Sliced Lattice Gaussian Sampling: Convergence Improvement and Decoding Optimization

Sampling from the lattice Gaussian distribution has emerged as a key problem in coding and decoding while Markov chain Monte Carlo (MCMC) methods from statistics offer an effective way to solve it. In this paper, the sliced lattice Gaussian sampling algorithm is proposed to further improve the convergence performance of the Markov chain targeting at lattice Gaussian sampling. We demonstrate that the Markov chain arising from it is uniformly ergodic, namely, it converges exponentially fast to the stationary distribution. Meanwhile, the convergence rate of the underlying Markov chain is also investigated, and we show the proposed sliced sampling algorithm entails a better convergence performance than the independent Metropolis-Hastings-Klein (IMHK) sampling algorithm. On the other hand, the decoding performance based on the proposed sampling algorithm is analyzed, where the optimization with respect to the standard deviation $\sigma >0$ of the target lattice Gaussian distribution is given. After that, a judicious mechanism based on distance judgement and dynamic updating for choosing $\sigma $ is proposed for a better decoding performance. Finally, simulation results based on multiple-input multiple-output (MIMO) detection are presented to confirm the performance gain by the convergence enhancement and the parameter optimization.