On the correlation between Boolean functions of sequences of random variables
On the correlation between Boolean functions of sequences of random variables
复制标题
关于随机变量序列的布尔函数之间的相关性
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
S. Pradhan
中科院分区：
文献类型：
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作者：
Farhad Shirani Chaharsooghi;S. Pradhan
在本文中，我们建立了一个新的不等式，它将有效长度以及作用于两个相关随机变量序列的任意一对布尔函数输出之间的最大相关性联系在一起。我们推导出了这些函数输出之间相关性的一个新的上界。这个上界在涉及公共信息的各个学科中是有用的。我们基于维森豪森（Witsenhausen）在最大相关性方面的[2]界限进行研究。之前的上界没有考虑布尔函数的有效长度。这个新界限的一个可能应用是描述多终端通信中的通信 - 协作权衡。在这个问题中，由于问题中的率失真约束，布尔函数的有效长度存在下界，并且由于问题的多终端性质，不同节点的输出相关性也存在下界。
In this paper, we establish a new inequality tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a new upper-bound on the correlation between the outputs of these functions. The upper-bound is useful in various disciplines which deal with common-information. We build upon Witsenhausen's [2] bound on maximum-correlation. The previous upper-bound did not take the effective length of the Boolean functions into account. One possible application of the new bound is to characterize the communication-cooperation tradeoff in multi-terminal communications. In this problem, there are lower-bounds on the effective length of the Boolean functions due to the rate-distortion constraints in the problem, as well as lower bounds on the output correlation at different nodes due to the multi-terminal nature of the problem.