On Non-Interactive Simulation of Binary Random Variables

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