Performance of signature registers in the presence of correlated errors

In signature analysis, aliasing is usually examined under the independent or the q-ary symmetric error model. In contrast to the independent error model, the q-ary error model assumes space correlation among outputs. However, both independent and q-ary error models assume that the errors resulting from consecutive test vectors are independent over time. This assumption is reasonable for combinational circuits but certainly unrealistic for sequential logic circuits as the outputs of a sequential circuit depend on the previous state as well as the current input vector. For this reason a new error model, called the generalised time dependent q-ary (GTDQ) error model, is proposed. This error extends the q-ary error model to consider both space and time correlation. A second parameter c is used to model the time correlation. By modelling the signature analyser as a Markov process the authors obtain a closed form expression for exact aliasing probability for arbitrary test length for a class of multiple-input-linear automata-signature-registers (MILASRs). An early verifiable criterion is given to determine whether a MILASR falls into this category. Finally, experimental results are provided for some real sequential circuits.