CCF-BSF: CIF: Small: Coding Techniques for Emerging Storage Technologies.

磁介质和闪存是目前存储海量数据的主要平台。随着对存储容量需求的增长，人们正在探索新的方法来增加这种介质的密度，并且正在开发新的纳米级技术，例如基于忆阻器的存储器。该项目涉及分析这些新兴存储技术的信息存储能力的基本限制，以及设计接近这些限制的编码方案。该项目的理论部分需要信息理论和离散数学的新方法，而新的编码技术的发展将理论的范围扩展到实践中，加速了新的商业技术的发展。该项目为研究生提供了一个刺激的研究环境，并有助于电气工程和计算机科学课程的发展。在磁存储领域，研究了晶粒和伊辛通道容量的下界和上界；在这些信道中纠正错误的编码结构；并将这些结果推广到非二进制信道模型。多电平闪存的研究涉及一维胞间干扰信道容量边界的计算；构建在一、二、三维空间对抗细胞间干扰的代码；并设计代码，以减轻细胞的磨损和擦除程序在闪存中的不对称性。对于基于忆阻器的存储器，研究课题包括设计对行和列具有权值约束的二维码；二维权重约束数组覆盖到另一个约束数组的快速方法设计以及对约束的汉明连通性概念的研究。

Magnetic media and flash memories are currently the main platforms used for mass data storage. As the need for storage capacity grows, new methods are being explored to increase the density in such media, and new nano-scale technologies, such as memristor-based memories, are being developed. This project concerns the analysis of fundamental limits on the information storage capability of these emerging storage technologies, as well as the design of coding schemes to approach those limits. The theoretical component of the project requires new approaches in information theory and discrete mathematics, while the development of new coding techniques extends the reach of the theory into practice, hastening the evolution of new commercial technologies. The project provides a stimulating research environment for graduate students, and contributes to curriculum development in electrical engineering and computer science. In the domain of magnetic storage, the research addresses lower and upper bounds on the capacity of grain and Ising channels; the construction of codes that correct errors in these channels; and the extension of these results to non-binary channel models. The research on multilevel flash memories involves computing bounds on the capacity of the one-dimensional inter-cell interference channel; constructing codes that combat inter-cell interference in one, two, and three dimensions; and designing codes that mitigate the wear of cells and the erase-program asymmetry in flash memories. For memristor-based memories, research topics include the design of two-dimensional codes with weight constraints on the rows and columns; the design of fast methods for overwriting a two-dimensional weight-constrained array onto another constrained array; and the study of the notion of Hamming connectedness of constraints.