HP Labs Technical Reports
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Maximizing the Entropy of a Sum of Independent Random Variables
Keyword(s): majorization; multiple access channel; time sharing
Abstract: This abstract contain mathematical formulae which cannot be represented here. Let X (subscript 1),. . . ,X(subscript n) be n independent, symmetric random variables supported on the interval [-1,1] and let S(subscript n) = Sigma(superscript n, subscript i)=1 X(subscript i) be their sum. We show that the differential entropy of S(subscript n) is maximized when X(subscript 1), . . . ,X(subscript n-1) are Bernoulli taking on +1 or -1 with equal probability and X(subscript n) is uniformly distributed. This entropy maximization problem is due to Shlomo Shamai  who also conjectured the solution(superscript 1).
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