Methods for Approximate Adders Reliability Estimation Based on PTM Model

Approximate adders have become a focus of approximate circuit design. However, there has been a lack of appropriate methods to evaluate their reliability. The existing analytical methods for accurate circuits cannot be applied to approximate circuits directly, and the Monte-Carlo simulation is time-consuming. Some metrics such as worst-case error, error distance, mean error distance and normalized error distance have been used to describe the reliability characters and arithmetic performance of approximate circuits, but they cannot directly calculate the reliability. This paper presents two methods for approximate adders reliability estimation based on the probabilistic transfer matrix (PTM) model. The first method takes the sum of the probabilities of all acceptable outputs as the probability of acceptable result corresponding to each input. The second method calculates the probability of acceptable result according to the deviation between the acceptable output and exact output. The reliability of approximate adders is calculated by combining the probabilities of the input vectors and those of the corresponding acceptable results. Experimental results demonstrate the validity and accuracy of the proposed methods.