Lattice-Reduction-Aided Gibbs Algorithm for Lattice Gaussian Sampling: Convergence Enhancement and Decoding Optimization

Abstract

Sampling from the lattice Gaussian distribution has emerged as an important problem in coding, decoding, and cryptography. In this paper, lattice reduction technique is adopted to Gibbs sampler for lattice Gaussian sampling. First, with respect to lattice Gaussian distribution, we show the convergence rate of systematic scan Gibbs sampling is characterized by the Hirschfeld-Gebelein-Renyi maximal correlation among the multivariate of being sampled. Then, Lattice-reduction-aided Gibbs algorithm is proposed to sample from an equivalent lattice Gaussian distribution but with less correlated multivariate, thus leading to a better Markov mixing. After that, we extend the proposed lattice-reduction-aided Gibbs sampling to lattice decoding, where the choice of the standard deviation for the sampling is fully investigated. A customized solution that suits for each specific decoding case by Euclidean distance is given, which results in a better tradeoff between Markov mixing and sampler decoding. Based on it, a startup mechanism is also proposed for Gibbs sampler decoding, where decoding complexity can be reduced without performance loss. Moreover, the recycling Gibbs sampling that exploits the potential of samples is also considered to improve the decoding performance in lattice decoding. Simulation results based on large-scale uncoded multiple-input multiple-output detection are presented to confirm the performance gain and complexity reduction.