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Bounds and analysis of aliasing errors in linear feedback shift registers

Aliasing errors in linear feedback shift registers (LFSRs) used as signature analysis registers in self-testing networks are considered. A bound on aliasing is established by a straightforward algebraic analysis of LFSRs. It is calculated as a function of p, the probability of an error occurring at an output of the network under test. This bound is robust but is only good for p close to 1/2. To investigate the question of what happens to aliasing errors in general, the function of LFSRs is modeled by a Markov process and a solution is obtained by the z-transform. It is shown that for p>1/2 the aliasing probability for primitive polynomials converges much faster to the final steady-state value than for nonprimitive polynomials. For values of p >