An analysis of the probabilistic behavior of linear feedback signature registers

The authors present an analysis technique useful for studying the probabilistic behavior of signature analysis registers, which is in turn useful for studying the aliasing problem. The technique is applicable to all linear-feedback signature analysis registers, i.e. characterized by any linear-feedback polynomial, including multiple-input signature registers. The basis for the technique is the calculation of a sequence of probabilities where the ith element of the sequence corresponds to the probability that one particular stage of the linear-feedback signature register (LFSR) is in the state 0 or 1 after the ith bit has been shifted in the LFSR. The complexity for calculating such a single-stage state probability sequence is linear in time and space. The authors generalize such sequences to k-stage state probability sequences