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IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 46, NO. 2, MARCH 2000 367 The Common Randomness Capacity of a Network of
 

Summary: IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 46, NO. 2, MARCH 2000 367
The Common Randomness Capacity of a Network of
Discrete Memoryless Channels
Sivarama Venkatesan, Member, IEEE, and Venkat Anantharam, Fellow, IEEE
Abstract--In this paper, we generalize our previous results on
generating common randomness at two terminals to a situation
where any finite number of agents, interconnected by an arbitrary
network of independent, point-to-point, discrete memoryless chan-
nels, wish to generate common randomness by interactive commu-
nication over the network. Our main result is an exact characteri-
zation 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 ob-
tain a purely combinatorial result, viz., a characterization of (the
incidence vectors of) the spanning arborescences rooted at a spec-
ified vertex in a digraph, and having exactly one edge exiting the
root, as precisely the extreme points of a certain unbounded convex
polyhedron, described by a system of linear inequalities.
Index Terms--Common randomness, interactive communica-
tion, polyhedral characterization, spanning arborescences, strong

  

Source: Anantharam, Venkat - Department of Electrical Engineering and Computer Sciences, University of California at Berkeley

 

Collections: Engineering