Independent Metropolis-Hastings-Klein algorithm for lattice Gaussian sampling
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 overcom...
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| Vydáno v: | Proceedings / IEEE International Symposium on Information Theory s. 2470 - 2474 |
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| Médium: | Konferenční příspěvek Journal Article |
| Jazyk: | angličtina |
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01.06.2015
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| ISSN: | 2157-8095, 2157-8117 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Zheng Wang Cong Ling |
| Author_xml | – sequence: 1 givenname: Zheng surname: Wang fullname: Wang, Zheng – sequence: 2 givenname: Cong surname: Ling fullname: Ling, Cong |
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| Snippet | Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, a Markov chain Monte Carlo... |
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| SubjectTerms | Algorithm design and analysis Algorithms Convergence Decoding Gaussian Gaussian distribution lattice coding and decoding Lattice Gaussian sampling Lattices Markov chains Markov processes Mathematical analysis MCMC methods Metropolis-Hastings sampling Proposals Sampling Standard deviation |
| Title | Independent Metropolis-Hastings-Klein algorithm for lattice Gaussian sampling |
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