• Estimation in a subspace of the variations space-. Measurement matrices in
Equations 3.5 and 4.9 are not full rank. Thus, we should not expect to
estimate variations of all gates; i.e., null space of the measurement matrix
A, X(A) = {y ∈ Rn∣Ay = 0}, is not accessible.
Assume Aκ is a measurement matrix that includes K measurements (delay
or power). For a large K (say K > 1ÛN, where N is the number of
gates), range of Aχ, cover almost whole the variation space that can be
measured. Hence, we use singular vectors of Aχ as the comparison space.
By estimation in ne subspace, we mean estimation in direction of the first
ne singular vectors of Aχ.
• As it is explained in Section 3.2, we use multi-voltage power measurements
to construct the measurement matrix.
• We have used the exponential correlogram function to generate the varia-
tions (see 2.2). We have used the same function as 7(⅛∙,u) in Section 3.4.
6.2 Power tomography results
In this section, we evaluate performance of the ⅞-∏orm optimization, the ^ɪ-norrn
regularization, and TUSC for the chip tomography.
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