ALIASING PROBABILITY FOR MULTIPLE INPUT SIGNATURE ANALYZER

Formulation of closed form expressions for computing M1SR aliasing probability exactly had remained an unsolved problem. This paper presents single and multiple MISR aliasing probability expressions for arbitrary test lengths. A framework, based on algebraic codes, is developed for the analysis and synthesis of MISR-based test response compressors for BIST. This framework is used to develop closed form expressions for aliasing probability of MISR for arbitrary test length (so far only bounds have been formulated). A new error model, based on q-ary symmetric channel, is proposed using more realistic assumptions. Results are presented that provide the weight distributions for q-ary codes (q = 2m, where the circuit under test has m outputs). These results are used to compute the aliasing probability for the MISR compression technique for arbitrary test lengths. This result is extended to compression using two different MISR's. It is shown that significant improvements can be obtained by using two signature analyzers instead of one. This paper makes a contribution to coding theory as well. It provides the weight distribution of a class of codes of arbitrary length. Also formulated is an expression bounding from above the probability of undetected error for these codes. The distance-3 Reed-Solomon codes over GF(2m) become a special case of our results. © 1990 IEEE