Lattice Gaussian Sampling by Markov Chain Monte Carlo: Bounded Distance Decoding and Trapdoor Sampling

• Published in: IEEE transactions on information theory Vol. 65; no. 6; pp. 3630 - 3645
• Main Authors: Wang, Zheng, Ling, Cong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Bayesian analysis; bounded distance decoding; Complexity; Complexity theory; Convergence; Decoding; Gaussian distribution; large-scale MIMO detection; Lattice decoding; lattice Gaussian sampling; Lattices; Markov analysis; Markov chain Monte Carlo; Markov chains; Markov processes; MIMO communication; Monte Carlo simulation; Normal distribution; Sampling; Tradeoffs; trapdoor sampling
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2019.2901497

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. First, the spectral gap for the independent Metropolis-Hastings-Klein (MHK) algorithm is derived, which is then extended to Peikert's algorithm and rejection sampling; we show that independent MHK exhibits faster convergence. Then, the performance of bounded distance decoding (BDD) using MCMC is analyzed, revealing a flexible trade-off between the decoding radius and complexity. MCMC is further applied to trapdoor sampling, again offering a trade-off between security and complexity. Finally, the independent multiple-try Metropolis-Klein (MTMK) algorithm is proposed to enhance the convergence rate. The proposed algorithms allow parallel implementation, which is beneficial for practical applications.