Aliasing Probability Research Articles

Cyclic code weight spectra and BIST aliasing

In built-in self-test for logic circuits, test data reduction can be achieved using a linear feedback shift register. The probability that this data reduction will allow a faulty circuit to be declared good is the probability of aliasing. Based on the independent bit-error model, we show that the code spectra for the cyclic code generated by the feedback polynomial can be used to obtain an exact expression for the aliasing probability of a multiple input signature register when the test length is a multiple of the cycle length. Several cases are examined and, as expected, primitive feedback polynomials provide the best performance. Some suggestions to avoid peaks in the aliasing probability are given.

Circuit behavior modeling and compact testing performance evaluation

A realistic modeling of circuit output error patterns with random test inputs is suggested. The model can be used as the basis for accurate evaluation of the probability of aliasing in compact testing. For several example compression techniques, the following aspects are investigated: identification of the error patterns that cause aliasing; asymptotic effectiveness analysis; and comparative simulation study with a limited number of random test vectors applied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An analysis of the aliasing probability of multiple-input signature registers in the case of a 2/sup m/-ary symmetric channel

The aliasing probabilities of multiple-input signature registers (MISR) with m inputs for a 2/sup m/-ary symmetric channel, where each of the (2/sup m/-1) possible errors is equally likely, are analyzed. For this error model, the aliasing probabilities of MISRs are analyzed using the weight distributions of maximum-distance-separable (MDS) codes. The results show that the aliasing probabilities over the 2/sup m/-ary symmetric channel do not depend on the polynomials that characterize the MISRs. That is, for the 2/sup m/-ary symmetric channel, the aliasing probability of an MISR based on a primitive polynomial is exactly the same as one based on a nonprimitive one. In addition, it is observed that the aliasing probabilities, P/sub al/ (n), as a function of test length n, are monotonous for error probabilities p=0.2, 0.4, and 0.8. The aliasing probabilities of multiple MISRs based on Reed-Solomon codes are analyzed again for the 2/sup m/-ary symmetric channel, using the weight distributions of Reed-Solomon codes, which are MDS codes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comments on "Signature analysis for multiple output circuits" by R. David

The probability of a fault-free signature has been calculated in the above-named paper (see ibid., vol.C-35, no.9, p.830-7 (1986)) and in an earlier paper by the same author (see ibid., vol.C-29, no.7, p.668-73 (1980)). Implicitly, it was considered as the probability of masking due to signature analysis. It is shown here that this does not correspond exactly to the probability of aliasing. A new definition is given. The difference centers on the event where there are no bit errors in the data to be compressed. When the response of the circuit is correct, the signature is fault-free. However, there is no aliasing. >

An analytical model for the aliasing probability in signature analysis testing

The Markov chain model of linear feedback shift-registers (LFSRs) for signature analysis testing is analytically solved to obtain the exact expression of the aliasing error probability as a function of test length, error probability, and the structure of the feedback network. The dependence on feedback configuration is explored in depth, and it is proven that maximum-length LFSRs have the best performances with respect to aliasing, regardless of the particular structure of their feedback network. Simplified expressions of aliasing probability are also derived for use as practical tools to design LFSRs for IC signature analysis testing, and a heuristic criterion is given for the identification of peaks in aliasing probability. >