A Statistical Theory of Digital Circuit Testability

Formulation of closed form expressions for computingMISR aliasing probability exactly had remained an unsolved problem.This paper presents single and multiple MISR aliasing probability expres-sions for arbitrary test lengths. A framework, based on algebraic codes,is developed for the analysis and synthesis of MISR-based test responsecompressors for BIST. This framework is used to develop closed formexpressions for aliasing probability of MISR for arbitrary test length(so far only hounds have been formulated). A new error model, basedon q-ary symmetric channel, is proposed using more realistic assump-tions. Results are presented that provide the weight distributions forq-ary codes( q = 2m, where the circuit under test has m outputs).These results are used to compute the aliasing probability for the MISRcompression technique forarbitrary test lengths. This result is extendedto compression using two different MISR’s. It is shown that significantimprovements can be obtained by using two signature analyzers insteadof one. This paper makes a contribution to coding theory as well. Itprovides the weight distribution of a class of codes of arbitrary length.Also formulated is an expression bounding from above the probability ofundetected error for these codes. The distance-3 Reed-Solomon codesover GF(2m)become a special case of our results.