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.
Highlights
Lattice Gaussian distribution plays an important role in physical-layer of wireless communications
SIMULATION RESULTS the performance of the proposed Markov chain Monte Carlo (MCMC) sampling schemes for lattice Gaussian distribution are exemplified in the context of multi-input multi-output (MIMO) detection
We examine the decoding error probabilities to approximately compare the convergence performance of Markov chains
Summary
Lattice Gaussian distribution plays an important role in physical-layer of wireless communications. Problem (SVP) and the closest vector problem (CVP) [11], [12] To this end, sampling over lattice Gaussian distribution has been widely applied in multi-input multi-output (MIMO) communications for signal detection [13]–[15]. Due to the central role of lattice Gaussian distribution playing in physical-layer of wireless communications, its sampling algorithms become an important computational problem. As a basic MCMC method, the Gibbs algorithm, which employs univariate conditional sampling to build the Markov chain, has been introduced to lattice Gaussian sampling by showing its ergodicity [26]. In [36], the symmetric Metropolis-within-Gibbs (SMWG) algorithm was proposed for lattice Gaussian sampling to achieve the exponential convergence. In this paper, the computational complexity is measured by the number of arithmetic operations (additions, multiplications, comparisons, etc.)
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