Aliasing errors in linear automata used as multiple-input signature analyzers

This paper deals with the aliasing probability of multiple-input data compressors used in self-testing networks. It is shown that a far more general class of linear machines than linear feedback shift registers can be used for data compression purposes. The function of these machines is modeled by a Markov process. The steady-state value of the aliasing probability is shown to be the same as for single-input signature analysis registers. An easily verifiable criterion is given that allows one to decide whether a given linear machine falls into this class of multiple-input data compressors. The steady-state value of the aliasing probability is shown to be independent of the correlation of the data streams at the inputs of the data compressor. Two kinds of circuits are analyzed in more detail with respect to their aliasing properties: linear feedback shift registers with multiple inputs, and linear cellular automata. Simulation results show the effect of the next-state function on the steady-state value of the aliasing probability and the effect of correlation on the transient response.