Collaborative Research: Coding for Nano-Devices, Flash Memories, and VLSI Circuits

在过去的50年里，差错控制编码在通信和数据存储行业中取得了惊人的成功，实现了否则不可能实现的性能折衷。然而，直到最近才认识到，编码理论在通信和存储以外的应用中也同样有用。特别是，这个项目涉及到数字电路设计领域出现的许多问题。研究的问题来自广泛的技术，从纳米级电路和存储芯片到更传统的VLSI架构。在每种情况下，这些问题都是底层介质或系统的物理特性所固有的。在每一种情况下，该项目旨在表明，复杂的编码--基于深深植根于代数和组合编码理论的方法和思想--提供了显着的优势，从而使电路设计人员能够实现否则不可能实现的系统权衡。具体来说，该项目中进行的研究可以大致细分为以下四个重点领域：开发新的编码方案，用于有效解决和纠正下一代存储器纳米器件，特别是纳米线交叉开关的制造缺陷;基于最近突破性的浮动代码和秩调制编码思想，用于高密度闪存的先进编码技术;在超大规模集成电路中减少功率损耗和避免串扰的编码方案的发展，特别强调片内和片外总线在电路设计中应用编码理论中一系列著名的组合问题中发展起来的技术，包括覆盖阵列，分离码，交叉码和定性独立集族。

Over the past 50 years, error-control coding has been employed with spectacular success by the communications and data storage industries to achieve performance trade-offs that would have been otherwise impossible. What has been recognized only recently, however, is that coding theory could be just as useful in applications other than communications and storage. In particular, this project is concerned with numerous problems that arise in the area of digital circuit design. The problems studied come from a wide spectrum of technologies, ranging from nanoscale circuits and memory chips to more conventional VLSI architectures. In each case, these problems are inherent to the physics of the underlying medium or system. In each case, the project aims to show that sophisticated coding --- based upon methods and ideas deeply rooted in algebraic and combinatorial coding theory --- offers a significant advantage, thereby enabling circuit designers to achieve system trade-offs that would have been otherwise impossible.Specifically, the research carried out in this project can be roughly subdivided into the following four focus areas: Development of new coding schemes for efficient addressing and correction of manufacturing defects in next-generation memory nano-devices, in particular the nano-wire crossbar; Advanced coding techniques for high-density flash memories, based upon ground-breaking recent ideas of floating codes and rank-modulation coding; Development of coding schemes to reduce power dissipation and to avoid cross-talk in VLSI circiuts, with particular emphasis on both on-chip and off-chip buses; Applications to circuit design of the techniques developed in a range of well-known combinatorial problems in coding theory, including covering arrays, separating codes, intersecting codes, and qualitatively independent set families.