On the geometric ergodicity of Gibbs algorithm for lattice Gaussian sampling

Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, the conventional Gibbs sampling algorithm is demonstrated to be geometrically ergodic in tackling with lattice Gaussian sampling, which means its induced Markov chain conver...

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Bibliographic Details
Published in:ITW : 2017 IEEE Information Theory Workshop : 6-10 November 2017 pp. 269 - 273
Main Authors: Zheng Wang, Cong Ling
Format: Conference Proceeding
Language:English
Published: IEEE 01.11.2017
Subjects:
Conferences
Convergence
Correlation
Gaussian distribution
Information theory
lattice coding and decoding
Lattice Gaussian sampling
Lattices
Markov chain Monte Carlo
Markov processes
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Summary:Sampling from the lattice Gaussian distribution is emerging as an important problem in coding and cryptography. In this paper, the conventional Gibbs sampling algorithm is demonstrated to be geometrically ergodic in tackling with lattice Gaussian sampling, which means its induced Markov chain converges exponentially fast to the stationary distribution. Moreover, as the exponential convergence rate is dominated by the spectral radius of the forward operator of the Markov chain, a comprehensive analysis is given and we show that the convergence performance can be further enhanced by usages of blocked sampling strategy and choices of selection probabilities.
DOI:10.1109/ITW.2017.8278001