Hardware Reference
In-Depth Information
of the D/M phase, i.e., part of the mixer works as a “storage” unit. Therefore, in the
synthesis approach, there is no need to assign specific storage modules. An example
is as follows. S
1
and S
2
in Fig.
4.3
e represent the storage units inside the mixers
assigned to operations 1 and 2, respectively. Since the execution region of operation
6 overlaps with S
1
and S
2
, the outputs of mixing operations 1 and 2 can be directly
“fed” into operation 6 with no module-to-module transportation. After operation 6
is completed, the storage unit for the product droplet of operation 6 will overlap
with either S
1
or S
2
.
In this way, the module-placement and schedule for operations 1, 2,and6 are
obtained. After operation 6 is finished, the execution region of operation 6 will be
assigned for operation 8.
Next, operations 1, 2, 6,and8 are packaged as a “macro-operation” M
S
L
;
similarly, operations 3, 4, 7,and9 are packaged as M
S
R
asshowninFig.
4.3
f. The
schedule for operations 1
4 and 6
9 are:
f
1; 2; 3; 4
g
S
1
,
f
6; 7
g
S
2
,and
f
8; 9
g
S
3
.
Similarly, the placement of modules for M
S
L
, M
S
R
and N
R
in Fig.
4.3
f can be
determined based on their interdependency. The module for M
S
L
will be placed
“beside” the region occupied by M
S
R
, and after the completion of M
S
L
and M
S
R
,
N
R
will be mapped to the same region that is assigned to M
S
L
and M
S
R
.Inthis
way the schedule and resource assignment results for all the operations shown in
Fig.
4.3
a can be derived level by level.
Suppose we arbitrarily pick a node N
R
from the directed-tree structure shown in
Fig.
4.3
a, and label the set of operations on the left and right sub-trees of N
R
as S
L
and S
R
, respectively. Then the derived synthesis results of the proposed operation-
interdependency-aware synthesis algorithm have the following three characteristics:
Characteristic 1
: Operations in
S
L
and
S
R
are executed in two separate regions of
the biochip, i.e., they do not share any on-chip resources.
Characteristic 2
: Assume that
E
S
L
and
E
S
R
are the sets of electrodes where
operations in
S
L
and
S
R
are conducted, respectively, and
E
N
R
is the set of electrodes
that is assigned to operation
N
R
, then we have:
E
N
R
.E
S
L
[
E
S
R
/
.
Characteristic 3
: If the storage units assigned for operations in
S
L
and
S
R
are
written as
S
S
L
and
S
S
R
, respectively, and the storage unit assigned to operation
N
R
is written as
S
0
N
R
, then we have:
S
0
N
R
.S
S
L
[
S
S
R
/
.
Based on Characteristic 2, we conclude that the resource bound to an operation
(i.e., the module-placement) is determined in turn by its predecessor operations. For
a sequencing graph with a directed-tree structure, the resources for other operations
can be easily determined when resources assigned to operations represented by leaf
nodes are established.
For instance, the synthesis result for the sequencing graph shown in Fig.
4.3
a can
be determined as follows. According to the proposed resource binding steps, the
modules for operations 1 and 2 will be placed beside each other, and the modules
for operations 3 and 4 also will be placed beside each other. Since operations that
are scheduled in the same D/M phase are concurrently performed, we assume that
the size of the mixers allocated to all these operations are also the same. Without
