CCF SHF(Small): Some Codes Applicable to Flash Memories and Computer Systems

在过去的六十年中，差错控制码被广泛地用于提高计算机、通信和超大规模集成电路系统的可靠性。如果不使用适当的编码方法，几种常见的电子设备（手机、计算机、医疗电子设备、GPS等）在这个建议中，首先，一些错误控制码的多级闪存进行了研究。尽管与单级单元相比，多级单元的使用增加了闪存的密度，但它也带来了两个主要挑战。第一个是状态之间的电压差变窄，因此存在由于噪声引起的高概率误差。在这种情况下的误差性质可以被认为是有限大小的对称误差。第二个挑战是，为了将单元从较高值编程为较低值，需要擦除整个数据块，然后需要将每个单元仔细编程为所需值。为了做到这一点，使用许多迭代将电子注入到浮置栅极。因此，这是非常耗时的操作。写入时的电平过冲可以被认为是有限幅度的非对称误差。因此，通过使用有限幅度的非对称纠错码，可以潜在地提高闪存的速度和可靠性。有限幅度纠错检测是编码理论中的一个新概念。针对这类有限幅值误差，研究了一些基本理论和有效的码设计方法。闪存在手机、照相机、计算机系统、嵌入式系统等方面有着广泛的应用。闪存的市场价值在数百亿美元的数量级，并将在未来几年继续增长。所提出的代码预计将有助于提高这些存储器和计算机系统的速度和可靠性。

In the past six decades error control codes have been extensively used to improve the reliability in computer, communication and VLSI systems. Without the use of appropriate coding methods several of the common electronics devices (cell phones, computers, medical electronics, GPS, etc.) will not function in a reliable manner.In this proposal, first, some error control codes for multilevel flash memories are investigated. Even though the use of multilevel cells increases the density of the flash memories compared to single level cells it also imposes two major challenges. The first one is that the voltage difference between the states is narrowed and hence there is a high probability of errors due to noise. The error nature in such cases can be considered as symmetric errors of limited magnitude. The second challenge is that, in order to program a cell from an higher value to a lower value an entire block of data needs to be erased and then each and every cell needs to be carefully programmed to the desired values. In order to do this, electrons are injected to the floating gates using many iterations. Thus, this is a very time consuming operation. The overshoot of levels while writing can be considered as asymmetric errors of limited magnitude. Thus, by using asymmetric error correcting codes of limited magnitude the speed and reliability of the flash memories can potentially be improved. The concept of limited magnitude error correction and detection is new in coding theory area. Some fundamental theory and efficient code design methods are investigated for these types of limited magnitude errors. The other research problems are related to efficient design of unordered codes and balanced codes.Flash memories find wide applications in cell phones, cameras, computer systems, embedded systems, etc. The market value of the flash memory is in the order of tens of billions of dollars and will continue to grow in the coming years. The proposed codes is expected to help improve speed and reliability of these memory and computer systems.