CIF: Small: Many-User Information Theory: A New Paradigm

这一研究项目的目标是发展一种多用户信息理论，该理论研究具有大量源、发射器和/或接收器的模型的基本信息极限，这些源、发射器和/或接收器的种群大小与编码块长度相当甚至更大。这一新理论深深植根于经典的单用户和多用户信息理论，该理论通过研究具有固定(通常是少量)用户数量的无限编码块长度的渐近机制来表征通信系统(通常是单用户)的性能。对于用户数等于或大于块长度的系统，多用户信息理论通常只提供有限的结果。特别是，在块长度变为无穷大之后将用户数发送到无穷大，可能不会产生与根据某种关系同时将两者发送到无穷大相同的结果。在新的多用户信息论中，一个额外的维度，即用户维度，与块长度同时被发送到无穷大。多用户模型的具体示例包括多访问频道、多广播频道以及具有许多相关来源的模型等等。这项研究的一个重要组成部分是在多用户范例中寻求一种新的容量和容量区域的概念，因为传统的以每符号或每信道使用的比特数为单位的概念已经不适合这项任务。将在所有三个主要子领域，即信源编码、信道编码和率失真理论中得出变革性的结果。理想情况下，多用户信息论将为新兴和未来通信系统的设计提供亟需的指导，如传感器网络和机器对机器通信系统，并最终将影响人们生活的许多方面，包括医疗保健、交通、智能电网、智能家居、智能城市和公共安全。多用户信息论也可能与数学和物理科学的其他分支交叉受精，包括概率论、统计学和统计物理学。该项目还为本科生提供了许多机会，包括那些来自代表性不足的群体的学生，以获得STEM研究方面的经验。

The goal of this research project is to develop a Many-User Information Theory, which studies the fundamental information limits of models with a large number of sources, transmitters and/or receivers, whose population size is comparable or even larger than the coding blocklength. This new theory is deeply rooted in the classical Single-user and Multiuser Information Theory, which characterizes the performance of communication systems (often of a single user) by studying the asymptotic regime of infinite coding blocklength with a fixed (often small) number of users. For systems whose number of users is comparable to or larger than the blocklength, Multiuser Information Theory generally offers only limited results. In particular, sending the number of users to infinity after the blocklength goes to infinity may not yield the same result as sending the two to infinity simultaneously according to a certain relationship. In the new Many-User Information Theory, an additional dimension, namely, the user dimension, is simultaneously sent to infinity with the blocklength. Specific examples of many-user models include the many-access channel, the many-broadcast channel, and models with many correlated sources, among others. A crucial component of this research is to seek a new notion of capacity and capacity region in the many-user paradigm, as the traditional notion of rate in bits per symbol or per channel use becomes ill-suited for the task.This research project will push the envelope of Information Theory. Transformative results will be developed in all three major subfields, namely, source coding, channel coding, and rate-distortion theory. Ideally, Many-User Information Theory will provide much needed guidance for the design of emerging and future communication systems, such as sensor networks and machine-to-machine communication systems, and will eventually affect many aspects of people's lives, including healthcare, transportation, smart grid, smart home, smart city, and public safety. Many-User Information Theory is also likely to cross-fertilize with other branches of mathematical and physical sciences, including probability theory, statistics, and statistical physics. The project also provides many opportunities for undergraduate students, including those from underrepresented groups, to gain experience in STEM research.