Majority multiplexing-economical redundant fault-tolerant designs for nanoarchitectures

Motivated by the need for economical fault-tolerant designs for nanoarchitectures, we explore a novel multiplexing-based redundant design scheme at small (≤100) and very small (≤10) redundancy factors. In particular, we adapt a strategy known as von Neumann multiplexing to circuits of majority gates with three inputs and for the first time exactly analyze the performance of a multiplexing scheme for very small redundancies, using combinatorial arguments. We also develop an extension of von Neumann multiplexing that further improves performance by excluding unnecessary restorative stages in the computation. Our results show that the optimized three-input majority multiplexing (MAJ-3 MUX) outperforms the latest scheme presented in the literature, known as parallel restitution (PAR-REST), by a factor between two and four, for 48≤R≤100. Our scheme performs extremely well at very small redundancies, for which our analysis is the only accurate one. Finally, we determine an upper bound on the maximum tolerable failure probability when any redundancy factor may be used. This bound clearly indicates the advantage of using three-input majority gates in terms of reliable operation.