期刊
ENTROPY
卷 14, 期 6, 页码 1103-1126出版社
MDPI AG
DOI: 10.3390/e14061103
关键词
mutual information; non-Gaussianity; maximum entropy distributions; non-Gaussian noise
资金
- [PEST-OE/CTE/LA0019/2011-FCT]
- Fundação para a Ciência e a Tecnologia [PEst-OE/CTE/LA0019/2011] Funding Source: FCT
The application of the Maximum Entropy (ME) principle leads to a minimum of the Mutual Information (MI), I(X,Y), between random variables X,Y, which is compatible with prescribed joint expectations and given ME marginal distributions. A sequence of sets of joint constraints leads to a hierarchy of lower MI bounds increasingly approaching the true MI. In particular, using standard bivariate Gaussian marginal distributions, it allows for the MI decomposition into two positive terms: the Gaussian MI (I-g), depending upon the Gaussian correlation or the correlation between 'Gaussianized variables', and a non-Gaussian MI (I-ng), coinciding with joint negentropy and depending upon nonlinear correlations. Joint moments of a prescribed total order p are bounded within a compact set defined by Schwarz-like inequalities, where I-ng grows from zero at the 'Gaussian manifold' where moments are those of Gaussian distributions, towards infinity at the set's boundary where a deterministic relationship holds. Sources of joint non-Gaussianity have been systematized by estimating I-ng between the input and output from a nonlinear synthetic channel contaminated by multiplicative and non-Gaussian additive noises for a full range of signal-to-noise ratio (snr) variances. We have studied the effect of varying snr on I-g and I-ng under several signal/noise scenarios.
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