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CIF: Small: Capacity via Symmetry

CIF：小：对称容量

基本信息

批准号：
1718494
负责人：
Henry Pfister
金额：
$ 51.42万
依托单位：
Duke University
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：
2017-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1718494&HistoricalAwards=false
关键词：
CIF Small Capacity via Symmetry

项目摘要

Information theory studies the fundamental laws that govern information processing systems. For instance, the Shannon Capacity of a noisy channel is the largest rate (in bits per channel use) that bits can be reliably communicated. Information theory has had an enormous impact on how information is acquired, processed, compressed, and transmitted. Examples include channel coding and data compression, both of which are used extensively in Internet and cellular communications. This project focuses on connections between performance and codebook symmetry. One part focuses on using symmetry to help low-complexity decoders achieve near-optimum performance for codes relevant to 5G cellular standards. This project will also train several graduate students, hence an important broader impact of this project is the production of highly-trained workers in electrical engineering and computer science.Many theoretical results in information theory use random codebooks to encode messages. Researchers have long sought families of deterministic algebraic codes that provably achieve capacity. In a recent breakthrough, the PI and his coauthors showed that sequences of sufficiently symmetric codes achieve capacity on the binary erasure channel. Since Reed-Muller codes satisfy the required symmetry condition, we now know that such a code family was discovered by Muller in 1954, only 6 years after Shannon's introduction of channel capacity! The project focuses on whether symmetric codebooks can be used in more general settings to approach information-theoretic limits. In particular, the goals are to determine: (i) How general is the phenomenon of capacity via symmetry? (ii) What performance gains can be achieved in practice by exploiting symmetries? (iii) Can symmetry be utilized to approach the information-theoretic limits of other problems?

信息论研究支配信息处理系统的基本规律。例如，有噪声信道的香农容量是比特可以可靠通信的最大速率（以每个信道使用的比特为单位）。信息论对信息的获取、处理、压缩和传输产生了巨大的影响。例子包括信道编码和数据压缩，这两者都广泛用于互联网和蜂窝通信。这个项目的重点是性能和码本对称性之间的联系。其中一个部分侧重于使用对称性来帮助低复杂度解码器实现与5G蜂窝标准相关的代码的接近最佳性能。该项目还将培养几名研究生，因此该项目的一个重要的更广泛的影响是在电气工程和计算机科学方面培养训练有素的工作人员。信息论中的许多理论成果使用随机码本来编码信息。长期以来，研究人员一直在寻找可证明达到容量的确定性代数码家族。在最近的一项突破中，PI和他的合著者表明，足够对称的代码序列在二进制擦除信道上实现了容量。由于Reed-Muller码满足所需的对称条件，我们现在知道这样的码族是在1954年由Muller发现的，仅在香农引入信道容量的6年之后！该项目的重点是对称码本是否可以用于更一般的设置，以接近信息理论的限制。特别是，目标是确定：（一）如何普遍的现象是通过对称的能力？(ii)在实践中，利用对称性可以获得哪些性能增益？(iii)对称性可以用来接近其他问题的信息论极限吗？

项目成果

期刊论文数量（12）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Unifying the Clifford hierarchy via symmetric matrices over rings

DOI：
10.1103/physreva.100.022304
发表时间：
2019-02
期刊：
Physical Review A
影响因子：
2.9
作者：
Narayanan Rengaswamy;Robert Calderbank;H. Pfister
通讯作者：
Narayanan Rengaswamy;Robert Calderbank;H. Pfister

Bounds on the List Size of Successive Cancellation List Decoding

连续取消列表解码的列表大小的界限

DOI：
10.1109/spcom50965.2020.9179593
发表时间：
2020
期刊：
2020 International Conference on Signal Processing and Communications (SPCOM
影响因子：
0
作者：
Coskun, Mustafa Cemil;Pfister, Henry D.
通讯作者：
Pfister, Henry D.

The Replica-Symmetric Prediction for Random Linear Estimation With Gaussian Matrices Is Exact