论文标题
灰色 - 双重对称二进制来源和高斯来源的惠纳和共同信息区域
Gray--Wyner and Mutual Information Regions for Doubly Symmetric Binary Sources and Gaussian Sources
论文作者
论文摘要
非convex优化在多用户信息理论和相关领域中起关键作用，但通常很难解决。灰色 - 惠纳源编码系统的速率区域（或几乎等效地，相互信息区域）是非convex优化的典型示例，其单字母的表达是由Gray和Wyner给出的。但是，由于此表达式所涉及的优化的非凸度，因此没有任何已知分析表达的非平凡离散来源。在本文中，我们提出了一种解决非凸优化问题的新策略。通过这种策略，我们提供了双对称二进制源（DSB）的分析表达，该二进制源（DSB）在1974年积极地确认了灰色和怀特纳的猜想。我们还为高斯源提供了共同信息区域的分析表达，并提供（或恢复）灰色灰色区域的分析表达式，用于两个dsb和gaussian saguss和gauss的分析表达。我们的证明策略依赖于辅助测量技术和最佳传输差异区域的分析表达。
Nonconvex optimization plays a key role in multi-user information theory and related fields, but it is usually difficult to solve. The rate region of the Gray--Wyner source coding system (or almost equivalently, the mutual information region) is a typical example in nonconvex optimization, whose single-letter expression was given by Gray and Wyner. However, due to the nonconvexity of the optimization involved in this expression, previously, there was none nontrivial discrete source for which the analytic expression is known. In this paper, we propose a new strategy to solve nonconvex optimization problems. By this strategy, we provide the analytic expression for the doubly symmetric binary source (DSBS), which confirms positively a conjecture of Gray and Wyner in 1974. We also provide the analytic expression of the mutual information region for the Gaussian source, and provide (or recover) the analytic expressions of the lossy Gray--Wyner region for both the DSBS and Gaussian source. Our proof strategy relies on an auxiliary measure technique and the analytical expression of the optimal-transport divergence region.
