The common randomness capacity of a finite network of channels

S. Venkatesan, V. Anantharam
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Abstract

Consider a finite number of agents interconnected by an arbitrary network of independent, point-to-point, discrete memoryless channels. The agents wish to generate common randomness by interactive communication over the network. Our main result is an exact characterization of the common randomness capacity of such a network, i.e. the maximum number of bits of randomness that all the agents can agree on, per step of communication. As a by-product, we also obtain a description by linear inequalities of the blocking-type polyhedron whose extreme points are precisely the incidence vectors of all arborescences in a digraph, with a prescribed root of out-degree 1.
有限信道网络的一般随机容量
考虑由任意的独立的、点对点的、离散的无内存通道网络相互连接的有限数量的代理。智能体希望通过网络上的交互通信产生共同的随机性。我们的主要结果是对这种网络的共同随机容量的精确描述,即每一步通信中所有代理可以同意的最大随机位数。作为副产物,我们也得到了阻塞型多面体的线性不等式描述,该多面体的极值点恰好是有向图中所有树形的关联向量,给定的根为出次为1。
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