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The problem of distributed function computation is studied, where functionsto be computed is not necessarily symbol-wise. A new method to derive aconverse bound for distributed computing is proposed; from the structure offunctions to be computed, information that is inevitably conveyed to thedecoder is identified, and the bound is derived in terms of the optimal rateneeded to send that information. The class of informative functions isintroduced, and, for the class of smooth sources, the optimal rate forcomputing those functions is characterized. Furthermore, for i.i.d. sourceswith joint distribution that may not be full support, functions that arecomposition of symbol-wise function and the type of a sequence are considered,and the optimal rate for computing those functions is characterized in terms ofthe hypergraph entropy. As a byproduct, our method also provides a conceptuallysimple proof of the known fact that computing a Boolean function may require aslarge rate as reproducing the entire source.

On Distributed Computing for Functions with Certain Structures