On the Entropy Computation of Large Complex Gaussian Mixture Distributions

TL;DR

This paper introduces a sphere decoding-based method to efficiently approximate the entropy of large Gaussian mixture distributions, significantly reducing computational complexity while maintaining accuracy, especially in communication systems.

Contribution

It presents a novel sphere decoding approach for entropy approximation of large Gaussian mixtures, enhanced by SNR region-based optimization, applicable to communication channel analysis.

Findings

Reduced complexity in entropy computation for large Gaussian mixtures

Accurate mutual information estimation with finite constellation modulations

Effective approximation validated through Monte-Carlo simulations

Abstract

The entropy computation of Gaussian mixture distributions 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.