MELECON
'85
I Volume
11:
Digi al Signal P ocessing
A. Luque, A.
R.
Figuei as Vidal, V. Cappellini (eds.)
Else ie Science Publishe s B. V. (No h·Holland)
I©
IEEE 1985 179
PERFOMANCE
COMPARISON
OF
32
KBPS
ADPCM
CODERS
IN
NOISE-FREE
AND
NOISY
ENVIRONMENTS.
* ** *
En ique
Masg au
,
F ancisco
Ruiz- 1a nez
and
Jose
B.
Ma ino
*
E.T.S.I.Telecomunicaci6n,U.P.C.,
Ba celona,
Spain.
**
Cen o
de
In es igaci6n
de
I.N.T.E.L.S.A.,
Mad id,
Spain.
In
his
pape
a
compa a i e
s udy
o
se e al
schemes
o
Adap i e
Di e en ial
Pulse
Code
Modula ion
(ADPCM)
wi h
backwa d
adap a ion
is
p esen ed.
The
wo k
he e
epo ed
shows
a
adeo
be ween
a
good
signal- o-noise
a io
and
a
low
deg ada ion
o
he
ecei ing
quali y
owing
o
ansmission
e o s
in
noisy
channels.
On
his
second
poin ,
he
CC
ITT
s anda d
exhibi s
a
supe io
beha io
o
he
es
o
he
schemes,
whe eas
i s
signal- o-noise
a io
will
esul
in
2
o
3 dB
less
han
all
he
schemes
i
ansmission
e o s
a e
no
conside ed.
In
addi ion,
a
supe io
pe omance
(a ound
2 dB)
o
encode s
using
la ice
p edic o s
wi h
espec
o
hose
using
ans e sal
p edic o s
is
also
shown.
1.
In oducci6n
Du ing
he
las
yea s
a
g ea
numbe
o
ADPCM
encode s
o
speech
signal
and
oice-band
da a
a
a es
o
24
and
32
Kbps.
ha e
appea ed.
Thei
good
pe omances
as
well
as
hei
popula i y
ha e
made
he
CCITT
o
es ablish
a
s anda d
ADPCH
a
32
Kbps
/1/.
Depending
on
he
adap a ion
ype
o
he
p edic o ,
he
ADPC -1'
s
a e
classi ied
in o
wo
la ge
g oups.
Namely,
ADPCM's
wi h
o -
wa d
adap a ion
o
wi h
backwa d
adap a-
ion.
The
i s
one
need
o
send
an
addi-
ional
side
in o ma ion
o
he
ecei e ,
since
he
p edic o
coe icien s
a e
upda-
ed
in
he
ansmi e
on
he
basis
o
he
exac
inpu
signal,
being
his
in o ma ion
no
a ailable
a
he
ecei e .
The
ansmi-
ssion
speed
inc ease
ha
his
ep esen s
make
hen
less
a ac i e
and,
in
ac ,
he
CCITT
s anda d
belongs
o
he
g oup
o
Backwa d
Adap i e-DPCM.
Some
wo ks
con aining
compa a i e
s udies
be ween
ADPC 1
encode s
ha e
appea ed
in
a
sca e ed
and
no
homogeneous
way.
Recen -
ly,
hese
wo ks
ha e
been
commen ed
in
e-
e ence
/2/,
showing
he
di icul y
c ea ed
by
hei
unhomogenei y
when
pe omances
ha-
e
o
be
compa ed.
In
his
wo k
we
unde ake
he
compa a i e
s udy
o
he
mos
usual
schemes,
be ween
hem
he
CCITT
s anda d,
unde
he
same
condi ions
and
including
noise- ee
and
noisy
ansmission
channels.
2.
ADPCM
sys ems.
Figu e
l
despic s
he
gene al
scheme
o
an
CH
2185-7/85/0000-0179(8)/$01.00
© 1985 IEEE
ADPCM
sys em
which,
as
i
is
well-known,
is
composed
a[
wo
main
blocks:
he
adap i e
quan ize
and
he
adap i e
p edic o .
The
combina ion
o
di e en
s uc u es
o
bo h
blocks
lead
o
a
g ea
a ie y
o
po-
ssible
ADPC/<1
sys ems.
Nex ,
we
will
b ie ly
desc ibe
he
di e en
ypes
o
bo h
blocks
which
will
be
conside ed
in
his
pape .
x (
n)
+-
e(n)
eq(n)
+
Qan ize
-
~(n)
..
+
+
P edic o
l
x(n)
Figu e
l.
Gene al
scheme
o
an
ADPCM
encode
2.1
Adap i e
Quan ize
An
adap i e
quan ize
consis
in
a
in a-
ian
quan ize
p eceded
by
a
signal-
scaling,
which
allows
he
adap a ion
o£
he
quan ize
dynamic
ange
o
he
inpu
si<;J-
nal.
Thus,
a
be e
p o i
o
he
quan ize
bi s
numbe
is
achie ed
and,
he e o e,
a
mo e
accu a e
ep esen a ion
o
he
inpu
signal.
The e
is
a
popula
adap i e
quan-
ize
in
he
li e a u e,
de elopped
by
se e al
au ho s
(Jayan ,Goodman,Mi a)/3/
and
ha
will
be
conside d
he e.
The
scale
ac o
is
calcula ed
on
he
basis
o
he
p e ious
ou pu
le el
o
he
quan ize
and
he
p e ious
scale
ac o .
To
educe
he
p opaga ion
e ec
ha
would
be
p oduced
-
180
E.
Masg au
e
al.
in
he
ob en ion
o
scale
ac o s
in
ecep-
ion
i
a
ansmission
e oc
occu eJ,
a
leakage
ac oc
S
is
used,
so
ha
he
ac-
ual
scale
ac o
c(n)
1s
ob ained
as
ollows:
c(n)
= i•l.
(n-l).c(n-l)B
l ; B <
1.
he e
~1.
(n-1)
i s a
mul iplie
assigned
o
l1e
le.Jel
i
o
he
ou pu
quan ize
in
he
p e ious
sample.
The
alues
oE
hese;
mul iplie s
ha e
been
ob ained
as
/4/
wi h
a B
ac o
o
63/64.
This
quan ize
is
used
in
all
ADPCM
sys ems
he e
conside d,
excep
in
he
case
o
he
CCITT
s andacd,
which
ep esen s
a
slig h
modi ica ion
o
ha
one.
In
his
case,
he
scale
ac o
p esen s
wo
wo king
modes:
a
as
mode,
o
a
speech
signal,
and
a
slow
mode
o
da a.
The
leakage
ac o
alue
is
o
31/32.
De ails
can
be
ound
in
ei:e en-
ces
/1,3/.
2.2
Adap i e
P edic o .
The
p edic o
unc ion
is
ob aining
he
mos
exac
p edic ion
o
he
ac ual
inpu
sample,
so
ha
he
di e ence
be ween
he
wo
alue ,
o
p edic ion
e o ,
be
mini-
mum.
The
dynamic
ange
educ ion
o
he
signal
o
be
quan ized
allows
a
mo e
accu-
a e
ep esen a ion
o
his,
and
he e o e,
a
smalle
quan iza ion
e o .
Since
he
adap a a ion
is
o
backwa d
ype,
inpu
signal
p edic ion
mus
be
done
on
he
basis
o
he
p e ious
econs uc ed
sam-
ples,
which
di e
om
he
eal
ones
in
he
quan iza ion
e o .
The
e o
o
be
minimized
is
he
quan ized
p edic ion
e
co ,
which
is
he
only
a ailable
in
he
ecep ion.
All
he
p edic o s
usec;l
a e
o
FIR
ype
I
excep
in
he
case
o
CCITT
s anda d,
which
is
he
IIR
ype.
The
algod hm
he e
consi-
de ed
a e
he
ollowing:
a).
T ans e sal
LMS
no malized
(LMS).
b).
G adien
Adap i e
La ice
(GAL).
c).
G adien
Adap i e
La ice
wi h
Two
Pa co s
(GAL2).
d).
Exac
Leas
Squa es
Adap i e
La ice
(LSAL).
e).
CCITT
s anda d:
Recu si e
Signed
G adien .
Equa iond
o
upda ing
he
coe icien s
in
e e y
case
a e
b ie ly
exp essed
as
o-
llows:
a)
LMS
no malized.
am(n+l)=am(n)
+
P(n).p
e
(n)
x(n-m)
q
wi h
A p
x(n)=
E a
(n)
~(n-m)
m=l
m
x(n)
P(n)
~(n)
+ e
(n)
q
(
l-w)x
2(
n)
+
wP(n-1)
p:
p edic oc
o de .
b)
GAL
The
la ice
p edic o
s uc uce
is
shown
in
Figu e;
2.
2 2
P
(n)=(l-w)~e
(n)+
(n-l))+wP
(n-1)
m m m m
x(n
)
Figu e
2.
La ice
p edic o
es uc u e
c)
GAL2
In
his
case,
wo
di e en s
Pa co
coe -
icien s,
Ke
and
K
,
a e
conside ed.
m m
Ke
+l(n+l)=Ke
+l(n)+
a
em+l(n) m(n-1)
m m
P
(n-l)
m
. e
em+l(n)=em(n)-K
m+l(n) m(n-1)
m+l(n)= m(n-1)-K
m+l(n)em(n)
2
P
(n-1)=(1-w)
(n-l)+wP
(n-2)
m m m
e 2 e
P
(n)=(l-w)e
(n)+wP
(n-1)
m m m
d)
LSAL
K
(n+l)=wK
(n)+(l-y
1
(n)
)e
(n)
(n-1)
m m
m-
m m
Ke
(n+l)
m
Km(n+l)
P
(n-1)
m
•
32
KBPS
ADPCM
Code s in Noise-F ee and Noisy En i onmen s 181
e e
P 1
(n+l)=P
(n+l)
-
m+
m
P
l(n+l)=P
(n)
-
m+
m
K2
(n+l)
m
P
(
n-l)
m
K2 (
n+l)
m
(
(1-
Y 1 (
n+
1)
) (
n)
) 2
m-
m
ym(n+l}=ym_
1
(n+l)+----~~~----~-----
P
(n)
m
e)
CCITT
s anda d.
In
his
case
he
p edic o
is
o
IIR
ype
wi h
wo
ze os
and
six
poles.The
esp es-
sions,
which
will
no
w i e
he e,
can
be
ound
in
e e ence
/1/.
3.
Empi ical
Resul s.
As
a
es
signal
he
ollowing
sen ence
was
u e ed
in
spanish:
'Es a
es
una
p ueba
de
senal
de
oz'.
To
do
ha ,
encode s
and
de-
code s
o
e e y
p oposed
sys em
ha e
been
simula ed~
aking
in o
accoun
he
lack
ca-
se
as
well
as
he
p esence
oE
ansmission
e o s.
In
he
e alua ion
o
he
ob ained
esul s
se e al
measu es
we e
used.
The
global
signal- o-noise
a io,
i.e.,
a e aged
along
he
whole
speech
eco d
(
200
blocks);
he
SNRSE:G,
ob ained
~y
a e aging
he
mean
alue
o
he
SNR
o
all
blocks;
he
p edic o
gain
GP,
wich
ela es
he
inpu
signal
powe
o
he
p edic ion
e o
powe
a
he
quan ize
inpu ;
and
he
sa u a ion
a e
P
o
pe cen age
o
samples
in
which
he
quan ize
is
sa u ed.
Fi s ly,
he
ou
sys ems
con aining
FIR
p edic o s
we e
un
o
di e en s
alues
o
hei
con e gence
pa ame e s,
o
o de s
l
o
7,
and
se e al
u e ances
including
males
and
emales
speake s.
I
was
obse ed
ha
a
ou h
o de
was
a
good
elec ion,
being
ile
mo e
adcqua es
pa ame e
alues
shown
in
Table
I.
w p
0.15
0.98
4
GAL
0.01
0.99
4
GAL2
0.01
0.99
4
LSAL
0.01 0.99
4
Table
I.
Pa ame e
choices
o
FIR
algo i hms
Figu es
3
and
4
despic
he
ajec o ies
o
he
SNR
a e aged
in
e e y
block
(
256
by-
es
/
block)
o
each
o
he
cases
cspcci ied
in
Table
I
and
male
speake .
Figu e
3.
SNR
ajec o ies
o
LMS
and
GAL2
algo i hms
Figu e
4.
SNR
ajec o ies
o
GAL
and
LSAL
algo i hms.
I ,
I~.:/
E
~--------~----~--'
Figu e
5.
SNR
e sus
p edic o
o de
o
FIR
cases.
In
Figu e
5
i
can
be
obse ed
ha
he
imp o emen
o
he
SNR
when
inc easing
he
p edic o
o de
eaches
i s
maximum
om
o de
4.
Abo e
his
alue,
he
imp o emen
is
almos
null
and
e en
a
deg ada ion
o
he
SNR
occu s
in
he
cases
o
he
simples
algo i hms
such
as
GAL
and
LMS.
This
e ec
is
due
o
he
coe icien s
noise
(p opo -
ional
o
he
o de )
being
g a e
han
he
imp o emen
in oduced
by
he
p edic ion
wi h
a
highe
o de .
In
Figu e
5 ,
he
supe io i y
o
he
la icce
p edic o
ype
-
182 E.
Masg au
e
al.
o e
he
ans e sal
one
is
shown.
On
he
con a y,
one
can
be
susp issed
when
con-
side ing
he
small
di e ences
ha
he
i s
ones
exhibi .
In
pa icula ,
he
op imal
cha ac e is ic
o
LSAL
algo i hm
could
make
us
expec
an
imp o emen
o e
he
es
o
he
algo i hms.
In
his
case,
he
pe omance
o
GAL2
and
LSAL
a e
almos
he
same,
being
his
ac
al eady
e i ied
in
o he
wo ks
/5/.
Nex ,
he
compa a i e
esul s i>b ained
in
he
ou
FIR
ype
cases
o
4
o de
a e
shown
in
Table
II
oge he
wi h
hose
co esponding
o
ha
p oposed
by
he
CCITT.
SNR
SNRSEG
GP
P
SNRSEG
P£
=10-
3
LMS
29.96
18.3
13.35
.2
GAL
31.15
18.63
14.43
.13
GAL2
31.30
18.7
14.92
.14
LSAL
31.37
18.99 15.15
.17
CCITT
27.9
16.5
13.95
.49
14.5
Table
II.
Pe omance
Compa ison
o
he
i e
ADPCM
sys em.
All
magni udes
in
dB
excep
P.
As
i
can
be
obse ed,
he
esul s
ob ained
in
case
o
noise- ee
channels
a e
clea ly
be e
hose
encoded
by
a
la ice
p edic-
o ,
he
wo s
pe omance
co esponding
o
he
CCITT
s anda d.
Nex ,
a
noisy
en i onme~~s
was
simula ed
wi h
an
e o
a e
o
10 ,
si ua ion
wich
equi:ces
a
leas
s abili y
in
he
decoding
p ocess.
Unde
hese
condi ions,
all
he
FIR
algo i hms
exhibi ed
a
g ea
endency
o
di e ge,
wich
makes
i s
use
impossible.
On
he
con a y,
he
CCITT
s anda d
shows
a
s able
beha io ,
and
he
deg:cada ion
o
i s
pe omances
consis s
in
a
loss
o
a:cound 2
dB
(in
SNRSEG)
wi h
espec
o
he
noise-
ee
channel
case.
I
is
ob ious
ha
in
he
case
o
he
CCITT
s anda d
he
quali y
le el
has
been
:ceduced
in
he
op imal
ansmission
condi ions
in
bene i
o
a
be e
beha io
in
ad e se
condi ions.
This
is
ca ied
ou
by
he
use
o
a
smalle
leakage
pa ame e
in
he
quan-
ize
and
he
in oduc ion
o
a
simila
pa-
ame e
in
he
p edic o
coe icien s
up-
da e.
The
p edic o
ze:cos
a e
also
cons-
ain s
o
inne
pa s
o
he
uni
ci cle
so
!1a
he
impulse
esponse
o
he
o e all
sys em
o
one
sample
o
e o:c.
This
cons-
ain s
is
compensa ed
by
in oducing
poles
in
he
p edic o
(ze:cos
in
he
o e all
sys-
em
esponse).
4.
Conclussions.
A
compa a i e
s udy
o
he
pe omances
o
se e al
ADPCM
sys ems
has
been
p esen ed.
The
main
consequencences
de i ed
om
his
s udy
a e
he
ollowing:
la ice
p edic o s
p o ide
pe omance
(a ound
2
dB
in
SNR)
ans e sal
one.
a
be e
han
he
-among
he
la ice
algo i hms,
he
di e-
ences
a e
small,
indis iguishable
in
an
un eliable
audi ion,
being
he
so
called
GAL2
a
easonable
elec ion
o
quali y-
complexi y.
-
he
ou h
o de
seem
he
mos
ap opia e
o
all
FIR
algo i hms.
-
he
CCITT
s anda d
encode
shows a
good
comp omise
be ween
SNR
and
low
deg ada ion
unde
ansmission
e o:c
condi ions.
Unde:c
hese
las
condi ions,
in
he
decoding
p:cocess,
he
FIR
algo:ci hms
a e
no
s able
and
hey
canno
wo k
wi hou
p e ious
modi ica ions.
5.
Re ences.
/1/.
D a
Recomenda ion
G.
7zz.
Ad-hoc
G oup
on
32 Kbps
ADPCM
Algo i hms.
Tempo a y
Documen . No embe
83.
/2/.J.D.Gibson.
'Adap i e
P edic ion
o
Speech
Encoding'.IEEE
ASSP
Magazine,
pp
12-16.
July
1984.
/3/.N.S.Jayan ,P.Noll.
Digi al
Coding
o
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/4/.D.Mi a,B.Go z.
'An
Adap i e
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Sys em
Designed
o
Noisy
Channels
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Digi al
Implemen a ions'.
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/5/
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'A
Compa ison
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•