On Non-Interactive Simulation of Binary Random Variables
On Non-Interactive Simulation of Binary Random Variables
复制标题
二元随机变量的非交互式模拟
DOI：
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复制
发表时间：
2019
影响因子：
2.5
通讯作者：
V. Tan
中科院分区：
文献类型：
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作者：
Lei Yu;V. Tan
我们利用离散傅立叶分析的证明技术和编码理论中的现有结果，推导出二进制随机变量非交互式模拟问题的新界限。文献中以前的界限是通过应用关于最大相关性或超收缩性的数据处理不等式得到的。我们表明，我们的界限是尖锐的，在某些制度。事实上，对于问题参数的一个特定实例，我们的主要结果解决了由E。2017年的莫塞尔。作为我们分析的副产品，建立了二元分组码的平均距离和距离枚举数的各种新性质。
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 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. Indeed, for a specific instance of the problem parameters, our main result resolves 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.