On the Sub-Optimality of Single-Letter Coding Over Networks
On the Sub-Optimality of Single-Letter Coding Over Networks
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DOI：
10.1109/tit.2019.2917434
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发表时间：
2017-05
影响因子：
2.5
通讯作者：
Farhad Shirani;S. Pradhan
中科院分区：
文献类型：
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作者：
Farhad Shirani;S. Pradhan
在本文中，我们建立了一个新的界限，将有效长度和最大相关性与任意的布尔函数的输出之间的最大相关性，该函数在两个相关随机变量的序列上运行，我们在输出之间的相关性上得出了一个新的上限。这些功能都可以在许多领域的问题中找到涉及通用信息的问题。考虑到相关性的布尔功能的有效长度。 Boolean函数。为了结合两个分布式BBC的输出之间的相关性。
In this paper, we establish a new bound 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 may find applications in problems in many areas which deal with common information. We build upon Witsenhausen’s result [1] on maximum correlation. The present upper bound takes into account the effective length of the Boolean functions in characterizing the correlation. We use the new bound to characterize the communication-cooperation tradeoff in multi-terminal communications. We investigate binary block-codes (BBC). A BBC is defined as a vector of Boolean functions. We consider an ensemble of BBCs which is randomly generated using single-letter distributions. We characterize the vector of dependency spectrums of these BBCs. We use this vector to bound the correlation between the outputs of two distributed BBCs. Finally, the upper bound is used to show that the large blocklength single-letter coding schemes studied in the literature are sub-optimal in various multi-terminal communication settings.