7,384 research outputs found
Infinite-message Interactive Function Computation in Collocated Networks
An interactive function computation problem in a collocated network is
studied in a distributed block source coding framework. With the goal of
computing a desired function at the sink, the source nodes exchange messages
through a sequence of error-free broadcasts. The infinite-message minimum
sum-rate is viewed as a functional of the joint source pmf and is characterized
as the least element in a partially ordered family of functionals having
certain convex-geometric properties. This characterization leads to a family of
lower bounds for the infinite-message minimum sum-rate and a simple optimality
test for any achievable infinite-message sum-rate. An iterative algorithm for
evaluating the infinite-message minimum sum-rate functional is proposed and is
demonstrated through an example of computing the minimum function of three
sources.Comment: 5 pages. 2 figures. This draft has been submitted to IEEE
International Symposium on Information Theory (ISIT) 201
Zero Error Coordination
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, Renyi 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
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