CIF: Small: Poisson matching: A new tool for information theory

通常通过研究通信方案的概率分布来证明通信问题的良好设计的存在性，并表明良好设计以正概率存在。这被称为随机编码方法。在这个项目中开发的泊松匹配技术是这类方法中的一种新方法，它具有比以前更严格的延迟约束的通信问题的优点。这对于物联网等新兴现代应用以及包括远程手术和无人驾驶车辆在内的通信通道控制场景非常重要。由于泊松匹配方法能够在存在延迟约束的情况下工作，因此在涉及多个智能体相互作用的问题中，泊松匹配方法似乎特别有希望发现更好的方案。这类问题在网络中无处不在，并且先前拒绝尝试使用早期可用的随机编码方法。该项目的目标是开发泊松匹配技术的使用，以开发涉及多个代理的通信，估计和控制问题的良好设计。泊松匹配引理可以被认为是这样一种方式，即接收者可以访问发送者可以访问的随机变量的噪声版本，但仍然可以与发送者协调，从泊松过程中挑选出相同的点，错误概率随着发送者和接收者之间相互信息的增加而减少。这个引理可以用来在许多核心的一次性信息论问题中给出非常明确的错误概率边界——这些边界通常与之前最知名的此类边界一样好，甚至更好。在其核心，泊松匹配引理是一种方法，允许多个代理，有一些潜在的随机变量的相关视图，协调他们的行动。该项目旨在通过研究泊松匹配引理在涉及多个代理的通信、估计和控制问题中的应用，从更广泛的角度发展泊松匹配引理的力量。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The existence of good designs for communication problems is often demonstrated by studying probability distributions over communication schemes and showing that good ones exist with positive probability. This is called a random coding methodology. The Poisson matching technique to be developed in this project is a novel method of this kind, which has the advantage of working for communication problems with more stringent delay constraints than was previously possible. This is important for emerging modern applications such as the Internet of Things and in scenarios involving control over communication channels, including remote surgery and unmanned vehicles. Because of its ability to work when there are delay constraints, the Poisson matching approach seems particularly promising for discovering better schemes in problems involving multiple agents interacting with each other. Such problems are ubiquitous in networks and have previously resisted attempts to use the earlier available random coding approaches. The goal of this project is to develop the use of the Poisson matching technique in developing good designs for problems of communication, estimation and control involving multiple agents.The Poisson matching lemma can be thought of as a way in which a receiver, having access to a noisy version of a random variable that the sender has access to, can nevertheless coordinate with the sender to pick out the same point from a Poisson process with a probability of error that diminishes as the mutual information increases between the sender and the receiver. This lemma can be used to give very sharp bounds on error probabilities in many of the core one-shot information theory problems - these bounds are usually as good as or better than the previously best known such bounds. At its heart, the Poisson matching lemma is a methodology allowing multiple agents, having related views of some underlying random variable, to coordinate their actions. The project aims to develop the power of the Poisson matching lemma from this more broad perspective, by studying its use in problems of communication, estimation and control involving multiple agents.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.