Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the independent Metropolis-Hastings-Klein (MHK) algorithm is derived, which is then extended to Peikert's algorithm and rejection sampling; we show that independent MHK exhibits faster convergence. Then, the performance of bounded distance decoding using MCMC is analyzed, revealing a flexible trade-off between the decoding radius and complexity. MCMC is further applied to trapdoor sampling, again offering a trade-off between security and complexity. Finally, the independent multiple-try Metropolis-Klein (MTMK) algorithm is proposed to enhance the convergence rate. The proposed algorithms allow parallel implementation, which is beneficial for practical applications.Comment: submitted to Transaction on Information Theor

On the Geometric Ergodicity of Metropolis-Hastings Algorithms for Lattice Gaussian Sampling

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, the classic Metropolis-Hastings (MH) algorithm from Markov chain Monte Carlo (MCMC) methods is adapted for lattice Gaussian sampling. Two MH-based algorithms are proposed, which overcome the restriction suffered by the default Klein's algorithm. The first one, referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm, tries to establish a Markov chain through an independent proposal distribution. We show that the Markov chain arising from the independent MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast regardless of the initial state. Moreover, the rate of convergence is explicitly calculated in terms of the theta series, leading to a predictable mixing time. In order to further exploit the convergence potential, a symmetric Metropolis-Klein (SMK) algorithm is proposed. It is proven that the Markov chain induced by the SMK algorithm is geometrically ergodic, where a reasonable selection of the initial state is capable to enhance the convergence performance.Comment: Submitted to IEEE Transactions on Information Theor

Analysis and Optimization of Cellular Network with Burst Traffic

In this paper, we analyze the performance of cellular networks and study the optimal base station (BS) density to reduce the network power consumption. In contrast to previous works with similar purpose, we consider Poisson traffic for users' traffic model. In such situation, each BS can be viewed as M/G/1 queuing model. Based on theory of stochastic geometry, we analyze users' signal-to-interference-plus-noise-ratio (SINR) and obtain the average transmission time of each packet. While most of the previous works on SINR analysis in academia considered full buffer traffic, our analysis provides a basic framework to estimate the performance of cellular networks with burst traffic. We find that the users' SINR depends on the average transmission probability of BSs, which is defined by a nonlinear equation. As it is difficult to obtain the closed-form solution, we solve this nonlinear equation by bisection method. Besides, we formulate the optimization problem to minimize the area power consumption. An iteration algorithm is proposed to derive the local optimal BS density, and the numerical result shows that the proposed algorithm can converge to the global optimal BS density. At the end, the impact of BS density on users' SINR and average packet delay will be discussed.Comment: This paper has been withdrawn by the author due to missuse of queue model in Section Fou

Polar Coding for the Cognitive Interference Channel with Confidential Messages

In this paper, we propose a low-complexity, secrecy capacity achieving polar coding scheme for the cognitive interference channel with confidential messages (CICC) under the strong secrecy criterion. Existing polar coding schemes for interference channels rely on the use of polar codes for the multiple access channel, the code construction problem of which can be complicated. We show that the whole secrecy capacity region of the CICC can be achieved by simple point-to-point polar codes due to the cognitivity, and our proposed scheme requires the minimum rate of randomness at the encoder

Markov Chain Monte Carlo Algorithms for Lattice Gaussian Sampling

Sampling from a lattice Gaussian distribution is emerging as an important problem in various areas such as coding and cryptography. The default sampling algorithm --- Klein's algorithm yields a distribution close to the lattice Gaussian only if the standard deviation is sufficiently large. In this paper, we propose the Markov chain Monte Carlo (MCMC) method for lattice Gaussian sampling when this condition is not satisfied. In particular, we present a sampling algorithm based on Gibbs sampling, which converges to the target lattice Gaussian distribution for any value of the standard deviation. To improve the convergence rate, a more efficient algorithm referred to as Gibbs-Klein sampling is proposed, which samples block by block using Klein's algorithm. We show that Gibbs-Klein sampling yields a distribution close to the target lattice Gaussian, under a less stringent condition than that of the original Klein algorithm.Comment: 5 pages, 1 figure, IEEE International Symposium on Information Theory(ISIT) 201

Area Spectral Efficiency Analysis and Energy Consumption Minimization in Multi-Antenna Poisson Distributed Networks

This paper aims at answering two fundamental questions: how area spectral efficiency (ASE) behaves with different system parameters; how to design an energy-efficient network. Based on stochastic geometry, we obtain the expression and a tight lower-bound for ASE of Poisson distributed networks considering multi-user MIMO (MU-MIMO) transmission. With the help of the lower-bound, some interesting results are observed. These results are validated via numerical results for the original expression. We find that ASE can be viewed as a concave function with respect to the number of antennas and active users. For the purpose of maximizing ASE, we demonstrate that the optimal number of active users is a fixed portion of the number of antennas. With optimal number of active users, we observe that ASE increases linearly with the number of antennas. Another work of this paper is joint optimization of the base station (BS) density, the number of antennas and active users to minimize the network energy consumption. It is discovered that the optimal combination of the number of antennas and active users is the solution that maximizes the energy-efficiency. Besides the optimal algorithm, we propose a suboptimal algorithm to reduce the computational complexity, which can achieve near optimal performance.Comment: Submitted to IEEE Transactions on Wireless Communications, Major Revisio

Poly[[diaquadi-μ-dicyanamido-nickel(II)] bis­(pyridinium-4-olate)]

The title compound, {[Ni(C2N3)2(H2O)2]·2C5H5NO}n, is a centrosymmetric two-dimensional coordination polymer with a layer (4,4) network structure. The asymmetric unit is compossed of an NiII atom, which sits on an inversion center, a μ-1,5-bridging dicyanamide anion, a water mol­ecule, and a free 4-hydroxy­pyridine mol­ecule present in the zwitterionic pyridinium-4-olate form. The NiII atom is coordinated in a slightly distorted N4O2 octa­hedral geometry by four bridging dicyanamide ligands and two trans water mol­ecules. In the crystal, the two-dimensional networks are linked via N—H⋯O and O—H⋯O hydrogen bonds, forming a three-dimensional network