An Exact Estimation Algorithm of Error Propagation Probability for Sequential Circuits

In advanced integrated circuit technology, the soft error tolerance is low. Soft errors ultimately lead to failure in VLSIs. We propose a method for the exact estimation of error propagation probabilities in sequential circuits whose FFs latch failure values. The failure due to soft errors in sequential circuits is defined using the modified product machine. The modified product machine monitors whether failure values appear at any primary output. The behavior of the modified product machine is analyzed with the Markov model. The probabilities that the failure values latched into the flip-flops (FFs) appear at any primary output are calculated from the state transition probabilities of the modified product machine. The time required for solving simultaneous linear equations accounts for a large portion of the execution time. We also propose two acceleration techniques to enable the application of our estimation method to larger scale circuits. These acceleration techniques reduce the number of variables in simultaneous linear equations. We apply the proposed method to ISCAS'89 and MCNC benchmark circuits and estimate error propagation probabilities for sequential circuits. Experimental results show that total execution times for the proposed method with two acceleration techniques are up to 10 times lesser than the total execution times for a naive implementation.