Hardware Reference
In-Depth Information
Tabl e 3. 9
Compaction ratio
of Method I and Method II
corresponding to different
values of N
max
in
interpolation-based dilution
bioassay
S
O
S
I
S
II
N
max
(MB)
R
I
I
(MB)
R
II
II
(MB)
3
14.29
20.51
0.97
0.84
29.83
1.53
0.58
5
17.51
20.74
1.05
0.94
30.19
1.67
0.64
8
21.72
20.77
1.03
1.02
30.27
1.64
0.70
respectively. When N
max
D
3, the histogram for the time span of effective dictionary
entries is shown in Fig.
3.9
b.
The error dictionary can be compacted by Method I and Method II discussed
in Sect.
3.5
. When setting the value of N
max
as 3, 5, and 8, the corresponding
simulation results are presented in Table
3.9
. The parameters of Table
3.7
are defined
in Sect.
3.8.1
.
In the realistic fault simulation setup considered here, we set the distribution
function of R
c
as r
c
N.1; 0:035
2
/. We run the parameter various-aware fault
simulation for 1000 times. When a droplet is split by electrowetting forces F
1
and
F
2
,and
k
F
1
k
kF
2
k
1:10 (or
k
F
2
k
kF
1
k
1:10), then we assume that an error occurs.
Among the simulation results of the 1,000 runs, 426 runs have one error
occurring, 129 runs have two errors, and none of the runs lead to more than two
errors. The simulation results corresponding to five runs can be found in Table
3.8
.
We can find that the response time and the total completion time of the bioassay are
reduced using the proposed dictionary-based re-synthesis procedure.
3.8.3
Mixing Tree Bioassay
In this part, we present the simulation results for a biochemical benchmark designed
in [
23
]. The biochemical benchmark is a solution preparation procedure, which has
seven different kinds of reagent. The sequencing graph of the benchmark can be
found in Fig.
3.10
[
23
]. The final output is the droplet which has the mixing ratio
of 2
W
3
W
5
W
7
W
11
W
13
W
87 [
23
]. The bioassay has 37 operations, and the
number of droplets consumed is 10. When the bioassay runs on an 8
8 array,
the completion time of the bioassay is 60 s. For all the 740 dictionary entries, the
numbers of droplets consumed in error recovery are no more than 4. This is because
in the protocol of mixing tree bioassay, each mixing/dilution operation generates a
redundant copy droplet. These redundant droplets are stored on the biochip and they
can be utilized during error-recovery process. Hence only a small number of extra
droplets need to be dispensed for recovering the errors.
For compaction Method I, the compaction ratios for the dictionary entries vary
from 2:1 to 13:4. The average compaction ratio for these entries is 4:8 and the
standard deviation is 3:2. For compaction Method II, the compaction ratios for the
dictionary entries vary from 2:8 to 18:2. The average compaction ratio for these
entries is 6:6 and the standard deviation is 4:4. The size of the error dictionary can
be reduced from 6:15 to 1:18 MB (Method I) and 0:87 MB (Method II).
