On the maximum entropy of the sum of two dependent random variables
On the maximum entropy of the sum of two dependent random variables
复制标题
关于两个因随机变量之和的最大熵
DOI：
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发表时间：
1994
影响因子：
2.5
通讯作者：
Zhen Zhang
中科院分区：
文献类型：
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作者：
T. Cover;Zhen Zhang
研究了任意相依随机变量X和Y的微分熵h（X+Y）在X和Y的边际密度固定相等的约束下的最大化问题。在X和Y具有相同的固定边际密度f的约束下，证明了max[h（X+Y）]=h（2X）当且仅当f是对数凹的.当X=Y时达到最大值。如果f不是对数凹的，则最大值严格大于h（2X）。例如，同分布的高斯随机变量具有对数凹密度，并且满足max[h（X+Y）]=h（2X），其中X=Y。在这个方向上更一般的不等式应导致加性噪声信道反馈的容量界限。>
Investigates the maximization of the differential entropy h(X+Y) of arbitrary dependent random variables X and Y under the constraints of fixed equal marginal densities for X and Y. We show that max[h(X+Y)]=h(2X), under the constraints that X and Y have the same fixed marginal density f, if and only if f is log-concave. The maximum is achieved when X=Y. If f is not log-concave, the maximum is strictly greater than h(2X). As an example, identically distributed Gaussian random variables have log-concave densities and satisfy max[h(X+Y)]=h(2X) with X=Y. More general inequalities in this direction should lead to capacity bounds for additive noise channels with feedback. >