SHF: Small: Some Error Correcting Codes for Computer Systems

错误控制码在实现现代计算机系统、DVD、照相机等的高可靠性操作中发挥着重要作用。在该项目中，将开发适用于高密度闪存的新的纠错码类。闪存的市场收入估计为每年1000亿美元。PI与领先的闪存行业（美光）密切合作。虽然这使得纠错码的开发特别是在应用的实际背景下，这项研究的结果不仅可以很容易地过渡到行业，它还将通过讲座，研讨会和课程开发在PI机构培训学生，博士后和未来的行业研究人员。在本项目中，将考虑多级闪存，其中每个单元可以具有4或8个电压电平。实验表明，闪存的误码率随着编程/擦除次数的增加而增加。此外，据观察，大多数的错误是有限的大小和减少类型。错误特性的错误统计研究证明，L1距离码更适合于克服闪存中的错误。新的类的L1距离码将使用基本对称函数的概念来开发。该项目还将考虑在高速数据总线和通信系统中插入和删除重复符号的纠错码的设计。此外，理论和代码开发的闪存可以潜在地扩展到设计高效的高阶谱空码的光盘和磁存储器。

Error control codes play a major role in achieving high reliable operations of modern computer systems, DVDs, cameras, etc. In this project new classes of error correcting codes suitable for high density flash memories are to be developed. The market revenue of flash memories is estimated to be $100B per year. The PI has close collaboration with leading Flash memory industry (Micron). While this enables development of error correcting codes specifically in the practical context of applications, the results of this research will not only be easily transitioned to industry, it will also train students, postdocs and future industry researchers via lectures, seminars and course development at the PIs institution. In this project, multi-level flash, in which each cell can have 4 or 8 voltage levels, will be considered. Experiments indicate that the bit error rate of flash memory worsens as the Program/Erasure count increases. In addition, it is observed that most of the errors are of limited magnitude and of decreasing type. Study of error statistics of error characteristics justify that the L1 distance codes are more suitable to overcome errors in flash memories. New classes of L1 distance codes are to be developed using the concepts of elementary symmetric functions. The project will also consider the design of error correcting codes for insertion and deletion of repeated symbols in high speed data bus and communication systems. Furthermore, the theory and codes to be developed for flash memories can potentially be extended to design efficient high-ordered-spectral-null codes for optical discs and magnetic memories.