Physical redundancy for defect tolerance : example designs and fundamental limits

Abstract

This project analyzes designs for physical redundancy which are modeled abstractly as a bipartite graph. The goal is to determine the characteristics of graph structures which optimize the trade-off between the number of edges and the number of redundant components or nodes needed while correcting a deterministic number of worst-case errors. This thesis looks at finite-sized designs, asymptotically large designs with finite error correcting values, and designs with asymptotically large error correcting values. Results include some small optimal graph structures and fundamental limits on what the optimal design structure can achieve for the cases where a small number of errors are corrected and for where the number of errors to be correctly grows asymptotically.