Closed Form Aliasing Probability For Q‐ary Symmetric Errors

Abstract

In Built-In Self-Test (BIST) techniques, test data reduction can be achieved using Linear Feedback Shift Registers (LFSRs). A faulty circuit may escape detection due to loss of information inherent to data compaction schemes. This is referred to as aliasing. The probability of aliasing in Multiple-Input Shift-Registers (MISRs) has been studied under various bit error models. By modeling the signature analyzer as a Markov process we show that the closed form expression derived for aliasing probability previously, for MISRs with primitive polynomials under q-ary symmetric error model holds for all MISRs irrespective of their feedback polynomials and for group cellular automata signature analyzers as well. If the erroneous behaviour of a circuit can be modelled with q-ary symmetric errors, then the test circuit complexity and propagation delay associated with the signature analyzer can be minimized by using a set of m single bit LFSRs without increasing the probability of aliasing.