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.
