Independent Metropolis-Hastings-Klein algorithm for lattice Gaussian sampling

机译：独立Metropolis-Hastings-Klein算法进行格子高斯采样

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Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, a Markov chain Monte Carlo (MCMC) algorithm referred to as the independent Metropolis-Hastings-Klein (MHK) algorithm is proposed for lattice Gaussian sampling, which overcomes the restriction on the standard deviation confronted by the Klein algorithm. It is proven that the Markov chain arising from the proposed MHK algorithm is uniformly ergodic, namely, it converges to the stationary distribution exponentially fast. Moreover, the rate of convergence is explicitly calculated in terms of the theta series, making it possible to predict the mixing time of the underlying Markov chain.

机译：从晶格高斯分布采样正在成为编码和密码学中的一个重要问题。本文提出了一种马尔可夫链蒙特卡罗（MCMC）算法，称为独立Metropolis-Hastings-Klein（MHK）算法，用于格子高斯采样，克服了Klein算法对标准偏差的限制。事实证明，提出的MHK算法产生的马尔可夫链是遍历遍历的，即以指数级速度快速收敛到平稳分布。此外，收敛速度是根据theta级数明确计算的，从而可以预测基础马尔可夫链的混合时间。

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《IEEE International Symposium on Information Theory》|2015年|2470-2474|共5页
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Wang Zheng; Ling Cong;
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Lattice Gaussian sampling; MCMC methods; Metropolis-Hastings sampling; lattice coding and decoding;

机译：格子高斯采样; MCMC方法; Metropolis-Hastings采样;晶格编码和解码;

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1. 基于KLD采样改进的高斯粒子滤波算法 [J] . 周翟和, 钟雨露, 曾庆喜, 南京航空航天大学学报（英文版） . 2020,第004期
2. Lattice-Reduction-Aided Gibbs Algorithm for Lattice Gaussian Sampling: Convergence Enhancement and Decoding Optimization [J] . Wang Zheng, Huang Yang, Lyu Shanxiang IEEE Transactions on Signal Processing . 2019,第16期

机译：格形高斯采样的格减少辅助吉布斯算法：收敛性增强和解码优化
3. Sampling from discrete Gaussians for lattice-based cryptography on a constrained device [J] . Nagarjun C. Dwarakanath, Steven D. Galbraith Applicable algebra in engineering, communication and computing . 2014,第3期

机译：从离散高斯抽样以在受限设备上进行基于晶格的加密
4. Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources [J] . Lee T, Girolami M, Sejnowski T Neural computation . 1999,第2期

机译：使用扩展Infomax算法对亚高斯和超高斯源进行独立分量分析
5. Independent Metropolis-Hastings-Klein Algorithm for Lattice Gaussian Sampling [C] . Zheng Wang, Cong Ling IEEE International Symposium on Information Theory . 2015

机译：独立大都会 - Hastings-Klein算法用于格子高斯采样
6. New and efficient algorithms to solve the time-dependent Schroedinger equation for larger systems: Local propagating Gaussians and extending the viability of the Herman-Kluk propagator. [D] . Anderson, Sybil Michelle. 2002

机译：解决大型系统时间相关的Schroedinger方程的新型高效算法：局部传播的高斯分布和扩展Herman-Kluk传播器的生存能力。
7. Validation of Correction Algorithms for Near-IR Analysis of Human Milk in an Independent Sample Set—Effect of Pasteurization [O] . Gynter Kotrri, Gerhard Fusch, Celia Kwan, 2016

机译：独立样本集中母乳近红外分析校正算法的验证—巴氏杀菌的效果
8. Quadratic Time, Linear Space Algorithms for Gram-Schmidt Orthogonalization and Gaussian Sampling in Structured Lattices [O] . Lyubashevsky, Vadim, Prest, Thomas 2015

机译：结构格的Gram-Schmidt正交化和高斯采样的二次时间，线性空间算法
9. Ternary Weak-Signal Detection in Non-Gaussian Noise: A Preliminary Analysis for'H sub 0:N vs H sub 1: N + S sub 1 vs H sub 2: N + S sub 2' with Independent Sampling [R] . Middleton, D., Kelly, J. G. 1992

机译：非高斯噪声中的三元弱信号检测：'H sub 0：N vs H sub 1：N + s sub 1 vs H sub 2：N + s sub 2'的独立采样的初步分析

Independent Metropolis-Hastings-Klein algorithm for lattice Gaussian sampling

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