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Polynomials and computing functions of correlated sources

We consider the source coding problem of computing functions of correlated sources, which is an extension of the Slepian-Wolf coding problem. We observe that all the discrete functions are in fact restrictions of polynomial functions over some finite field. Based on this observation, we demonstrate how to use Elias' Lemma to enlarge the coding rate region (compared to the Slepian-Wolf region) for a certain class of polynomial functions. We present a classification result about polynomial functions regarding this coding problem. The result is conclusive in the two-sources scenario and, in fact, gives another interpretation of a result by Han and Kobayashi [1, Theorem 1].