Closed Form Aliasing Probability For Q-ary Symmetric Errors

Geetani Edirisooriya

doi:10.1155/1996/29412

Abstract

In Built-In Self-Test (BIST) techniques, test data reduction can be achieved using Linear Feedback Shift Registers (LFSRs). A faulty circuit may escape detection due to loss of information inherent to data compaction schemes. This is referred to as aliasing. The probability of aliasing in Multiple-Input Shift-Registers (MISRs) has been studied under various bit error models. By modeling the signature analyzer as a Markov process we show that the closed form expression derived for aliasing probability previously, for MISRs with primitive polynomials under q-ary symmetric error model holds for all MISRs irrespective of their feedback polynomials and for group cellular automata signature analyzers as well. If the erroneous behaviour of a circuit can be modelled with q-ary symmetric errors, then the test circuit complexity and propagation delay associated with the signature analyzer can be minimized by using a set of m single bit LFSRs without increasing the probability of aliasing.

Highlights

A digital circuit can be tested by applying an appropriate set of test vectors to its inputs and comparing the actual response of the circuit with the correct or desired response
Aliasing in single input linear feedback shift registers (LFSRs) and Multiple-Input Shift-Registers (MISRs) have been studied by several researchers [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] under various bit error models to compute Pal" In this work we use the q-ary error model which considers correlated errors among Circuit Under Test (CUT) outputs 10,15,16]
We show that if the output error patterns of a faulty CUT can be approximated by the q-ary error model, the propagation delay due to feedback path can be minimized by using a set of m single bit Linear Feedback Shift Registers (LFSRs) without increasing the probability of aliasing

Summary

INTRODUCTION

A digital circuit can be tested by applying an appropriate set of test vectors to its inputs and comparing the actual response of the circuit with the correct or desired response. Aliasing in single input linear feedback shift registers (LFSRs) and MISRs have been studied by several researchers [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] under various bit error models to compute Pal" In this work we use the q-ary error model which considers correlated errors among Circuit Under Test (CUT) outputs 10,15,16]. In section (2) we derive a closed form expression for aliasing probability for MISRs and group cellular automata signature registers using the q-ary symmetric error model. In section (4) we conclude with a brief summary

EXACT ALIASING PROBABILITY

MINIMUM COMPLEXITY MISR

DISCUSSION AND CONCLUSIONS