Bounds and analysis of aliasing errors in linear feedback shift registers
T.W. Williams, Wilfried Daehn, M. Gruetzner, C.W. Starke · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · 1988
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>