论文标题
通过傅立叶变换上的非交互源模拟
On Non-Interactive Source Simulation via Fourier Transform
论文作者
论文摘要
考虑了非相互作用源模拟（NIS）方案。在这种情况下，一对分布式代理Alice和Bob观察了基于关节分配$ p_ {x，y} $生成的分布式二进制二进制二进制内存源$（x^d，y^d）$。代理商希望产生一对离散的随机变量$（u_d，v_d）$，带有联合分布$ p_ {u_d，v_d} $，以便$ p_ {u_d，v_d} $收敛到总变量距离，总变量距离为目标$ q_ {u q_ {u，v} $，因为输入块bloves bloxplengt $ d $ d $ d $ demptty asmptty asmpttoty asmpttoty asmpttoty asmpttoty asmppt asmpttoty asmpptottothy asmpttottothy asmptottoty。内边界和外部边界是在分布集$ q_ {u，v} $上获得的，可以在给定输入分布$ p_ {x，y} $的情况下产生。为此，提供了从一组分布组中的二主映射$ q_ {u，v} $到星形串联集合的结合。通过利用离散傅立叶分析的证明技术以及一种新颖的随机舍入技术，为这些星形凸套装中的每一个都得出了内部和外部边界，并颠倒上述的生物映射，从$ q_ {u，v} $和$ p_ {x，y} $的$ q_ {u，v e}的$ q_ {u，v e}的$ q_ {U， $ p_ {x，y} $。界限适用于输出字母$ \ MATHCAL {U} $和$ \ MATHCAL {V} $具有任意有限大小的NIS情况。在二进制输出字母的情况下，外部结合恢复了以前最著名的外部界限。
The non-interactive source simulation (NISS) scenario is considered. In this scenario, a pair of distributed agents, Alice and Bob, observe a distributed binary memoryless source $(X^d,Y^d)$ generated based on joint distribution $P_{X,Y}$. The agents wish to produce a pair of discrete random variables $(U_d,V_d)$ with joint distribution $P_{U_d,V_d}$, such that $P_{U_d,V_d}$ converges in total variation distance to a target distribution $Q_{U,V}$ as the input blocklength $d$ is taken to be asymptotically large. Inner and outer bounds are obtained on the set of distributions $Q_{U,V}$ which can be produced given an input distribution $P_{X,Y}$. To this end, a bijective mapping from the set of distributions $Q_{U,V}$ to a union of star-convex sets is provided. By leveraging proof techniques from discrete Fourier analysis along with a novel randomized rounding technique, inner and outer bounds are derived for each of these star-convex sets, and by inverting the aforementioned bijective mapping, necessary and sufficient conditions on $Q_{U,V}$ and $P_{X,Y}$ are provided under which $Q_{U,V}$ can be produced from $P_{X,Y}$. The bounds are applicable in NISS scenarios where the output alphabets $\mathcal{U}$ and $\mathcal{V}$ have arbitrary finite size. In case of binary output alphabets, the outer-bound recovers the previously best-known outer-bound.
