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
Hlavní autoři: Wang, Zheng, Ling, Cong
Médium: Konferenční příspěvek Journal Article
Jazyk:angličtina
Vydáno: IEEE 01.06.2015
Témata:
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
ISSN:2157-8095, 2157-8117
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Shrnutí: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.
Bibliografie:ObjectType-Article-2
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ObjectType-Conference-1
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SourceType-Conference Papers & Proceedings-2
ISSN:2157-8095
2157-8117
DOI:10.1109/ISIT.2015.7282900