Mathematical methods in communication Lecture 7
نویسنده
چکیده
I. DIFFERENTIAL ENTROPY AND THE GAUSSIAN CHANNEL A. Differential Entropy Let X be a random variable with a continuous alphabet. • FX(x) = Pr(X ≤ x) Cumulative Distribution Function {CDF}. F (x) is a short notation for FX(x). • fX(x) = dFX(x) dx Probability Density Function {PDF} (in this course we will assume that the derivative exists). f(x) is a short notation for fX(x). Definition 1 ( Differential Entropy.) The differential entropy h(x) of a continuous random variable X with density f(x) is defined as h(X) , − ∫
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