Zero error coordination

Mahed Abroshan, A. Gohari, S. Jaggi
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引用次数: 4

Abstract

In this paper, we consider a zero error coordination problem wherein the nodes of a network exchange messages to be able to perfectly coordinate their actions with the individual observations of each other. While previous works on coordination commonly assume an asymptotically vanishing error, we assume exact, zero error coordination. Furthermore, unlike previous works that employ the empirical or strong notions of coordination, we define and use a notion of set coordination. This notion of coordination bears similarities with the empirical notion of coordination. We observe that set coordination, in its special case of two nodes with a one-way communication link is equivalent with the “Hide and Seek” source coding problem of McEliece and Posner. The Hide and Seek problem has known intimate connections with graph entropy, rate distortion theory, Rényi mutual information and even error exponents. Other special cases of the set coordination problem relate to Witsenhausen's zero error rate and the distributed computation problem. These connections motivate a better understanding of set coordination, its connections with empirical coordination, and its study in more general setups. This paper takes a first step in this direction by proving new results for two node networks, including capacity characterizations for the linear case.
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零误差协调
在本文中,我们考虑一个零错误协调问题,其中网络的节点交换消息,能够完美地协调他们的行动与彼此的个别观察。先前的协调工作通常假设误差渐近消失,而我们假设精确的零误差协调。此外,与以往使用经验或强协调概念的作品不同,我们定义并使用了集合协调的概念。这种协调概念与经验的协调概念有相似之处。我们观察到,在两个节点具有单向通信链路的特殊情况下,集合协调等同于McEliece和Posner的“捉迷藏”源编码问题。众所周知,捉迷藏问题与图熵、速率失真理论、r互信息甚至误差指数有着密切的联系。集合协调问题的其他特殊情况涉及到Witsenhausen的零错误率和分布式计算问题。这些联系促使我们更好地理解集合协调,它与经验协调的联系,以及它在更一般情况下的研究。本文在这个方向上迈出了第一步,证明了两个节点网络的新结果,包括线性情况下的容量表征。
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