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.
