Abstract
Consider separate encoding of correlated sources X^{n}=(X_{l}, \cdots ,X_{n}), Y^{n} = (Y_{l}, \cdots ,Y_{n}) for the decoder to reliably reproduce a function \{F(X_{i}, Y_{i})\}^{n}_{i=1} . We establish the necessary and sufficient condition for the set of all achievable rates to coincide with the Slepian-Wolf region whenever the probability density p(x,y) is positive for all (x,y) .
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