1998 Fi h IEEE In e na ional Wo kshop on Cellula Neu al Ne wo ks and hei Applica ions, London, England, 14-17 Ap il 1998
I
Fou -Quad an One-T ansis o -Synapse o High-Densi y
CNN
Implemen a ions
R. Dominguez-Cas o, A. Rod iguez-V zquez,
S.
Espejo,
R.
Ca mona
Ins . de Mic oelec onica de Se illa
-
Cen o Nac. de Mic oelec onica
-
C.S.I.C.
-
Uni e sidad de Se illa,
Ed . CICA, C/Ta ia s/n, 41012-Se illa, SPAIN.
Phone: +34
5
4239923;
FAX:
+34
5
4231832; email: [email p o ec ed]
ABSTRACT:
This pape p esen s a linea ; , ou -quad an s, elec ically-p og ammable, one- ansis o synapse
s a egy applicable o he implemen a ion
o
gene al massi ely-pa allel analog p ocesso s in
CMOS
echnology.
I
is specially sui ed o
ansla ionally-in a ian p ocessing
a ays wi h local connec i i y, and esul s in a signGCan
educ ion in a ea occupa ion and powe dissipa ion
o
he basic p ocessing uni s. This allows highe in eg a ion
densi ies and he e o e, pe mi s he in eg a ion o la ge a ays on a single chip.
1.
In oduc ion
The mos impo an end in he elec onic implemen a ion o
CNNs
is he maximiza ion o he numbe o elemen a y p o-
cessing uni s ha can be placed in a single chip. This mus be combined wi h he achie emen o an accep able accu acy o
he sys em pa ame e s. The i s end imposes a s ong commi men in he design o he cell ci cui y: a ea-e iciency. A sec-
ond bu also impo an objec i e is powe -economy. Un o una ely, in analog p ocessing ci cui s, a ea and powe consump ion
o indi idual de ices a e di ec ly ela ed o accu acy
[
1).
The e o e, he selec ion
o
a ci cui s a egy as simple as possible o
he p esc ibed p ocessing unc ion is c ucial.
This pape p oposes a one- ansis o , ou -quad an s, elec ically-p og ammable, linea synapse o he implemen a ion o
massi ely-pa allel analog-a ay p ocesso s in
CMOS
echnologies. The p oposal is easily ex ensible o gene al a i icial neu al
ne wo ks.
2.
Analog-A ay-P ocesso s Elemen a y
Uni s
Each p ocessing uni (o
cell)
in a massi ely-pa allel analog-a ay p ocesso can be cha ac e ized by an in e connec ion
pa em and by an speci ic p ocessing unc ion. These cha ac e is ics a e o en conside ed in a ian om cell o cell, esul ing
in an addi ional simpli ica ion o he elec onic implemen a ion. This p ope y, commonly e e ed o as spa ial in a iance o
uni o mi y, will be assumed wi hou loss o gene ali y.
A common cha ac e is ic o massi ely-pa allel analog p ocessing algo i hms is he
local
compu a ion (wi hin each cell
c)
o a weigh ed agg ega ion o con ibu ions om he cells in i s neighbo hood,
N
yc
=
1
Aixi
(1)
i=l
The agg ega ed signal
yc
is hen used as inpu o a
p ocessing-block
which ealizes some speci ic unc ion, and gene a es
an ou pu
xc
ep esen a i e o he cell s a e. In um, his ou pu cons i u es he (unscaled) con ibu ion o he cell o i s neigh-
bo s. This gene al cell a chi ec u e is illus a ed in Figu e 1. The ou pu
xi
o
each neighbo is weigh ed by a coe icien
A;,
which is independen o he pa icula ecep o cell
c
unde he assumed spa ial uni o mi y. Excep o speci ic pu pose sys-
ems i is gene ally equi ed ha he scaling coe icien s (o
weigh s)
Ai
be elec ically p og ammable, o e sa ili y easons.
-.-
W!
WN
Analog
weigh -con ml
bus
Figu e
1.
Gene al a chi ec u e
o
an analog-p ocessing-a ay elemen a y p ocessing uni (cell).
A a sys em le el, he equi ed numbe o signal-scaling ci cui -blocks (o
synapses)
can be compu ed as
N
imes he num-
be o cells.
The
associa ed a ea and powe consump ion, as well as he ob ious e ec s o he synapse accu acy on he o e all
pe o mance o he sys em, ende s he selec ion o he synapse ci cui y a c ucial issue in he design o in eg a ed analog a ay
p ocesso s.
3.
Elec ically-P og ammable Synapses
Elec ically p og ammable synapses mus be d i en by he
inpu signal
xi,
and by a
weigh signal
w;
used o p og am he
scaling coe icien
Ai.
Unde he assumed spa ial uni o mi y, only
N
di e en weigh alues will coexis h oughou he a ay.
The e o e, a educed numbe
(N)
o
global nodes
(common o all cells in he ne wo k) sa is y he p og amming- ela ed ou ing
equi emen s
o
he
a ay,
i
he p og amming
signals
wi
a e
codi ied as ol ages. Since e e y cell ou pu
xc
is ansmi ed o
N
synapses loca ed wi hin i s
N
neighbo ing cells, i is also app op ia e ha synapse inpu signals
x;
be codi ied as ol ages.
Finally, because scaled signals mus be added a he inpu o each cell’s p ocessing block, i is con enien ha synapse ou pu
0-7803-4867-2/98/$10.0001998
IEEE
243
signals
A+;
be gi en in cu en o m, elimina ing he need o a dedica ed summing ci cui .
Al hough he equi ed unc ionali y o a p og ammable analog synapse may sugges he use o linea analog mul iplie s,
he e a e some speci ic ci cums ances common o almos e e y analog-a ay p ocessing algo i hm which expand he se o
selec able ci cui blocks.
Fi s no e ha while he synapses ou pu cu en
is
expec ed o be linea wi h he inpu signal
xi,
i
is
no equi ed o be lin-
ea wi h he weigh signal
wi,
whose unc ion is simply o allow weigh a ia ions in some p esc ibed ange. The e o e, unc-
ion
A,(w,)
may be nonlinea in gene al.
Second, in almos e e y analog-a ay p ocessing algo i hm, he weigh alues a e in a ian du ing p ocessing. The e o e,
he dynamic esponse wi h espec o he weigh signal is o li le conce n and, mo e impo an , a e se ing he weigh alues,
any e o o de ia ion om he ideal beha io independen o he inpu signal
xi
(bu in gene al dependen on
wi)
may be can-
celled using au oze oing, be o e pe o ming he p ocessing unc ion.
This is a good p ac ice in gene al because he o se o he agg ega ed signal is gi en by he addi ion o he ou pu -cu en
o se o he
N
synapses d i ing each cell. Indeed, his
is
o en he dominan e o sou ce o his class o sys ems.
In he las yea s, synapse ci cui s based on
MOS
ansis o s ope a ing in hei ohmic egion ha e been employed by se e al
au ho s
[2],
[3].
The choice is based on a combined es ima ion
o
se e al pe o mance igu es (including a ea occupa ion,
accu acy, linea i y, p og amming weigh ange, signal- ange, and powe e iciency) which p edic s impo an ad an ages as
compa ed o o he classes o synapse ci cui s based on he quad a ic law o
MOS
ansis o s in sa u a ion, o he exponen ial
law o bipola ansis o s and
MOS
ansis o s in weak in e sion.
Rega dless he amily, p ac ically all synapse ci cui s employ di e en ial o ully di e en ial a chi ec u es o achie e ou -
quad an s beha io and also o linea i y easons. Typical examples include hose synapses based on di e en ial pai s, like he
Gilbe mul iplie
[4],
and also he synapses employed in
[2]
and
[3].
In addi ion o he la ge complexi y o he synapse, his
usually o ces he use o di e en ial o ully di e en ial a chi ec u es in he p ocessing block as well, hus esul ing in a sub-
s an ial inc ease in a ea occupa ion.
In he ollowing sec ion we p opose a one- ansis o , ou -quad an s, elec ically-p og ammable synapse ci cui wi h sin-
gle-ended a chi ec u e.
4.
A
One-T ansis o Synapse Ci cui
well-known i s -o de app oxima ion
The DC cu en o an
MOS
ansis o ope a ing in i s s ong-in e sion ohmic egion can be desc ibed by he ollowing
whe e
and
e e y symbols
has
i s well es ablished meaning in
MOS
li e a u e.
Eq.
(2) p edic s an
inc emen ally
linea ela ion be ween and
Vcs
,
and an
app oxima ely
linea dependence wi h
VDS
o
DS
<<
2
[
cS
-
+ SB)]
.
These conside a ions ha e been widely exploi ed o many applica ions, including
MOS
implemen-
a ions o ac i e RC il e s
[5],
analog mul iplie s o RF communica ion ci cui s
[6]
and also synapse ci cui s o massi ely-
pa allel analog p ocessing sys ems
[2],
[3]
using di e en ial a chi ec u es.
The use o a single ansis o
o
implemen an elec ically p og ammable synapse wi h signals ep esen ed by single-ended
ol ages equi es ha one o he di usion e minals be se o a ixed ol age le el. The ga e and he o he di usion e minals
can hen be employed as inpu poin s, while he ou pu is ob ained om he cu en lowing ou o he ixed- ol age di usion
e minal. This is concep ually illus a ed in Figu e 2a in which a nulla o and a DC ol age sou ce ep esen he ideally null-
impedance inpu e minal o he p ocessing block in Figu e
1.
Such a i ual- e e ence le el is equi ed because he ou pu
impedance o he synapse is low due o i s ope a ion in he ohmic egion. The inpu impedance a he di usion inpu
is
also
low, while ha a he ga e inpu is high. Two al ema i es can hen be conside ed: using he ga e e minal o
xi
and he di u-
sion e minal o
wi,
o he o he way a ound. This has implica ions on he ou pu -impedance equi emen s o ei he he cell
p ocessing-block o he ol age sou ces d i ing he analog-weigh con ol bus, bu he majo decision ac o is ela ed o lin-
ea i y.
Equa ion (2)
is
alid only o
DS
2
o
and he e o e, he use o he no a ion in oduced in Figu e 2a equi es an independen
conside a ion o he wo possible cases
A
5
L
and
A
s
VL
.
S ill, simple analysis esul s in he ollowing combined exp ession
o
IN,
alid in ei he o he wo cases,
wi h
No e ha he second summand in
(5)
is independen
o
Vc
and ha he i s summand is linea wi h
G
.
Since we need a
244
linea beha io
wi h
espec o one o he inpu s
(xi)
and we can elimina e any sys ema ic o se
in
a p e ious s ep,
i
seems
s aigh o wa d ha we can chose
xi=
G
and
wi
A
,
as shown in Figu e 2a.
--
Figu e
2.
a) One ansis o synapse concep , b) Cell ( op) and pe iphe al (bo om) ci cui y o independen - e ms subs ac ion.
The e is s ill ano he issue ela ed o he ob en ion o a ou -quad an s beha io . While he wo possibili ies
VA
2
VL
and
A
5
L
p o ide double sign capabili y o he weigh ,
C
mus always be posi i e. The e o e we mus selec
a
su icien ly
high
e e ence le el on he ga e ol age o ac as he ze o le el o
xi.
Le
us
de ine:
(7)
x-
-
x
+
VXO
=3
,
=
x
-
Vxo
=xi
and in he same manne , e e ing he weigh ol age o
L
,
his is, selec ing
IV0
=
L
,
we ha e
w
=
i
+
VL
*
,
=
w
-
VL
=
w;
Using his new no a ion, equa ions
(5)
and
(6)
can be ew i en espec i ely as:
V
whe e bo h
,
and
,~
can be ei he posi i e o nega i e and s ill, he i s summand in
(9)
is linea wi h
V,
and he
second one is independen o
,
.
We de ine he weigh and he ou pu o se o he synapse, espec i ely,
as
G(Vw)
=
PV,
(11)
]"(Vu.)
=
G(V )(V
-I'
-
-2
i
x0
T L
"1
2
This allows
(9)
o be w i en in he ollowing o m
lN(VW' V$
=
G(V,,V,
+
10(V,)
Le
us
now assume ha we can elimina e he e m
~~( ,~),
Then, we can de ine
lN= +/o~ln
=
IN-I,,-Ai~;
and ew i e (1
3)
as
IJV,<, V,)
=
G(Vu.)VX
(1
5)
which is he equa ion o
a
ou -quad an s, elec ically-p og ammable, linea analog synapse.
This
elies only on
he
sepa a ed
dependencies shown in
(13),
and no on he speci ic o ms o
G( ,)
and
I~(V,J,
a
ac ha will
become ele an o he conside a ion o second o de e ec s in
a
la e sec ion
5.
Cell
and
Con ol Ci cui y
In o de o p ese e he high a ea e iciency p o ided by he one- ansis o synapses, he ci cui y employed wi hin each
cell
o
he
elimina ion
o
he
N
second summands (one pe synapse) should be
as
simple
as
possible.
This
is
made
easie
by
he ac ha he cell ci cui y i sel compu es he
sum
o
hese summands, which can he e o e be elimina ed al oge he .
Unde he assumed spa ial in a iance
o
he
weigh signals, common
o
mos analog-a ay p ocessing sys ems, he e m o
245
be elimina ed in each cell is also spa ially in a ian . The e o e, we can ep oduce i s alue in a small ci cui y, sha ed by all he
cells in he ne wo k and placed a he pe iphe y o he cell a ay, and subs ac i a he inpu nodes o each cell p ocessing
block. This can be achie ed, wi hou addi ional cos in he cell ci cui y, h ough p ope
weigh -dependen biasing
o
he p o-
cessing-block inpu s age.
As an example, Figu e 2b desc ibes
a
simple echnique. The op
pa
o
he igu e ep esen s he cell ci cui y (iden ical o
Figu e
1
using one- ansis o synapses) which includes a
class-A
inpu s age as pa o he p ocessing-block inpu ci cui y
(bias cu en sou ce is no shown o simplici y). The ci cled ansis o pe o ms he subs ac ion o he
N
second summands in
(13). The lowe pa o he igu e desc ibes he equi ed biasing de ices, placed a he pe iphe y
o
he cell-a ay and sha ed by
he whole ne wo k.
This echnique elies on he use o
ma ched
cu en -con eyo s
[4]
a he pe iphe al ci cui y and a he inpu node o he
cells p ocessing-block. Thei elec onic implemen a ion can be shown o be highly e icien in e ms o a ea and powe con-
sump ion
[3].
I
migh be a gued ha la ge-dis ance misma ch e ec s could esul in
cancella ion
e o s o
he independen e ms. How-
e e , as men ioned ea lie , i is gene ally con enien o employ au oze oing echniques. Such au oze oing, which can be easily
implemen ed wi h a ea-e icien cu en memo ies [7] in he cases conside ed (cu en -ou pu synapses), would elimina e he
cancella ion e o as well. Indeed, he use o au oze oing may ende unnecessa y he p oposed subs ac ion ci cui y, since i
could be used o elimina e he comple e sum o independen e ms a he han hei emaining e o . Al hough combining high-
signal- anges and high-absolu e-accu acy is o en di icul , he ecen ly p oposed class o
S21
cu en memo ies
[SI
may p o-
ide a good solu ion.
6.
Ope a ion Limi s and Second O de E ec s
MOS
ansis o , which can be app oxima ed by
One undamen al limi a ion o he ope a ion ange
o
he p oposed synapse is imposed by he ohmic egion limi s o he
'GS'
'D.7'
i SB)
(1
6)
(17)
Subs i u ion o he p e iously employed no a ion in his equa ion yields he ollowing
lowe
limi o he ga e ol age
>{VL+V+VW)
; w' L
x-
VW'V+VL)
; w' L
Excep o his limi , no o he es ic ions exis on he p oposed synapse, on he basis o he i s o de model conside ed. I
can be shown ha he e is only one second o de e ec ,
mobiliy deg ada ion,
which ep esen s a ele an de ia ion om he
unc ional dependence exp essed in (1
3).
O he second o de e ec s a ec only o he p ecise o m o
G( ,+,)
and
I& ,)
,
some-
hing i ele an o ou discussion.
Mobili y deg ada ion models p edic
a
educ ion in he e ec i e ca ie s mobili y
(p
in equa ion
(3))
wi h ans e sal (no -
mal o channel su ace) elec ic ield, some hing ha a ec s ou p esen discussion because he ans e sal elec ic ield
depends on he ga e ol age and hus, he i s summand will no be linea wi h
,
.
Al hough he widely accep ed
simple
model o mobili y deg ada ion
[9].
p edic s
a
con inuous educ ion o he e ec i e mobili y s a ing jus abo e
Gs
=
+ sB),
he ac is ha in mos
echnologies, he e
is
an
app eciable
(-2.0~)
Gs
ange
abo e
+ SB)
wi hin which mobili y educ ion is negligi-
ble. Fu he mo e,
some
highe
le el
models accoun ing
o
mobili y deg ada ion employ
a
speci ic pa ame e o
de ine
a
ield h eshold below which
no
mobili y deg ada ion
occu s
(UCRZT
in
SPICE
le el
2
[IO]).
Rega dless
he con inuous
o
h esholded modelling
o
mobili y deg ada ion, we can always de ine
a
maximum
e ec i e
ga e
ol age
'GEhl,b.x
=
' GS- + SB)l
(19)
below which any easonable linea i y equi emen s
a e
sa is ied.
The
ope a ion o he synapse mus be es ic ed
o
his ange.
Pe o ming he app op ia e subs i u ions in
(19)
yields he ollowing
uppe
limi o he ga e ol age,
The selec ion o
L
and
X,,
mus be made based on he limi s imposed by (17) and
(20).
In um, his will esul in
an
uppe limi o he allowed signal anges o
,
and
,
.
Equa ion
(17)
can be ew i en as,
,
+
xo
,
+
VL
+
"+VL)
,
+
Vxo
2
VL
+
+ ,
+
VL)
; ,
2
0
; ,
2
0
(21
1
Le
us
deno e he signal anges
o
w
and
V,
by
IV,$(
<
VWma
and
IV,I
<
V,,,,
,
espec i ely. In he abo e equa ion, he
wo s -case limi o
,,,
is gi en by he i s inequali y when
V,
=
,~~~~
and
,
=
- xwax
,
which yields,
'xo
'
'L
+
"+'L)
+
Vwmax
+
Vxmax
(22)
246
Rega ding
L
,
i s alue mus be su icien ly high o p o ide oom o he minimum
V_
alue and also o some possible
loss o ol age ange due o he limi ed ou pu swing o he ci cui s gene a ing he analog weigh con ol signals, which we
deno e as
Wmin.
This is,
VL
2
'wmax
+
'Wmin
(23)
Because an uppe limi o he ol age anges exis due o mobili y deg ada ion, and also because we a e in e es ed in max-
imizing he signal anges and/o allowing a educed powe supply ope a ion, we will selec he minimum allowed alue o
L
.
Subs i u ing
L
=
imax
+
Wmin
in
(22)
esul s in a minimum alue o
X0,
Vx0
2
'Wmin
+
'hVwmax
+
'Wmin)
+
2 imax
+
'xmax
(24)
Again, we selec
xo
as i s minimum allowed alue. The esul ing maximum alue o
X
is
hen gi en by
X,,
=
X0
+
,,,,
,
his is,
V~ mx
=
'Wmin
+
"+'wmax
+
VWmin)
+
'Vwmax
+
"xmax
and he wo s
case
mobili y deg ada ion limi will be
imposed
by
he i s inequali y in
(20),
when
,
is
mini-
mum, his is,
w
=
L-
,:,,,
=
Wm n,
which
yields,
Vxmax
'
VWmin
+
V+Vwmin)
+
GEM^
Using
(25)
in o
(26),
yields,
(27)
1 1
wmax
+
xmax'
2
-'
GEMa
-
3
1
V+Vi max
+
'wmin)-
VP~min)]
Fo mode a e linea i y equi emen s, he igh hand side o he abo e equa ion akes alues in he ange o one ol o yp-
ical
CMOS
echnologies, which o
,,,,,
=
,,,,
p o ides a peak- o-peak signal ange o abou one ol o bo h
Vx
and
VIb
.
Figu e
3
illus a es he abo e discussion and shows he ol age dis ibu ion selec ed o a pa icula echnology: a s anda d
n-well,
0.8pm
CMOS p ocess a ailable h ough EUROPRACTICE. Wi h small changes, hese alues should be alid o mos
ypical
CMOS
echnologies. No e ha he minimum powe supply le el should be a leas sligh ly abo e
x,,,
=
3.4~
o p e-
=3
0
L=
IV
xo
-
7
'GEM~
+
V+V~min)
-
2.8
Figu e
3.
Vol age ange dis ibu ion o synapse ope a ion.
en he possible
loss
o
ol age ange due o he limi ed ou pu swing o he p ocessing block. S ill,
an
op imiza ion o he ou -
pu swing o bo h he analog weigh con ol d i e s and he ou pu s age o he p ocessing block should allow he ope a ion o
he p oposed synapse wi h powe supply le els in he ange o 3.3 , wi h simila signal swings o
V,
and
w
.
Figu e
4
p o ides
an
addi ional insigh in o he selec ion o
L
and
xo
alues and he associa ed signal anges. I shows
he allowed ope a ion egion, delimi ed by (17) and
(20)
in he
x.
w
plane, wi hin which a squa ed ange (unde he assump-
ion
V imax
=
VXmax
)
o signals
,
and
V,
,
cen e ed a ound
( ~ xo)
,
mus be de ined. The g aphs co espond o
L
=
I
and
he speci ic pa ame e s o he echnology being employed. No e ha al hough appa en ly, an app eciable inc ease in signal
anges could be ob ained by inc easing he alues o
L
and
x0,
his is no ue in gene al because he limi s imposed by (17)
and
(20)
will also shi wi h
L
.
In iew
o
(27), he inc ease would be small. On he o he hand, i would equi e a la ge
powe supply.
-0.4~
<
V,,
S
0.4~
x
ly-
@
1.51
Ill
F
0
VL
"W
Figu e
4.
Signal anges delimi ed by ohmic egion and mobili y deg ada ion limi s.
247

7.
Resul s
In his sec ion we will illus a e he beha io o he p oposed synapse in a speci ic n-well, 0.8pm CMOS echnology a ail-
able h ough EUROPRACTICE. Figu e 5 con ains HSPICE le el 2 simula ed ans e cha ac e is ics
o
he p oposed synapse.
T ansis o s sizes a e
W=
6pm and
L
=
24pm. These geome ies co espond o easonable sizes in a p ac ical applica ion, in
which a
low
aspec a io
se es o he pu poses o ha ing easonable cu en le els h ough he analog weigh -con ol lines, as
well as mode a e powe dissipa ion in he chip. La ge channel a eas ( ela i e o echnology esolu ion) a e equi ed o ma ch-
ing conside a ions
[
11. S ill, low esolu ion echnologies a e highly con enien o ma ching conside a ions and also because
mos o he cell a ea is usually dedica ed o con ac s, ou ing, and ac i e egion sepa a ions.
Figu e 5a e lec s he o al ansis o cu en
IN
e sus he o al ga e ol age
Vx,
o di e en alues o he weigh signal
ol age
W
.
The alue o
L
is
1.0~.
Values o
,,
,
ela i e o
VL,
ange om
-
0.4~ (lowe ace) o
+
0.4~
(uppe ace) in
50m inc emen s. The mobili y deg ada ion e ec s a e clea ly isible a he igh side, while hose ela ed o he pinch-o
egion can be obse ed a le side, specially o posi i e alues o
,~
.
The egion a ound
x0
=
3.0~
e lec s he beha io p e-
dic ed by (13). Figu e 5b shows he esul ob ained a e subs ac ing he independen e m
~~( ,),
by means o he ci cui y
desc ibed in Figu e 2b. Wo -case
( ,,
=
0.4~)
o al ha monic dis o ion (THD)
is
below
0.05%
a
1Hz
and 0.7% a 1MHz.
Simila esul s a e ob ained om he p-channel e sion o he ci cui y.
Figu e
5.
HSPICE le el-2 simula ions
o
he p oposed synapse: a) Cu en
IN
in Figu e
2
e sus ga e ol age
V,
o
di e en alues
o
V,.
b)
Cu en
I,,
=
IN
-
I,
ob ained using he ci cui y desc ibed in Figu e 2b.
8.
Conclusions
This pape has p oposed and discussed an elec ically p og ammable, one- ansis o , ou -quad an s linea synapse s a -
egy o massi ely-pa allel analog a ay p ocessing sys ems, based on MOS ope a ion in he iode egion. Signal anges o
bo h he inpu and he weigh signal a e in he ange o l pp, and o al ha monic dis o ion is below 0.7% a IMHz. Ope a ion
om educed powe supplies o abou 3.3~ seems easible. The p oposed synapse ci cui esul s in a subs an ial educ ion
in
a ea and powe consump ion o he basic cell, as compa ed o adi ionally employed synapses based
on
di e en ial o ully-
di e en ial a chi ec u es. This allows he ealiza ion o a ay p ocesso s wi h a la ge numbe o uni s in he same chip.
Acknowledgmen :
This wo k has been unded by Spanish CICYT unde con ac TIC96-1392-C02-02 (SIVA: Ac i e Vision
In eg a ed Sys em).
9.
Re e ences
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13
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248