IEEE Consumer Electronics Magazine - July 2018 - 93

input design is the associative law. According to this law, the grouping of addends
(for addition) or the grouping of factors
(for multiplication) does not affect the result. In our proposed approach, the grouping of addends and factors is changed. For
example, as shown in Figure 3, the final
output y ^nh adds the output of operations 3, 4, 6, and 8. The grouping of addends is changed from y ^nh = ^^^opn.3 +
opn.4h + opn.6h + opn.8h t o y ^nh =
(opn.3 + ^^opn.4 + opn.6h + opn.8hh . The
associative-law-based transformed design
is shown in Figure 4.

with the module library, termination criteria, and controlling BFOA parameters.

EXPERIMENTAL RESULTS
Table 1 shows a comparison between
the original design and the proposed

.167

x (n ) x (n - 3)

+

(1)

COMMUTATIVE-LAW-BASED
TRANSFORMATION

.50

(n --2)
x (n - 1) x (n
2) .33

y (n - 2)

(3)

×

×

(6)

×

(8)

×

(4)

The third algebraic-law-based transformation applied to further optimize the
input design is the commutative law.
According to the commutative law, the
arrangement of addends or factors
does not affect the result. In our proposed approach, the arrangement of
addends and factors is changed. For
example, as shown in Figure 4, the ar rangement of addends is changed from
y ^n h = ^operation 3 + ^^operation 4 +
operation 6h + operation 8hh to y ^nh =
^^operation 8 + ^operation 4 + operation
6hh + operation 3h . The commutative
law-based transformed design is shown
in Figure 5.

transformation approach. The design
cost is calculated based on (1) [3]. For
all of the benchmarks [4], a reduction in
design cost is achieved due to the proposed algebraic transformations. The
modification of nodes directly affects

+

(5)

+

(7)

+

(9)

y (n )
FIGURE 4. The associative-law-based transformed design.

.33

y (n - 2)

(8)

×

.167

x (n ) x (n - 3)

.50

x (n - 2) x (n - 1)

(6)

×

+

(1)

(3)

×

(4) ×

EXPLORING LOW-COST
TRANSFORMED DESIGN
USING BFOA

(5)

In the proposed approach, low-cost
design is obtained through BFOA-driven
DSE [2]. BFOA consists of three phases:
1) chemotaxis, 2) replication, and 3)
elimination dispersal. In the proposed
DSE process, the algebraic transformbased DFG is provided as an input, along

(7)

+

+

(9)

+
y (n )

FIGURE 5. The commutative-law-based transformed design.

Table 1. A comparison of the proposed design with the original design.
Benchmark

IIR

Original Design

Proposed Design

Design Solution

Area (μm2)

Latency (ps)

Cost

Design Solution

Area (μm2)

Latency (ps)

Cost

1(+), 2(*)

178.2

1,029.4

−0.18

1(+), 2(*)

177.5

830.7

−0.27

ARF

2(+), 2(*)

199.0

2,573.5

−0.30

2(+), 2(*)

199.0

2,374.8

−0.32

FIR

3(+), 3(*)

298.4

1,396.4

−0.29

3(+), 3(*)

298.4

1,396.4

−0.29

IDCT

4(+), 3(*)

319.9

2,084.3

−0.30

4(+), 3(*)

319.9

2,084.3

−0.30

DCT

4(+), 2(*)

241.8

2,283.0

−0.31

4(+), 2(*)

241.8

2,283.0

−0.31

July 2018

^

IEEE Consumer Electronics Magazine

93
Table of Contents for the Digital Edition of IEEE Consumer Electronics Magazine - July 2018
