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

CIF:Small：基于准结构化码的网络信息论的代数和概率基础

基本信息

批准号：
1717299
负责人：
Sandeep Sadanandarao
金额：
$ 36.99万
依托单位：
Regents of the University of Michigan - Ann Arbor
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2020-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1717299&HistoricalAwards=false
关键词：
CIF Small Toward Algebraic Probabilistic

项目摘要

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.

交通系统、电力系统、气候环境监测系统、教育系统等现代基础设施日益通过信息网络互联。最近的一项预测预测，人类对信息消费和随之而来的信息互连的渴望永无止境。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应对这一挑战。该项目从通信/信息/信号处理理论的角度开发了网络中信息的高效分布式编码和解码的新思想和技术。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，并以新课程开发和学生参与的形式广泛传播研究成果。该项目考虑两个关键概念：（i）结构化代码与非结构化代码； (ii) 共同信息。它们之间的新的基本联系被揭示，这激励了针对构成网络构建块的通信问题开发新的统一编码框架。该项目以最近开发的三项关键创新为基础：（i）准结构化代码，涵盖从完全结构化代码到完全非结构化代码的范围，其性能可以使用单字母信息量来表征； (ii) 会议三个或更多随机变量（或终端）之间的共同信息，这些随机变量表征联合概率分布中的新结构，这是在网络中开发新信息编码策略的关键； (iii) 使用计算高效的编码和解码算法接近信息理论速率区域的网络的实用代码构造。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，作为开发适合具有挑战性的多用户信息理论问题的计算高效的编码和解码算法的先驱。