X-Canceling MISR architectures for output response compaction with unknown values

In this paper, an $X$-tolerant multiple-input signature register (MISR) compaction methodology that compacts output responses containing unknown $X$ values is described. Each bit of the MISR signature is expressed as a linear combination in terms of $X{\rm s}$ by symbolic simulation. Linearly dependent combinations of the signature bits are identified with Gaussian elimination and xored to remove $X$ values and yield deterministic values. Two $X$-canceling MISR architectures are proposed and analyzed with industrial designs. This paper also shows the correlation between the estimated result based on idealized modeling and the actual data for real circuits for error coverage, hardware overhead, and other metrics. Experimental results indicate that high error coverage can be achieved with $X$-canceling MISR configurations and it highly correlates with actual results.