CIF: Small: Ordered Metrics and Their Applications

CIF：小：有序指标及其应用

• 批准号: 1217245
• 负责人: Alexander Barg
• 金额: $ 47.23万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1217245&HistoricalAwards=false
• 关键词: CIF; Small; Ordered; Metrics; Their

The central theme of this project is research into properties and applications of polar codes, a new method of coding information for transmission over noisy channels that for the first time realizes the full potential of Shannon's theorems that relate to data rate and transmission reliability. Polar codes have been shown to advance a range of classical and new information-theoretic problems that rely on efficient encoding of the data. This project addresses properties of polar codes in nonbinary communication channels, the design of optimal polarizing transformations, and applications to unequal error protection, hierarchical source coding, broadcast channels, signal design, and other problems of importance for network communication.The analysis of polar codes and their applications in this project relies on the concept of ordered distances that have been shown to control the reliability of transmitted symbols on nonbinary channels. Ordered distances contribute new ideas to the study of linear codes and related concepts such as multipartite and hierarchical secret sharing schemes. The project draws on these ideas to study new algebraic polarization transformations as well as the advances in the theory of linear code-based constructions for a number of models of practical communication systems.

该项目的中心主题是研究极性编码的特性和应用，极性编码是一种用于在噪声信道上传输的编码信息的新方法，首次实现了与数据速率和传输可靠性相关的香农定理的全部潜力。极性编码已经被证明可以推进一系列依赖于数据有效编码的经典和新的信息论问题。本项目探讨非二进制通信信道中极性码的特性，优化极化变换的设计，以及在不等错误保护、分层源编码、广播信道、信号设计和其他网络通信重要问题中的应用。极性码的分析及其在本项目中的应用依赖于有序距离的概念，有序距离已被证明可以控制非二进制信道上传输符号的可靠性。有序距离为线性码和相关概念的研究提供了新的思路，如多方和分层秘密共享方案。该项目利用这些思想来研究新的代数极化变换，以及用于实际通信系统的许多模型的基于线性码的结构理论的进展。