Hardware Reference
In-Depth Information
Tabl e 3. 2
Synthesis results corresponding to a pair of errors
Errors
Synthesis result
Operation
ts
(s)
te
(s)
Resource
Location
State (1, 4):
Errors in
{Mix 1, Mix 4}
Re-Mix 4
15
18
2 4 Mixer
(2, 2)
Mix 5
18
21
2
4 Mixer
(2, 2)
State (1, 5):
Errors in
{Mix 1, Mix 5}
Operation
ts
(s)
te
(s)
Resource
Location
Re-Mix 5
21
24
2
4 Mixer
(6, 4)
3.2.3
Dictionary Entries for Multiple-Operation Errors
Based on the re-synthesis solutions corresponding to single-error cases, we can
further explicitly consider all the cases with more than one error and generate
the re-synthesis resolutions. Consider the dictionary entries shown in Table
3.1
.
Assume that an error has already occurred at Mix 1 and the FSM running on the
FPGA has entered State 1. For the re-synthesis solution in State 1, there are three
operations: Mix 4, Mix 5, and Re-Mix 1; here Re-Mix 1 is the recovery operation
for Mix 1. Since we assume that no errors occur in error recovery operations, only
Mix 4 and Mix 5 are considered as candidates for the next error, and we need to
generate recovery solutions for both of them. Finally we derive the re-synthesis
results corresponding to pairs of errors {Mix 1, Mix 4} and {Mix 1, Mix 5}; see
Tab le
3.2
. These solutions are stored as two entries at the second level of the error
dictionary. The “parent node” of these two entries is the entry that corresponds to
the solution for the single error in Mix 1.
Note that each entry that corresponds to the occurrence of multiple errors
contains only the re-synthesis result from the time moment that the latest error is
detected to the time moment that the entire bioassay is finished. For example, the
dictionary entry that corresponds to State (1, 4) shown in Table
3.2
contains two
error operations, i.e., Mix 1 and Mix 4. According to the synthesis results shown
in Table
3.1
, the error that occurs in Mix 1 is detected earlier than the error that
occurs in Mix 4. Therefore, the dictionary entry records the re-synthesis result from
the 15th second (i.e., the time moment that the error occurs in operation Mix 4
is detected) to the 21st second (i.e., the time moment that the entire bioassay is
completed). The time span of this dictionary entry is 6 s.
3.2.4
Consideration of Error-Recovery Cost and Reduction
in the Number of Dictionary Entries
For low-cost disposable biochips, the cost of samples and reagents used in the
experiments can be higher than the cost of biochips. When an error occurs on
the biochip, the additional number of droplets needed in error recovery needs to
