4.3.3 Gates on the irregular grids
As we saw in Section 3.3.3, in practice because of area and logic gate constraints,
the gates are not located on regular grids. An example of gate placement is shown
in Figure 3.6. Similar to Section 3.3.3, we overcome this problem by using a dense
regular grid such that the center of each gate is close to some grid point for all
the gates in the circuit. We assign the variation of each gate gu to the point on
the regular grid that is closest to the center of the gate. If there are more than
one closest points, we select one of them randomly. The remaining grid points
are assigned to free variables that do not correspond to physical gates and do not
affect the measurements.
The remainder of the measurement process is similar to Section 4.3.2. The
points on the regular grid are mapped to a column vector 1 which is measured by
a measurement matrix A as in Equation 4.11. Note that if the г-th element of
the 1 is a free variable not assigned to any gate variation, then г-th column of A is
zero. The vector 1 is still spatially correlated, and therefore sparse in the wavelet
domain, and can be recovered through s in Equation 4.12. From the recovered 1
the free variables can be ignored since they do not correspond to physical gates.
50
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