CAREER: A Unified Approach to Iterative and Universal Methods for Signal Processing and Communications

辛格摘要：将理论方法应用到实际系统中最困难的方面之一是将现实世界的问题转化为可管理的理论模型。通常，问题的许多方面要么难以简明建模，要么完全未知。例如，在许多商业和军事应用中，需要能够在各种可能的环境中运行的紧凑、高效的设备。这项研究正在开发一个框架，用于明确地处理无线和水声通信、信号估计和检测以及预测等重要领域中的这种不确定性。特别是，这项研究利用了信息论文献中一些新的和令人兴奋的方法来处理不确定性和复杂性。在无损信源编码和竞争性在线算法的当代应用的推动下，正在通过开发稳健的信号处理方法来解决不确定性和可变性问题。这种通用算法可以为处理各种自适应估计问题中的不确定性提供一种特别有效的手段。这些策略包括通用估计和均衡策略，它们可以在没有信号或信道的先验知识的情况下渐进地实现调谐到所使用的信号或信道的最优滤波器的性能。通过使用在研究Turbo码和低密度奇偶校验码中使用的图形模型和迭代处理技术，这些算法可以实际实现并集成到复杂度相对较低的更大系统中。像因子图这样的迭代算法为通常单独处理的各种任务的联合优化提供了自然的框架。受迭代译码和Turbo码接近容量性能的激励，本研究正在开发实用、高效的迭代算法，用于单用户和多用户信道上符号间干扰的数字通信的联合检测、估计和译码。这一研究计划的教育部分包括在本科生和研究生层面上的重大课程开发，以及在研究生指导方面的大力投资。这项研究的一个关键方面包括本科生积极参与正在进行的研究。歌手努力水平声明：在推荐的支持水平上，安德鲁·辛格将尽一切努力满足该项目最初的努力范围和水平。

Singer ABSTRACT:One of the most difficult aspects of the application of theoretical methods to practical systems lies in the translation of a real-world problem into a manageable theoretical model. Often there are a number of aspects of the problem that are either difficult to model concisely, or that are completely unknown. For example, in many commercial and military applications, compact, efficient devices are desired that can operate in a wide range of possible environments. This research is developing a framework for explicitly dealing with such uncertainties in a number of important areas such as wireless and underwater acoustic communications, signal estimation and detection, and forecasting.In particular, this research leverages some of the new and exciting methods for dealing with uncertainty and complexity from the information theory literature. Problems of uncertainty and variability are being addressed through the development of robust signal processing methods motivated by contemporary applications in lossless source coding and competitive on-line algorithms. Such universal algorithms can provide a particularly effective means for handling uncertainty in a variety of adaptive estimation problems. These include universal estimation and equalization strategies which without prior knowledge of the signal or channel can asymptotically achieve the performance of the optimal filter tuned to the signal or channel in use. These algorithms can be practically implemented and integrated into larger systems with relatively low complexity through the use of graphical models and iterative processing techniques used in the study of turbo codes and low-density parity check codes. Iterative algorithms such as factor graphs provide a natural framework for the joint optimization of a variety of tasks typically treated separately. Motivated by the near-capacity achieving performance of iterative decoding and turbo-codes, this research is developing practical, efficient iterative algorithms for joint detection, estimation and decoding of digital communications over single and multi-user channels with inter-symbol interference. The educational component of this research program includes significant curriculum development at both the undergraduate and graduate levels, and a strong investment in the mentoring of graduate students. A key aspect of this research includes the active involvement of undergraduates in ongoing research.Singer LEVEL OF EFFORT STATEMENT:At the recommended level of support, Andrew Singer will make every attempt to meet the original scope and level of effort of this project.