THEORETICAL AND APPLIED ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 2 |2023 |JUNE
Compac and Ene gy E icien QCA Based Hamming
Encode o E o De ec ion and Co ec ion
P emananda BELEGEHALLI SIDDAIAH , Megha PUTTASWAMY , Naga ika KAMAT
Depa men o Elec onics and Telecommunica ion Enginee ing, R.V. College o Enginee ing,
Myso e Rd, RV Vidyanike an, 560059 Bangalo e, Ka na aka, India
[email p o ec ed], meghapswam[email p o ec ed], naga ikak[email p o ec ed]
DOI: 10.15598/aeee. 21i2.4794
A icle his o y: Recei ed Oc 31, 2022; Re ised Ap 15, 2023; Accep ed May 11, 2023; Published Jun 30, 2023.
This is an open access a icle unde he BY-CC license.
Abs ac . Quan um-do Cellula Au oma a (QCA)
a e p e e ed o ealizing logic ci cui s a nanoscale
dimensions along wi h a high le el o in eg a ion and
minimal ene gy consump ion. Hamming code is a se
o en opy codes used o e o de ec ion and co ec-
ion in communica ion sys ems. E o de ec ion and
co ec ion is ca ied ou wi h he help o pa i y bi s
which a e appended wi h he o iginal bi s. Designing
a Hamming encode in nanoscale has i s own me i s
such as op imized a ea, educed ene gy dissipa ion and
lowe QCA cos . This wo k p oposes wo QCA-based
(7, 4) Hamming encode designs; mul ilaye (p oposed-
1) and coplana (p oposed-2) s uc u e wi h a ea and
ene gy analysis. P oposed-1 encode has achie ed
educ ion o cell a ea by 12.5 %, 34.58 %in e ms o
cell coun , and educ ion in o al ene gy dissipa ion o
26.8 %when compa ed o e e ence encode . P oposed-
2 encode has achie ed educ ion o 18.75 %in a ea,
44.15 %in e ms o cell coun , and 16.5 %in o al en-
e gy dissipa ion when compa ed o e e ence encode .
In e ms o QCA cos , educ ion o 12.5 %is achie ed
in case o p oposed s uc u es. The ene gy dissipa ed
in he p oposed designs is less compa ed o e e ence
encode . P oposed-2 s uc u e is mo e e icien com-
pa ed o mul ilaye and e e ence encode in e ms o
cell coun , cell a ea and QCA cos . The QCA ci cui s
a e ealized in QCADesigne and analyzed ene gy in
QCADesigne -E.
Keywo ds
Clocking, coplana , ene gy dissipa ion,
Hamming encode , mul ilaye , QCA.
1. In oduc ion
A eplacemen o he widely used CMOS echnology is
equi ed since i is eaching i s physical limi s. One o
he bes subs i u es o CMOS echnology is Quan um-
do Cellula Au oma a (QCA). The di icul ac o s o
nano-compu e and nano-communica ion de ices in-
clude de ice densi y, ope a ion speed and powe loss.
E ec i e a ea u iliza ion a he nanoscale is a ba ie
o building high powe consump ion a chi ec u e in
CMOS [1]. A nanoscale echnology no ed o i s low
ene gy powe dissipa ion, apid swi ching imes, high
ope a ing equencies, and compac size QCA. A he
nanoscale, i is u ilized o c ea e combina ional and
sequen ial logic ci cui s.
Gallium A senide is one o he semiconduc o s used
o make quan um do s. The columbic o ce o a -
ac ion be ween he QCA cells causes sel -p oduc ion
in cellula au oma a. High swi ching speed, small
de ice size, and ex emely low powe consump ion a e
all ea u es o QCA [2]. He e, elec ons play a c ucial
pa in bo h he ansmission o digi al in o ma ion and
nume ous logic ope a ions.
QCA ci cui s o e many bene i s, including
de ice sh inkage wi h as e swi ching imes, and lowe
ene gy/ powe consump ion. In o ma ion can be p o-
cessed as e in QCA design, which also educes en-
e gy dissipa ion a he nanoscale. Con a y o con en-
ional CMOS echnology, QCA manda es he use o
a clock o bo h combina ional and sequen ial ci cui s.
The quan um do s a e a c ucial pa o he QCA. I is
a h ee-dimensional s uc u e ha holds an elec-
on, i.e., elec ical cha ge. QCA dec eases he
da a p ocessing la ency, inc easing ope a ion speed
and equency [3]. A QCA cell, Majo i y Vo e
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(MV) ga e and in e e , and a simula ion ype
se up make up he de ice. Fo he pu pose o
building digi al logic ci cui s wi h highe in eg a ion
and low ene gy consump ion, QCA is a p omising
al e na i e o CMOS echnology.
The da a p o ided du ing digi al ansmission may
be dis o ed by noise and o he en i onmen al condi-
ions. In he e en o any ansmission e o , da a loss
happens. An e o happens when he inpu da a and
he ansmi ed da a do no ag ee. Impo an da a is
los as a esul o he e o . Da a is con eyed as bi s, o
’0’ and ’1’. The pe o mance o he en i e sys em could
be a ec ed by any change o one o he bi s. When he
bi ’0’ is changed o he bi ’1’ o ice e sa, bi e o s
happen [1].
Hamming codes o linea block codes a e he se o
codes which pe o m e o de ec ion and co ec ion by
adding pa i y bi s he eby gi ing ise o an e ec i e
e o co ec ion coding sys em. Basically, in Hamming
communica ion ne wo k, edundancy bi s a e added o
e o de ec ion and co ec ion. The ac ual message
da a and pa i y bi s a e ansmi ed in coded o ma
o e he channel. When he ecei e ge s he coded
signal, i sepa a es he pa i y bi s om he message
bi and i he e o is de ec ed, i is u he co ec ed.
A (7, 4) Hamming encode encodes 4 bi s o da a in o
7 bi s by including h ee pa i y bi s [4].
The wo k p oposes wo op imized (7, 4) Hamming
encode designs. The objec i e o his p oposed wo k
is o minimize he cell coun , cell a ea, QCA cos
and ene gy dissipa ion by ealizing di e en con igu-
a ions o (7, 4) Hamming encode . Hamming encode
is ealized in bo h coplana and mul ilaye s uc u es.
All he s uc u es a e implemen ed and simula ed
using QCADesigne 2.0.3 and analyzed ene gy using
QCADesigne -E.
The pape is di ided in o di e en sec ions. The
li e a u e e iew was ca ied ou on di e en pape s
and ele an opics in Sec. 2. The basic QCA
echnology, design and implemen a ion o he p oposed
(7, 4) Hamming encode is w i en in Sec. 3. and
Sec. 4. , espec i ely. The esul s o he implemen a-
ion a e discussed in Sec. 5. The conclusions de i ed
a e discussed in Sec. 6.
2. Li e a u e Re iew
Quan um do Cellula Au oma a (QCA) is a new com-
pu ing pa adigm ha elies on quan um-mechanical
e ec s o pe o m logic ope a ions. I is a p omis-
ing echnology ha has he po en ial o e olu ionize
compu ing by p o iding high-speed, low-powe , and
high-densi y de ices.
Single-bi e o s can be ound i he pa i y coun in-
e s he numbe o ones is no he same. A da a bi may
be lipped by noise du ing ansmission. By adding
codes wi h a g ea e numbe o pa i y bi s, i is pos-
sible o ind wo-bi aul s, each o which is calcula ed
on a unique combina ion o bi s in he da a [4].
Fo wa d E o Co ec ion (FEC), which is used in
da a ansmission, e e s o a ecei e ’s capaci y o
ix aul s in he da a i ecei es. A ansmi ing s a-
ion mus ampli y he ansmi ed da a in o de o
make his possible. By using a block pa i y echnique,
Hamming codes educe he cos o implemen ing o -
wa d e o co ec ion. FEC can be implemen ed using
a ious codes, such as Hamming codes, Reed-Solomon
codes, and con olu ional codes. Each code has i s own
cha ac e is ics and ad an ages, and he choice o code
depends on he speci ic equi emen s o he communi-
ca ion sys em [5].
QCA clocks a e used o egula e and synch onize he
in o ma ion low. Addi ionally, i supplies he ci cui
wi h powe . The ou clock phases ha each cell in
a QCA has a e Swi ch, Hold, Release, and Relax.
The ba ie s a e aised du ing he i s phase ( he
swi ch phase), which esul s in an inc ease in he o ces
opposing he passage o elec ons inside each cell while
he mo emen o elec ons g adually declines inside he
cell [6].
In QCA, each cell con ains ou quan um do s. Two
ee elec ons ha a e posi ioned diagonally ac oss
om one ano he cha ge each cell. The elec ons a e
compelled o occupy he co ne -mos loca ion o he
cell as a esul o unnelling be ween adjacen do s
caused by mu ual elec os a ic o ces ( epulsion). Ad-
di ionally, he QCA cell has i s own dimensions, which
a e highly impo an when calcula ing a ea. These cells
ha e a heigh and b ead h o 18 nm and 2 nm, espec-
i ely, which sepa a es each one om i s neighbo [8].
In he Hamming code gene a o , supe luous bi s a e
used o enc yp message bi s. The ex a bi s posi ioned
a a ious loca ions in he message bi s a e known as
pa i y o edundan bi s. The ecei e ecei es he
code bi s, does a ecalcula ion o acqui e he e o
bi s, and hen comple es he equi ed calcula ion. The
Hamming encode wo ks by adding ex a bi s, called
pa i y bi s, o a message based on i s o iginal bi s. The
pa i y bi s a e calcula ed in a way ha allows he e-
cei e o de ec and co ec any single-bi e o s ha
may occu du ing ansmission. The numbe o pa i y
bi s added depends on he numbe o da a bi s being
encoded and he le el o e o co ec ion equi ed [9].
In QCA, he s a e o he quan um do s ep esen s
he bi s o he encoded message. To de ec a single-bi
e o in a Hamming encoded message using QCA, we
can use a majo i y unc ion, which is a basic building
block o QCA ci cui s. A majo i y unc ion accep s
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h ee inpu s and ou pu will be he majo i y alue o
hose inpu s [10].
In QCA, he clocking is achie ed by applying a pe i-
odic ol age signal o he cells o he a ay. This ol age
signal causes he elec on cha ge in he quan um do s
o oscilla e, which in u n causes he cells o ansi-
ion be ween di e en s a es. By ca e ully con olling
he iming and ampli ude o he clock signal, he QCA
a ay can be made o pe o m logic ope a ions wi h
high p ecision and e iciency [13].
Hamming code uses he pa i y bi s, simila ly o o he
e o de ec ion and co ec ion codes. These bi s a e
added o da a in o de o e i y i s accu acy when i is
ead o ecei ed du ing a da a ansmission. An e o -
co ec ion code can pinpoin he posi ion o a single bi
de ec wi hin a da a uni by using mul iple pa i y bi s.
3. Basics o QCA
3.1. QCA Cell
The mos elemen al componen o QCA is he QCA
cell. Each QCA cell con ains ou quan um do s, and
each o hem ep esen s an elec on in mo ion. The
holes a e compa able o he do s in he QCA cell i
he elec on is like he elec on in an a om in a cell
[12]. Addi ionally, he QCA cell has i s own dimen-
sions, which a e highly impo an when calcula ing
a ea. Each QCA cell is 2 nm apa om i s neigh-
bo ing cell and measu es 18 nm in heigh and b ead h.
Each o wo pola iza ions indica es one o he wo con-
igu a ions: P= +1 deno es logic high, while P=−1
deno es logic low as shown in Fig. 1.
Logic ’0’
P=-1
Logic ’1’
P=+1
Localised Elec ons
Fig. 1: QCA cell wi h pola i y ‘+1′and ‘−1′.
QCA Wi e: The simples a angemen ha is pos-
sible in QCA is by a anging he quan um do cells in
se ies. I he e is change in pola iza ion in any o he
ou cells, he emaining ou cells immedia ely syn-
ch onize o he pola iza ion o o he cells by columbic
in e ac ion be ween hem [11].
The MV ga e and in e e a e he ounda ion o
QCA. In he QCA logic, he MV ga e is he common
ga e. By swi ching he pola i y o one inpu o +1 o
−1, i can be made in o an AND o OR ga e. Th ee
inpu cells, one o e cell, and one ou pu cell make up
he MV ga e [10]. When c ea ing digi al ci cui s wi h
QCA and o he digi al building blocks like exclusi e
OR ga es, he in e e ga e is c ucial. The in e e
complemen s he inpu .
3.2. QCA Clocking
A clock is equi ed by e e y QCA ci cui in o de o
synch onize and egula e he in o ma ion low. I gi es
he ci cui he powe i needs o unc ion. The QCA
clock consis s o ou phases. The e is a 90◦lag be-
ween neighbo ing phases [11]. The po en ial ba ie s
ha impac a clus e o QCA cells o he clocking zone
a e s ill ele a ed o lowe ed, he clock changes phase.
The clocking sys em is demons a ed using he QCA
bina y wi e [4]. Sub-a ay 1 is ini ially swapped in ac-
co dance wi h he inpu ixed. Sub-a ay 2 hen begins
o swi ch while sub-a ay 1 mo es in o he hold phase.
Since sub-a ay 3 is in a elaxed s a e, i will no a ec
sub-a ay 2’s compu a ional s a e. Sub-a ay 1 eleases
a phase a he ollowing phase, while sub-a ay 2 is in
a hold s a e and supplies sub-a ay 3 wi h inpu .
In o ma ion is ans e ed in a pipeline ashion wi h
a90◦phase change om one clock zone o ano he [7].
3.3. Simula ion Engine and Se up
In QCA, he e a e wo echniques o design ci cui s:
using a cohe ence ec o wi h ene gy o a bi-s able
app oxima ion. In QCADesigne -E, cohe ence ec o s
wi h ene gy a e c ea ed. When compa ed o he cohe -
ence ec o , he Bi-s able app oxima ion is he as es
since i simula es he ci cui wi hou ime dependen-
cies. The cohe ence ec o wi h ene gy app oxima ion,
howe e , depends on ime [14]. The ene gy dissipa ion
measu emen s and calcula ions a e mo e accu a e when
using a ec o . When compa ed o bi-s able app oxi-
ma ion, i is slowe . Two o ms o simula ion ype se up
suppo he simula ion engine: exhaus i e and ec o
able [13].
The ec o able is p e e ed o la ge ci cui s
because all po en ial scena ios mus be es ed. The
abula ed da a o di e en engine se ups e e s o [15].
In QCA ci cui s, he QCA cell sizes a e also impo an .
The QCA cell’s heigh and b ead h a e bo h 18 nm, and
i s do ’s diame e is 5 nm. Each QCA cell is 2 nm apa
om i s neighbo ing cell. Laye sepa a ion is 11.5 nm,
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and adius o e ec is 65 nm. Ci cui s can be buil in
QCA in wo di e en ways: as single-laye s uc u es
o as mul ilaye s uc u es.
3.4. C osso e and Mul ilaye
Design
QCA has wo ypes o c osso e s namely, mul ilaye
and coplana . Single-laye designs a e easibly done
using coplana c osso e app oach. Fo coplana c oss-
ings, wo cell ypes a e equi ed ( egula and o a ed).
Ro a ed cells can be u ilized o coplana wi e c oss-
ing because, when p ope ly aligned, he egula cell
and he o a ed cell do no in e ac wi h each o he .
Simila o he many me al laye s in a s anda d ci cui ,
mul ilaye c osso e s employ mul iple laye s o cells.
Mul ilaye c osso e is simple o cons uc and has
a eliable signal connec ion.
4. Implemen a ion o (7, 4)
Hamming Encode s
Fo e ec i e communica ion, aul s can be de ec ed
and co ec ed using e o de ec ion and co ec ion ech-
niques. The me hod o e o de ec ion is used o iden-
i y e o s ha a e sen om he ansmi e o he
ecei e . The p ocess o ec i ying da a ha has been
ans e ed om ansmi e o ecei e is known as e -
o co ec ion. To ind and ix aul s, a Hamming code
ci cui is used. A sys ema ic e o de ec ion and co ec-
ion coding sys em is c ea ed by Hamming codes, which
do bo h e o de ec ion and co ec ion. Redundan-
cies a e essen ially employed in hese e o -co ec ing
codes o he pu pose o e o iden i ica ion and co -
ec ion. When he da a is ead o ecei ed, pa i y bi s
a e added o i in o de o e i y i s accu acy. An e -
o de ec ion-co ec ion code may loca e he da a uni
as well as de ec a single-bi e o in he da a uni
by using mo e han one pa i y bi . When da a is e-
cei ed by he ecei e , he pa i y bi s and he eal mes-
sage a e sepa a ed. I he e a e any p oblems, hey a e
ound and ixed. Pa i y bi s and he ac ual message a e
ans e ed oge he o e he channel.
The ealiza ion o he (7, 4) Hamming encode is in-
spec ed in QCA using he op-down app oach. The
block diag am o he (7, 4) Hamming encode is shown
in Fig. 2. P oposed designs consis o h ee 3-inpu
exclusi e OR ga es. In Fig. 2, I6, I5, I4, I3 ep e-
sen inpu s and E6, E5, E4, E3, E2, E1, E0 ep esen
ou pu s. In (7, 4) Hamming encode , he i s ou
ou pu bi s E6, E5, E4, E3 can be di ec ly ob ained
om he in o ma ion bi s. The nex h ee supe ision
bi s a e ob ained by conduc ing exclusi e OR ope a-
ion o he bi s as shown in Eq. (1), Eq. (2) and Eq. (3)
which implies ha h ee 3-inpu exclusi e OR ga es a e
equi ed, and ci cui a chi ec u e o he encode is as
illus a ed in Fig. 2.
E2 = I6MI5MI4,(1)
E1 = I6MI5MI3,(2)
E0 = I6MI4MI3.(3)
The QCA ci cui s o he p oposed-1 (7, 4) Ham-
ming encode and p oposed-2 (7, 4) Hamming encode
using QCADesigne a e shown in Fig. 3 and Fig. 4,
espec i ely. F om he QCA designs, i is analyzed ha
p oposed-1 mul ilaye (7, 4) Hamming encode occu-
pies an a ea o 0.16 µ2and equi es 123 cells, whe eas
p oposed-2 coplana (7, 4) Hamming encode design
equi es an a ea o 0.13 µ2and can be ealized using
105 cells, which is less compa ed o design in [4].
3 INPUT
XOR
3 INPUT
XOR
3 INPUT
XOR
I6
I5
I4
I3
E6
E5
E4
E3
E2
E1
E0
Fig. 2: Block diag am o (7, 4) Hamming encode ci cui .
I6
E6
I5
E5
I4
I3
E3
E1
E0
E4
E2
Fig. 3: P oposed-1 mul ilaye (7, 4) Hamming encode ci cui .
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I6
I4
I5
I3
E6
E3
E2
E0
E1
E5
E4
Fig. 4: P oposed-2 coplana (7, 4) Hamming encode ci cui .
The Hamming encode in [4] ollows mul ilaye
c osso e s uc u e which equi es highe cell coun and
cell a ea. Wi h he inc ease in a ea, he QCA cos will
also inc ease. The p oposed-2 coplana design o e -
comes hese d awbacks by using simple ga es wi h e-
duced numbe o cells and less a ea usage. The exclu-
si e OR ga es a e eplaced wi h cells which equi e less
a ea. The p oposed-2 coplana design consis s o h ee
exclusi e OR ga es wi h 11 cells whe eas he e e ence
ci cui [4] consis s o exclusi e OR ga es wi h 14 cells.
The ci cui has educed a ea wi h a smalle numbe o
cells. F om Eq. (1), Eq. (2) and Eq. (3), combina ion
o inpu s is conside ed o ob ain exclusi e OR ou pu s.
5. Resul s and Discussions
The esul s o Hamming encode s a e discussed in
his sec ion. The simula ion esul s o Hamming en-
code a e shown in Fig. 5 and he alues ob ained (cell
coun , cell a ea, and ene gy dissipa ion) a e abula ed
in Tab. 1 and Tab. 2, espec i ely. The inpu signals
named as I6, I5, I4, I3 a e ep esen ed in blue on
colo and he ou pu signals labeled as E1, E2, E3, E4,
E5, and E6 a e ep esen ed in yellow on colo . I is
clea ha he ou pu s E6, E5, E4, and E3 ag ee wi h
he inpu , while E2, E1, and E0 a e ob ained in acco -
dance wi h he supe ision ela ionship, demons a -
ing ha he encode has success ully ca ied ou he
in ended unc ion using Eq. (1), Eq. (2) and Eq. (3).
I is obse ed ha he p oposed s uc u es has an e -
ec i e a ea u iliza ion o 12.5 %in case o p oposed-1
and 18.75 %in case o p oposed-2 which is mo e e ec-
i e compa ed o [4]. The o al cell coun is educed
by 34.57 %in case o p oposed-1 and 44.15 %in case
o p oposed-2 compa ed o [4]. The o al cell a ea is
he p oduc o he numbe o cells and he single cell
dimension. The encode designed in [4] equi es a mo e
numbe o cells and hence o al cell a ea inc eases. The
p oposed-2 ci cui o e comes his limi a ion by using
coplana s uc u e.
max: 1.00e+000
min: -1.00e+000
I6
max: 1.00e+000
min: -1.00e+000
I5
max: 1.00e+000
min: -1.00e+000
I4
max: 1.00e+000
min: -1.00e+000
I3
max: 9.54e-001
min: -9.54e-001
E6
max: 9.54e-001
min: -9.54e-001
E5
max: 9.57e-001
min: -9.57e-001
E4
max: 9.57e-001
min: -9.57e-001
E3
max: 9.53e-001
min: -9.53e-001
E2
max: 9.53e-001
min: -9.53e-001
E1
max: 9.52e-001
min: -9.55e-001
E0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000
Simula ion Resul s
Fig. 5: Simula ion esul s o (7, 4) Hamming encode .
Tab. 1: Compa ison o (7, 4) Hamming encode s.
QCA
Pa ame e s [4] P oposed-1
(mul ilaye )
P oposed-2
(coplana )
Cell coun 188 123 105
To al a ea (µm2) 0.16 0.14 0.13
Cell a ea (nm2) 60912 39852 34020
La ency 0.5 0.5 0.5
Cos 0.04 0.035 0.0325
QCA cos unc ion is a p oduc o la ency and cell
a ea. The cos unc ion u ned ou o be 0.035 o
p oposed-1 mul ilaye encode ci cui and 0.0325 o
p oposed-2 coplana encode ci cui . F om Tab. 1, i
can be in e ed ha he QCA cos unc ion has d as-
ically educed when compa ed o ci cui in [4] which
makes he p oposed design highly op imized.
The ene gy dissipa ion alues o (7, 4) Hamming en-
code s ob ained is as lis ed in Tab. 2. The o al en-
e gy dissipa ion o p oposed-1 ci cui u ned ou o be
5.51·10−2eV. I can be analyzed ha he p oposed-1
mul ilaye Hamming encode has less ene gy dissipa-
ion compa ed o he one p oposed in [4], i.e., educ-
ion o 26.34 %is achie ed. Fo p oposed-2 coplana
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(7, 4) Hamming encode , ene gy analysis u ned ou o
be 6.23·10−2eV and educ ion in ene gy dissipa ion o
16.84 %was obse ed.
Tab. 2: Ene gy analysis o (7, 4) Hamming encode s.
Ene gy
Analysis [4] P oposed-1
(mul ilaye )
P oposed-2
(coplana )
A e age ene gy
dissipa ion (meV) 6.8 5.01 5.65
To al ene gy
dissipa ion (meV) 74.8 55.1 62.2
The p oposed Hamming encode designs a e bo h
cos and a ea e ec i e and dissipa es lesse ene gy
when compa ed o ci cui in [4]. Du ing he ene gy
analysis, i is obse ed ha p oposed-1 design has
lesse ene gy dissipa ion when compa ed o Hamming
encode in [4] and p oposed-2 design. T ade-o s can
be made in e ms o cell a ea and ene gy dissipa ion.
6. Conclusion and Fu u e
Resea ch
The p oposed wo k illus a es he ealiza ion o com-
pac (7, 4) Hamming encode s. CAD ools, QCADe-
signe and QCADesigne -E a e used o ealizing he
ci cui s and o ene gy analysis. The QCADesigne
is used o ealize he ci cui s and o measu e he
ci cui pa ame e s including cell coun , cell a ea, la-
ency, QCA cos and clock zone. QCADesigne -E is
used o de e mine o al and a e age ene gy dissipa ion.
P oposed-1 (7, 4) Hamming encode has achie ed an
imp o emen o 12.5 %in cell a ea and 34.57 %in
cell coun compa ed o [4]. P oposed-2 (7, 4) Ham-
ming encode has achie ed 18.75 % educ ion in a ea,
44.15 % educ ion in cell coun , and 12.5 % educ ion
in cos in compa ison o he [4]. P oposed -1 ci cui
has a educ ion o 26.4 %in a e age ene gy dissipa-
ion and p oposed-2 ci cui has achie ed a educ ion o
16.77 %. P oposed-2 ci cui is mo e e icien compa ed
o mul ilaye s uc u e in e ms o cell coun , cell a ea,
and QCA cos . The op imiza ion o he (7, 4) Ham-
ming encode can be done using mul ilaye concep s
which will u he yield be e esul s. The p oposed
design can be used o he implemen a ion o Hamming
decode and Hamming communica ion ne wo k in ad-
di ion using p oposed (7, 4) design, op imized (15, 11)
s uc u es can be ealized.
Au ho Con ibu ions
B.S.P concep ualized he idea, me hodology, design,
and analysis. Re iew o li e a u e, design me hodol-
ogy and implemen a ion we e con ibu ed by M.P. and
N.K. All au ho s con ibu ed o he analysis o he de-
sign and esul s and p o ided inpu s o he manusc ip .
All au ho s we e in ol ed in d a ing he pape om
he ini ial s ages, edi ing, and e ising he same.
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Abou Au ho s
P emananda BELEGEHALLI SIDDAIAH is as-
socia ed wi h R.V. College o Enginee ing, Bengalu u,
India. He is wo king as an associa e p o esso in he
Depa men o Elec onics and Telecommunica ion
Enginee ing and Senio IEEE membe . His main
a eas o in e es s a e in he ield o VLSI designs in
ASIC/FPGA, low powe , QCA, compac VLSI ci -
cui s, speech enhancemen , signal p ocessing, ene gy
ha es ing and communica ion. He has deli e ed
lec u es as a subjec expe in he Vis es a aya
Technological Uni e si y EDUSAT p og am. He has
e iewed se e al pape s o In e na ional Jou nals and
Con e ences and chai ed he session in he In e na-
ional Con e ences. He has published se e al esea ch
a icles in in e na ional jou nals and con e ences and
guides many p ojec s in his a ea o esea ch.
Megha PUTTASWAMY is pu suing he un-
de g adua e cou se in Elec onics and Telecommuni-
ca ions Enginee ing a R.V. College o Enginee ing,
Bengalu u, India. He ields o in e es s a e in digi al
design, VLSI designs, QCA, CMOS, coding and
c yp og aphy.
Naga ika KAMAT is pu suing he unde g ad-
ua e cou se in Elec onics and Telecommunica ions
Enginee ing a R.V. College o Enginee ing, Ben-
galu u, India. He ields o in e es s a e in Digi al
design, QCA, CMOS, and c yp og aphy.
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