Hardware Reference
In-Depth Information
Tabl e 3. 7
Compaction ratios
of Method I and Method II
corresponding to different
values of N
max
in exponential
dilution bioassay
S
O
S
I
S
II
N
max
(MB)
R
I
I
(MB)
R
II
II
(MB)
2
21.12
24.13
4.43
0.90
34.89
6.12
0.62
3
21.61
24.23
4.53
0.93
34.98
6.26
0.64
5
24.77
24.09
4.45
1.12
34.77
6.11
0.77
8
28.75
23.82
4.25
1.40
34.47
5.89
0.96
the 4,747 effective dictionary entries vary from 5 to 237 s. One of the dictionary
entries with the shortest time span corresponds to the error that occurs at the 208th
second; after recovering from the error, the entire bioassay is finished at the 213th
second. Therefore, the time span of this dictionary entry is 5 s. One of the longest
dictionary entries corresponds to two errors that occur at the 15th and 22nd second,
respectively; after recovering from these two errors, the entire bioassay finishes at
the 259th second. Hence, the time span of this dictionary is 237 s. Figure
3.7
bshows
the histogram for the time spans of the 4,747 effective dictionary entries.
The “coverage rate” shown in Table
3.6
is defined as the ratio between the
number of effective entries and the total number of entries in the error dictionary.
We find that recovery for 74.92 % of the errors that occur in a bioassay can be
accomplished using no more than two extra droplets.
3.8.1.2
Compaction for Error Dictionaries
The error dictionary can be compacted through Method I and Method II discussed
in Sect.
3.5
. When we set the value of N
max
as 2, 3, 5, and 8, the number of effective
entries in the error dictionary are different. In Table
3.7
, the original size of the
“effective error dictionary” is written as S
O
; the mean values for the compaction
ratios of all effective dictionary entries are written as R
I
(derived by Method I) and
R
II
(derived by Method II), respectively; the standard deviations for the compaction
ratio of all effective dictionary entries are written as
I
(derived by Method I) and
II
(derived by Method II), respectively. Finally, the sizes of the dictionary after
compaction are written as S
I
(derived by Method I) and S
II
(derived by Method II),
respectively.
From Table
3.7
, we can find that the total memory required to store the original
effective error dictionary is 21.12
28.75 MB, which is much larger than memory
available on a low-cost FPGA. After compaction, the final size of the compacted
dictionary can be smaller than 1 MB.
3.8.1.3
Fault Simulation Results
After the generation and compaction of the error dictionary, next we run fault
simulation for the exponential dilution bioassay.
