CIF: Small:Analog-to-Analog Compression: Fundamental Limits and Constructive Schemes

CIF：小型：模拟到模拟压缩：基本限制和建设性方案

• 批准号: 1319299
• 负责人: Emmanuel Abbe
• 金额: $ 47.5万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1319299&HistoricalAwards=false
• 关键词: CIF; Small; Analog; Compression; Fundamental

For analog signals of high dimension, compression methods relying on the acquisition and quantization of the entire signal may not always be possible. It is hence of interest to develop methods for compressing information directly from the analog to the analog (A2A) domain. Two philosophies have proven successful in addressing the general problem of conveying analog information through an analog medium: the Shannon theoretic approach and the compressed sensing approach. This research investigates a third approach, which blends the generality of the Shannon theoretic approach with the practicality of the compressed sensing approach. The fundamental limits of A2A compression are investigated in single and multi-signal settings, and constructive schemes are proposed to achieve these limits. The challenge of A2A compression is to achieve the maximal dimensionality reduction, i.e., a bandwidth reduction factor of the signal dimension per measurement, by exploiting prior knowledge about the signal, which may include, but it is not limited to sparsity. Wu-Verdú have shown that the Renyi Information dimension (RID) is the fundamental limit for i.i.d. signals with known distributions. The RID is a very coarse measure of information, as many different signals lead to the same RID. This research investigates other signal features that influence the A2A compression performance beyond RID, particularly in the non-asymptotic regime. It investigates the A2A compression of signals which do not have an i.i.d. known distribution, and of multi-signal settings, where correlations among signals can be exploited. Finally, it proposes constructive schemes to achieve the fundamental limits using polar codes.

对于高维的模拟信号，依赖于整个信号的获取和量化的压缩方法可能并不总是可能的。因此，开发用于将信息直接从模拟域压缩到模拟(A2a)域的方法是有意义的。有两种原理已被证明成功地解决了通过模拟介质传递模拟信息的一般问题：香农理论方法和压缩传感方法。本研究探讨了第三种方法，它融合了香农理论方法的一般性和压缩感知方法的实用性。研究了单信号和多信号环境下A2A型压缩的基本极限，并提出了实现这些极限的建设性方案。A2A压缩的挑战是通过利用关于信号的先验知识来实现最大降维，即每次测量的信号维度的带宽降低系数，其可以包括但不限于稀疏性。Wu-Verdú证明了Renyi信息维度(RID)是I.I.D.的基本极限。已知分布的信号。RID是信息的非常粗略的度量，因为许多不同的信号导致相同的RID。这项研究调查了影响RID以外A2A压缩性能的其他信号特征，特别是在非渐近区域。它调查没有I.I.D.的信号的A2A压缩。以及多信号设置的已知分布，其中可以利用信号之间的相关性。最后提出了利用极性码实现基本极限的构造性方案。