Toward Hardware-Redundant, Fault-Tolerant Logic for Nanoelectronics

This article provides an overview of several logic redundancy schemes, including von Neumannʹs multiplexing logic, N-tuple modular redundancy, and interwoven redundant logic. We discuss several important concepts for redundant nanoelectronic system designs based on recent results. First, we use Markov chain models to describe the error-correcting and stationary characteristics of multiple-stage multiplexing systems. Second, we show how to obtain the fundamental error bounds by using bifurcation analysis based on probabilistic models of unreliable gates. Third, we describe the notion of random interwoven redundancy. Finally, we compare the reliabilities of quadded and random interwoven structures by using a simulation-based approach. We observe that the deeper a circuitʹs logical depth, the more fault-tolerant the circuit tends to be for a fixed number of faults. For a constant gate failure rate, a circuitʹs reliability tends to reach a stationary state as its logical depth increases.