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Aliasing Errors in Signature in Analysis Registers

The authors discuss aliasing errors in signature analysis registers for self-testing networks and review analytical results. The results show that when p, the probability that an error will occur at a network output, is close to 1/2, there is a bound of the aliasing error. The analysis uses a graph to represent the probability of transition, the Markov process, and z-transforms to analyze the behavior of the signature analysis register. For very small p(p¿0) and very large p(p¿1), the aliasing error solution for primitive polynomials is a series of terms (1-¿)n in magnitude (where n is the number of random patterns being applied to the network or the length of the network output sequence). As compared with nonprimitive polynomials, whose solution is n(1-¿)n or n2(1-¿)n, in general primitive polynomials are much better with respect to aliasing. Simulation results are shown for aliasing errors for these polynomials, which give insight as to how aliasing occurs.