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We leverage proof techniques Fourier analysis and an existing result incoding theory to derive new bounds for the problem of non-interactivesimulation of binary random variables. Previous bounds in the literature werederived by applying data processing inequalities concerning maximal correlationor hypercontractivity. We show that our bounds are sharp in some regimes. For aspecific instance of problem parameters, our main result answers an openproblem posed by E. Mossel in 2017. As by-products of our analyses, various newproperties of the average distance and distance enumerator of binary blockcodes are established.

On Non-Interactive Simulation of Binary Random Variables