed as glomangiomyoma. Surgical excision was performed and no recurrence was observed after 5 years' follow-up

RESEARCH AND APPLICATION OF U-BIT CONSTRUCTION METHOD IN SUBWAY STATION ENGINEERING LOCATED IN SATURATED SOFT SOIL AREA

In order to solve the problems existing in the construction of underground structures located in the downtown of saturated soft soil area, such as insufficient construction site, complex adjacent structures and great impact on the surrounding environment, the construction method of underground bundled integrate tunnel(U-BIT) is proposed. In this method, after steel pipes jacking completed, concrete is filled into the pipes, and prestress is tensioned to make each independent pipe combined to form a whole bearing structure, so as to achieve the purpose of reducing the size of structural components, improving the structural stiffness and bearing capacity. Based on the structural mechanical properties test and the project of Wuding Road Station of Shanghai Metro Line 14, the failure mechanism of bundled integrate structure, the tension technology of prestressed tendons in narrow space and the variation rules of ground surface subsidence are systematically studied. The research shows that structural seam sections will be destroyed before pipe sections, so ensuring the mechanical performance of seam sections is very important to make sure the structural safety. Since each independent pipe is combined to form an overall stable structure under the prestress effect, the subsequent soil excavation has little influence on the tension of prestressed tendons and ground surface deformation. Therefore, the above construction method can control the ground surface subsidence effectively and reduce the influence of underground engineering construction on the surrounding environment.  &nbsp

Preparation of Antheraea pernyi

The goal of this study was to fabricate Antheraea pernyi silk fibroin (ASF) microparticles using electrospinning under mild processing conditions. To improve processability of the ASF solution, poly(ethylene oxide) (PEO) was used to regulate viscosity of ASF solution for electrospinning. It was found that the blend of ASF with PEO could form a bead-on-string structure with well spherical particles. Furthermore, aqueous ethanol and ultrasonic treatments could disrupt the nanofibrillar string structure between particles and ultimately produced water-insoluble ASF particles with submicron scale. Cell viability studies indicated that the ASF microparticles were nontoxic to EA926 cells. Moreover, fluorescent images based on FITC labeling showed that the ASF microparticles were easily uptaken by the cells. Aqueous-based electrospinning provides a potentially useful option for the fabrication of ASF microparticles based on this unique fibrous protein

A block minimum residual norm subspace solver with partial convergence management for sequences of linear systems

International audienceWe are concerned with the iterative solution of linear systems with multiple right-hand sides available one group after another with possibly slowly-varying left-hand sides. For such sequences of linear systems, we first develop a new block minimum norm residual approach that combines two main ingredients. The first component exploits ideas from GCRO-DR [SIAM J. Sci. Comput., 28(5) (2006), pp. 1651-1674], enabling to recycle information from one solve to the next. The second component is the numerical mechanism to manage the partial convergence of the right-hand sides, referred to as inexact breakdown detection in IB-BGMRES [Linear Algebra Appl., 419 (2006), pp. 265-285], that enables the monitoring of the rank deficiency in the residual space basis expanded block-wise. Secondly, for the class of block minimum norm residual approaches, that relies on a block Arnoldi-like equality between the search space and the residual space (e.g., any block GMRES or block GCRO variants), we introduce new search space expansion policies defined on novel criteria to detect the partial convergence. These novel detection criteria are tuned to the selected stopping criterion and targeted convergence threshold to best cope with the selected normwise backward error stopping criterion, enabling to monitor the computational effort while ensuring the final accuracy of each individual solution. Numerical experiments are reported to illustrate the numerical and computational features of both the new block Krylov solvers and the new search space block expansion polices