This talk, we consider an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a new upper-bound on the correlation between the outputs of these functions. The upper-bound is presented as a function of the `dependency spectrum' of the corresponding Boolean functions. Next, we investigate binary block-codes (BBC). A BBC is defined as a vector of Boolean functions. We consider BBC’s which are generated randomly, and using single-letter distributions. We characterize the vector of dependency spectra of these BBC’s. This gives an upper-bound on the correlation between the outputs of two distributed BBC’s. Finally, the upper-bound is used to show that the single-letter coding schemes in the literature are sub-optimal in various multi-terminal communication settings.