Using the Berlekamp-Massey algorithm to obtain LFSR characteristic polynomials for TPG

In built-in test pattern generation, a test cube is usually encoded or compressed by a seed vector that is used as the initial state of a Linear Feedback Shift Register (LFSR). The seed vector is found by solving a linear system of equations using a fixed (but arbitrarily chosen) characteristic polynomial for the LFSR In contrast, finding the LFSR characteristic polynomial to generate a given test cube provides more design freedom but results in a non-linear system of equations. In this paper, we address the latter problem using the Berlekamp-Massey (BM) algorithm. The BM algorithm is very efficient and obviates the need of solving a non-linear system, but it cannot work with don't care values. We present therefore a procedure that assigns the don't cares in a given test cube in such a way so as to minimize the resulting polynomial found by BM. Experimental results demonstrate the substantial improvement over a previous technique that assigns the don't cares greedily.