1. Sliced Lattice Gaussian Sampling: Convergence Improvement and Decoding Optimization
- Author
-
Zheng Wang, Ling Liu, and Cong Ling
- Subjects
Technology ,decoding ,Computer science ,Gaussian ,CHAIN MONTE-CARLO ,Markov process ,02 engineering and technology ,Standard deviation ,CAPACITY ,MIMO detection ,symbols.namesake ,Engineering ,0203 mechanical engineering ,SYSTEMS ,SEARCH ,1005 Communications Technologies ,0202 electrical engineering, electronic engineering, information engineering ,ALGORITHM ,Electrical and Electronic Engineering ,CODES ,Science & Technology ,lattice Gaussian sampling ,COMPLEXITY ,CHANNELS ,Stationary distribution ,Markov chain ,Coding ,0804 Data Format ,Engineering, Electrical & Electronic ,020302 automobile design & engineering ,020206 networking & telecommunications ,Markov chain Monte Carlo ,MCMC methods ,REDUCTION ,0906 Electrical and Electronic Engineering ,Rate of convergence ,Telecommunications ,symbols ,Algorithm ,Decoding methods - Abstract
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.
- Published
- 2021