Fault-tolerant analysis of TMR design with noise-aware logic

Due to the effect of thermal noise, ground bounce and process variations in nanometer process, the behavior of any logical circuit becomes increasingly probabilistic. In this paper, based on the noise model 5] on the input and output nodes of a probabilistic CMOS (PCMOS) gate, the correctness probabilities of four PCMOS primitive gates, NOT, NAND, NOR and XOR, can be firstly computed. Based on the concept of the probabilistic transfer matrices (PTMs) and the corresponding operations on PTMs for the serial and parallel compositions of the components in a well-formed circuit, the correctness probability of the output in a 3-input PCMOS majority circuit in a triple modular redundancy (TMR) design can be further computed. For a given circuit with smaller error, it is well known that a TMR design has good fault-tolerant characterization and the correctness probability of the original output is converged to 1. Under the use of noise-aware logic in a TMR design, it is obvious that the fault-tolerant characterization of a TMR design is degraded and the correctness probability of the original output is not converged to 1. The experimental results show that the improvement region of the correctness probability of the original output will be narrowed due to the noise effect on the gates in a 3-input PCMOS majority circuit.