1 research outputs found
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