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Sampling from the lattice Gaussian distribution has emerged as an importantproblem in coding, decoding and cryptography. In this paper, lattice reductiontechnique is adopted to Gibbs sampler for lattice Gaussian sampling. Firstly,with respect to lattice Gaussian distribution, the convergence rate ofsystematic scan Gibbs sampling is derived and we show it is characterized bythe Hirschfeld-Gebelein-R\'enyi (HGR) maximal correlation among themultivariate of being sampled. Therefore, lattice reduction is applied toformulate an equivalent lattice Gaussian distribution but with less correlatedmultivariate, which leads to a better Markov mixing due to the enhancedconvergence rate. Then, we extend the proposed lattice-reduction-aided Gibbssampling to lattice decoding, where the choice of the standard deviation forthe sampling is fully investigated. A customized solution that suits for eachspecific decoding case by Euclidean distance is given, thus resulting in abetter trade-off between Markov mixing and sampler decoding. Moreover, based onit, a startup mechanism is also proposed for Gibbs sampler decoding, wheredecoding complexity can be reduced without performance loss. Simulation resultsbased on large-scale MIMO detection are presented to confirm the performancegain and complexity reduction.

Markov chain Monte Carlo Methods For Lattice Gaussian Sampling: Lattice Reduction and Decoding Optimization