CIF: Small: New Directions in Network Information Theory

在网络信息理论中开发的大多数编码方案是使用香农随机编码技术的少数基本组件的组合。为了提高我们对这些随机编码方案的理解并使其在实践中应用，本研究探讨了网络信息理论中的三个重要问题。首先，本项目研究了同时解码规则，该规则易于分析，但足够强大，可以在干扰信道上实现最大可实现的随机编码速率。其次，本项目将在随机编码和同步解码方面获得的见解应用于索引编码问题，在索引编码问题中，多个消息通过一个单一的无噪声链路传递给具有不同侧信息的多个接收器。第三，本项目开发了一种基于随机编码、产品编码和迭代解码的串联编码架构，可以为将随机编码方案转换为实际的、可实现的编码技术提供一种系统的方法。网络信息论在我们的网络社会中扮演着越来越重要的角色，它研究网络上信息流的基本限制以及实现这些限制的最佳编码技术、协议和体系结构。本研究探讨了网络信息论中涉及干扰和广播的典型问题，为网络编码、无线通信、点对点网络和内容广播等几个重要应用中的最佳信息流提供了新的见解和新的数学工具。本研究开发的串联编码体系结构有可能为将网络信息理论中的理论概念转化为实际应用算法提供一个新的框架。

Most coding schemes developed in network information theory are combinations of a handful of basic components using Shannon's random coding technique. With the goal of advancing our understanding of these random coding schemes and making them applicable in practice, this research explores three important problems in network information theory. First, this project investigates the simultaneous decoding rule that is easy to analyze, yet powerful enough to achieve the maximum achievable rates of random coding over interference channels. Second, this project applies the insights thus gained on random coding and simultaneous decoding to the index coding problem, in which multiple messages are communicated through a single, noise-free link to multiple receivers with different pieces of side information. Third, this project develops a concatenated coding architecture based on random coding, product codes, and iterative decoding that can provide a systematic method for translating random coding schemes to practical, implementable coding techniques for real-world networks.Playing an ever-increasing role in our networked society, network information theory studies the fundamental limits on information flow over networks and the optimal coding techniques, protocols, and architectures that achieve these limits. This research investigates canonical problems in network information theory that involve interference and broadcast, offering fresh insights and new mathematical tools for optimal information flow in several important applications such as network coding, wireless communication, peer-to-peer networking, and content broadcasting. The concatenated coding architecture developed in this research has potential to provide a new framework for transforming theoretical concepts in network information theory into practical algorithms for applications.