A strengthened version of Shannon's entropy power inequality for the case where one of the random vectors involved is Gaussian is proved. In particular it is shown that if independent Gaussian noise is added to an arbitrary, multivariate random variable, the entropy power of the resulting random variable is a concave function of the variance (power) of the added noise. The strengthened inequality is shown to hold for the class of stable distributions.
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Max H. M. Costa (1985) studied this question.
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