On the Entropy Computation of Large Gaussian Mixture Distributions
Su Min Kim, Tan Tai Do, Tobias J. Oechtering, Gunnar Peters · 2015
The entropy computation of Gaussian mixture dis- tributions with a large number of components has a prohibitive computational complexity. In this paper, we propose a novel approach exploiting the sphere decoding concept to bound and approximate such entropy terms with reduced complexity and good accuracy. Moreover, we propose an SNR region- based enhancement of the approximation method to reduce the complexity even further. Using Monte-Carlo simulations, the proposed methods are numerically demonstrated for the computation of the mutual information including the entropy term of various channels with finite constellation modulations such as binary and quadratic amplitude modulation (QAM) inputs for communication applications. Index Terms—Gaussian mixture distribution, Entropy ap- proximation, Mutual information, Finite input alphabet, Sphere decoding