Aliasing probability transients

Test data reduction for digital systems is often accomplished through the use of a feedback shift register. This method, known as signature analysis, can exhibit error masking or aliasing. Recent analysis has shown that the use of a primitive polynomial for the register feedback can reduce the probability of aliasing. In this work we demonstrate that not all primitive polynomials are created equal. Some primitive polynomials can have very large transients in their aliasing probability. For example, 1 +X ¹³ +X ³³ can exhibit an aliasing probability more than a million times larger than its asymptotic value of 2^–33. An evaluation procedure is presented which can identify polynomials with good transient characteristics. Some recommended feedback polynomials are given.