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This paper establishes the capacity region for a class of source coding function computation setups, where sources of information are available at the nodes of a tree and where a function of these sources must be computed at its root. The capacity region holds for any function as long as the sources’ joint distribution satisfies a certain Markov criterion. This criterion is met, in particular, when...
In this paper we study the sum modulo two problem proposed by Körner and Marton. In this source coding problem, two transmitters who observe binary sources X and Y, send messages of limited rate to a receiver whose goal is to compute the sum modulo of X and Y. This problem has been solved for the two special cases of independent and symmetric sources. In both of these cases, the rate pair (H(X|Y),...
This paper investigates a distributed function computation setting where the underlying network is a rooted directed tree and where the root wants to compute a function of the sources of information available at the nodes of the network. The main result provides the rate region for an arbitrary function under the assumption that the sources satisfy a general criterion. This criterion is satisfied,...
A transmitter has access to X, a relay has access to Y, and a receiver has access to Z and wants to compute a given function ƒ(X, Y, Z). How many bits must be transmitted from the transmitter to the relay and from the relay to the receiver so that the latter can reliably recover ƒ(X, Y, Z)? The main result is an inner bound to the rate region of this problem which is tight when X - Y - Z forms a Markov...
A receiver wants to compute a function of two correlated sources separately observed by two transmitters. One of the transmitters is allowed to cooperate with the other transmitter by sending it some data before both transmitters convey information to the receiver. Assuming noiseless communication, what is the minimum number of bits that needs to be communicated by each transmitter to the receiver...
A receiver wants to compute a function f of two correlated sources X and Y and side information Z. What is the minimum number of bits that needs to be communicated by each transmitter? In this paper, we derive inner and outer bounds to the rate region which coincide in the cases where f is partially invertible and where one of the sources is constant. From the former case we recover the Slepian-Wolf...
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