Learnable Markov Chain Monte Carlo Sampling Methods for Lattice Gaussian Distribution

As a key ingredient of machine learning and artificial intelligence, the sampling algorithms with respect to lattice Gaussian distribution has emerged as an important problem in coding and decoding of wireless communications. In this paper, based on the conventional Gibbs sampling, the learnable del...

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Vydané v:	IEEE access Ročník 7; s. 87494 - 87503
Hlavní autori:	Wang, Zheng, Lyu, Shanxiang, Liu, Ling
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Piscataway IEEE 2019 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Algorithms Artificial intelligence Complexity Complexity theory Convergence Decoding Encoding Gaussian distribution Gibbs sampler decoding Lattice coding and decoding lattice Gaussian sampling Lattices Machine learning Markov analysis Markov chain Monte Carlo Markov chains Markov processes MIMO (control systems) Monte Carlo simulation Normal distribution Sampling methods Statistical analysis Wireless communications
ISSN:	2169-3536, 2169-3536
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Abstract	As a key ingredient of machine learning and artificial intelligence, the sampling algorithms with respect to lattice Gaussian distribution has emerged as an important problem in coding and decoding of wireless communications. In this paper, based on the conventional Gibbs sampling, the learnable delayed metropolis-within-Gibbs (LDMWG) sampling algorithm is proposed to improve the convergence performance, which fully takes the advantages of the acceptance mechanism from the metropolis-hastings (MH) algorithm in the Markov chain Monte Carlo (MCMC) methods. The rejected candidate by the acceptance mechanism is utilized as a learnable experience for the generation of a new candidate at the same Markov move. In this way, the overall probability of remaining the same state at the Markov chain is greatly reduced, which leads to an improved convergence performance in the sense of Peskun ordering. Moreover, in order to reduce the complexity cost during the Markov mixing, a symmetric sampling structure which greatly simplified the sampling operation is further introduced and the symmetric learnable delayed metropolis-within-Gibbs (SLDMWG) sampling algorithm is given. Finally, the simulation results based on multi-input multi-output (MIMO) detections are presented to confirm the convergence gain and the complexity reduction brought by the proposed sampling schemes.
AbstractList	As a key ingredient of machine learning and artificial intelligence, the sampling algorithms with respect to lattice Gaussian distribution has emerged as an important problem in coding and decoding of wireless communications. In this paper, based on the conventional Gibbs sampling, the learnable delayed metropolis-within-Gibbs (LDMWG) sampling algorithm is proposed to improve the convergence performance, which fully takes the advantages of the acceptance mechanism from the metropolis-hastings (MH) algorithm in the Markov chain Monte Carlo (MCMC) methods. The rejected candidate by the acceptance mechanism is utilized as a learnable experience for the generation of a new candidate at the same Markov move. In this way, the overall probability of remaining the same state at the Markov chain is greatly reduced, which leads to an improved convergence performance in the sense of Peskun ordering. Moreover, in order to reduce the complexity cost during the Markov mixing, a symmetric sampling structure which greatly simplified the sampling operation is further introduced and the symmetric learnable delayed metropolis-within-Gibbs (SLDMWG) sampling algorithm is given. Finally, the simulation results based on multi-input multi-output (MIMO) detections are presented to confirm the convergence gain and the complexity reduction brought by the proposed sampling schemes.
Author	Lyu, Shanxiang Wang, Zheng Liu, Ling
Author_xml	– sequence: 1 givenname: Zheng orcidid: 0000-0003-3528-558X surname: Wang fullname: Wang, Zheng email: z.wang@ieee.org organization: College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing, China – sequence: 2 givenname: Shanxiang surname: Lyu fullname: Lyu, Shanxiang organization: College of Information Science and Technology/College of Cyber Security, Jinan University, Guangzhou, China – sequence: 3 givenname: Ling surname: Liu fullname: Liu, Ling organization: Department of CT Lab, Huawei Technologies, Shenzhen, China
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SubjectTerms	Algorithms Artificial intelligence Complexity Complexity theory Convergence Decoding Encoding Gaussian distribution Gibbs sampler decoding Lattice coding and decoding lattice Gaussian sampling Lattices Machine learning Markov analysis Markov chain Monte Carlo Markov chains Markov processes MIMO (control systems) Monte Carlo simulation Normal distribution Sampling methods Statistical analysis Wireless communications
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Title	Learnable Markov Chain Monte Carlo Sampling Methods for Lattice Gaussian Distribution
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