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

在过去的50年里，错误控制编码在通信和数据存储行业取得了惊人的成功，实现了性能折衷，否则这是不可能的。然而，直到最近人们才认识到，编码理论在通信和存储以外的应用中也同样有用。特别地，本项目涉及数字电路设计领域中出现的许多问题。研究的问题来自广泛的技术范围，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-提供了一个显着的优势，从而使电路设计者能够实现原本不可能实现的系统权衡。具体而言，本项目开展的研究大致可分为以下四个重点领域：开发新的编码方案，以有效地解决和纠正下一代存储纳米器件，特别是纳米线交叉条的制造缺陷；基于最近突破性的浮动编码和秩调制编码思想的高密度闪存先进编码技术；开发编码方案，以降低功耗并避免VLSI电路中的串扰，特别强调片上和片外总线；将编码理论中一系列著名的组合问题应用于电路设计，包括覆盖阵列、分离码、相交码和定性独立集族。

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.