CIF:Small: Toward an Algebraic and Probabilistic Foundation for Network Information Theory based on Quasi Structured Codes

现代基础设施，包括交通系统、电力系统、气候和环境监测系统以及教育系统，越来越多地通过信息网络相互联系。最近的一项预测预测，人类对信息消费的渴望和随之而来的信息互联不会在短期内结束。网络信息理论旨在通过发展网络中信息存储、传输和处理的综合理论来解决这一挑战。本项目从通信/信息/信号处理理论的角度出发，开发网络中高效分布式信息编码和解码的新思想和新技术。该项目将与一个重要的教育和推广计划紧密结合，该计划包括两个重点领域：培训学生进行跨学科研究，以及以新课程开发和学生参与的形式广泛传播研究成果。该项目考虑了两个关键概念：(i)结构化代码与非结构化代码；（ii）公共信息。发现了它们之间的一个新的基本联系，这促使开发一个新的统一编码框架，以解决构成网络构建块的通信问题。该项目以最近发展起来的三个关键创新为基础：(i)准结构化代码，其范围从完全结构化代码到完全非结构化代码，其性能可以使用单字母信息量来表征；在三个或三个以上的随机变量（或终端）之间形成共同信息，这些随机变量（或终端）构成联合概率分布中的新结构，而联合概率分布是在网络中发展新的信息编码策略的关键；（iii）使用计算效率高的编码和解码算法接近信息论速率区域的网络的实用代码结构。该项目致力于对网络通信问题中的代数代码结构有一个基本的理解，作为开发计算效率高的编码和解码算法的先驱，以适应具有挑战性的多用户信息理论问题。

Modern infrastructure, including transportation systems, power systems, climate and environment monitoring systems, and education systems, are increasingly interconnected through information networks. A recent forecast predicts no end in sight for humanity's hunger for information consumption and the concomitant information interconnection. Network information theory aims to address this challenge by developing a comprehensive theory of information storage, transmission, and processing in networks. This project develops new ideas and techniques in efficient distributed encoding and decoding of information in networks from a communication/information/signal-processing theory perspective. The project will be tightly integrated with a significant education and outreach program consisting of two focus areas: training students in interdisciplinary research, and broadly disseminating research outcomes in the forms of new curricular development and student involvement. This project considers two key concepts: (i) structured codes versus unstructured codes; and (ii) common information. A new fundamental connection between them is uncovered, which motivates the development of a new unified coding framework for the communication problems that form the building blocks of networks. This project is pillared on three key innovations developed in the recent past: (i) Quasi-structured codes that span the spectrum from completely structured codes to completely unstructured codes and whose performance can be characterized using single-letter information quantities; (ii) Conferencing common information among three or more random variables (or terminals) that characterizes new structures in the joint probability distributions that are the key to developing new information coding strategies in networks; and (iii) Practical code constructions for networks that approach the information-theoretic rate region using computationally efficient encoding and decoding algorithms. This project strives for a fundamental understanding of the algebraic code structure in network communication problems, as a precursor to developing computationally efficient encoding and decoding algorithms adapted to challenging multi-user information theory problems.