##### Performance and Reliability Analysis and Optimization in Sub-45nm CMOS Circuits

Probabilistic Error Propagation in a Logic Circuit Using the Boolean Difference Calculus — A gate level probabilistic error propagation model is presented which takes as input Boolean function of the gate, signal probability, the probability for signal being “1”, and error probability at the gate inputs, and the gate error probability and generates the error probability at the output of the gate. The presented model uses the Boolean difference calculus and can be efficiently applied to the problem of calculating the error probability at the primary outputs of a multi-level Boolean circuit with a time complexity which is linear in the number of gates in the circuit. This is done by starting from the primary inputs and moving toward the primary outputs by using a post-order (reverse DFS) traversal. Experimental results demonstrate the accuracy and efficiency of the proposed approach compared to the other known methods for error calculation in VLSI circuits.