Slice Sampling for Lattice Gaussian Distribution

Sampling from the lattice Gaussian distribution has emerged as a key problem in coding and cryptography. In this paper, the slice sampling from Markov chain Monte Carlo (MCMC) is adopted to lattice Gaussian sampling. Firstly, the slice-based sampling algorithm is proposed to sample from lattice Gaussian distribution. Then, we demonstrate that the Markov chain arising from it is uniformly ergodic, namely, it converges exponentially fast to the stationary distribution. Moveover, the convergence rate of the underlying Markov chain is investigated, and we show the proposed slice sampling algorithm entails a better convergence performance than the independent Metropolis-Hastings-Klein (IMHK) sampling algorithm. Finally, simulation results based on MIMO detection are presented to confirm the performance gain by convergence enhancement.