We leverage proof techniques Fourier analysis and an existing result in coding theory to derive new bounds for the problem of non-interactive simulation of binary random variables. Previous bounds in the literature were derived by applying data processing inequalities concerning maximal correlation or hypercontractivity. We show that our bounds are sharp in some regimes. For a specific instance of problem parameters, our main result answers an open problem posed by E. Mossel in 2017. As by-products of our analyses, various new properties of the average distance and distance enumerator of binary block codes are established.

翻译：我们利用Fourier 分析法和现有的编码理论,为二进制随机变量的非互动模拟问题得出新的界限。文献以前的界限是通过在最大相关性或超包性方面应用数据处理不平等来得出的。我们表明,在某些制度下,我们的界限是尖锐的。在特定的问题参数实例中,我们的主要结果解决了2017年E. Mossel提出的一个尚未解决的问题。作为我们分析的副产品,我们建立了各种新特性,即二进制区块代码的平均距离和距离计算器。