SIGNAL PROCESSING
V:
Theo ies and Applica ions
L.
To es,
E.
Masg au,
and
M.A. Lagunas (eds.)
© Else ie Science Publishe s
B.
V.,
1990 1303
ROBUST
LPC
VECTOR QUANTIZATION BASED
ON
KOHONEN'S DESIGN ALGORITHM
Jose
A.
Rod iguez-Fonollosa, En ique Masg au, A.Mo eno
Depa amen de Teo ia del Senyal i Comunicacions
Uni e si a Poli ecnica de Ca alunya
Apdo. 30.002, 08080 Ba celona, Spain.
This pape desc ibes a Mul is age Vec o Quan iza ion scheme
in
which he codewo ds a e adap ed
o ollow he inpu s a is ics. This adap a ion is compu a ionally e y simple and equi es no
addi ional bi ansmission. The adap a ion algo i hm is shown o be closely ela ed wi h he ec o
quan ize design echniques known as LBG and Kohonen's. We ha e s udied he applica ion o he
de eloped scheme o quan ize he LPC pa ame e s and some esul s a e p esen ed in which he
esul ing adap i e s uc u e is shown o ou pe o m no only he non-adap i e mul is age ec o
quan ize bu also he con en ional ull-sea ch ec o quan ize .
1. INTRODUCTION
Vec o
quan iza ion
(VQ) is a simul aneous
quan iza ion o a sequence o samples o ec o .
This p ocess allows o make e ec i e use o he
in e ela ions
among
he
di e en
ec o
componen s and pe o mance a bi a ily close o he
ul ima e a e-dis o ion can be achie ed by VQ i h(
ec o dimension is high enough [1].
Ne e heless, he exponen ial g ow h in complexi y
o ces he use o low-dimensionali y
VQ
in
p ac ical
sys ems.
In
his case some kind o adap a ion is
necessa y
o
ob ain
adequa e
pe o mance,
specially when we deal wi h non-s a iona y inpu s
as
in
speech coding:
Se e al kinds o adap i e VQ-based coding
schemes can be ound in he li e a u e.
Fo
example, he popula CELP [2] can be seen as
an
adap i e ec o quan ize whose codewo ds a e
ame o ame adap ed o he inpu s a is ics
(au oco ela ion) by linea il e ing.
In
he wo k we desc ibe he e we ha e ollowed a
di e en app oach
in
which he adap a ion algo i hm
is di ec ly de i ed om he VQ design echniques.
The esul ing scheme will be use ul when some
local s a iona i ies a e expec ed in he inpu ec o
s a is ics.
In
his communica ion we explo e i s
applica ion o quan ize he LPC pa ame e s, Video
coding is ano he a ea in which his adap i e
quan ize has been shown o be use ul
[1
0].
l is well known ha , o a gi en bi a e, a speake
dependen codebook, i.e. designed o he speci ic
speake whose speech is being coded, would wo k
be e
han a speake -independen codebook.
The e o e, and adap i e quan ize is also expec ed
o ou pe o m a non-adap i e
one
when i
is
used o
quan ize he LPC pa ame e s. This scheme would
also
be
able o adap o o he a ia ions
in
he
speech spec um
as
hose due o he acous ic
en i onmen o he speake and o he eco ding
condi ions,
and
he esul will
be
an
inc ease
bo h
in
pe o mance
and
in
obus ness.
The adap i e ec o quan iza ion o he LPC
pa ame e s ha e been also s udied by o he
au ho s.
In
[3]
a sys em ha changed he codewo ds
in
ime is desc ibed. Ne e heless his change
c ea es he necessi y o ansmi ing he new ec o s
o he ecei e wi h a signi ican inc ease
in
bi - a e.
In
he scheme ha we p esen he mul is age
VQ
s uc u e [4] is shown o allow he edesign o he
quan ize o one s age using he in o ma ion gi en
by
he es o he s ages, he e o e,
no
addi ional bi
ansmission is needed.
In
[5] ec o linea p edic ion is used o make
e ec i e use o he conside able edundancy
be ween di e en speech ames wi hin one
phoneme. Ou app oach
can
also
be
iewed
as
a
ec o p edic o o educed complexi y. Fu he mo e
he quan ize is expec ed
o
ollow no only he local
s a iona i ies bu also he long e m (speake )
s a is ics o he inpu ec o s.
In
he ollowing sec ion o he pape
we
will i s
p esen he adap i e mul is age ec o quan iza ion
(AMSVQ) scheme. This scheme was p e iously
epo ed
in
[6] whe e he adap a ion algo i hm was
de i ed as
an
LMS
ype minimiza ion.
In
his pape ,
we ex end ou p elimina y epo and show he
close ela ion be ween he p oposed algo i hm and
he
VQ
design echniques known
as
LBG
[7] and
" Kohonen's [8].
1304
In
he las pa o he pape he de eloped scheme is
applied o he quan ize he LPC pa ame e s. We will
i s compa e he pe o mance o he adap i e wi h
he non-adap i e mul is age s uc u e and he ull-
sea ch VQ. Then his quan ized LPC pa ame e s a e
used
in
he CELP and he Mul ipulse code and bo h
he
SNR esul s and
he
subjec i e quali y is
discussed.
2.
DESCRIPTION
Mul is age ec o quan iza ion (MSVQ) has always
been seen as a subop imal
VQ
scheme wi h
educed complexi y and s o age.
l
consis s o
successi ely
app oxima ing he inpu
ec o
in
se e al cascaded VQ s ages, whe e he inpu ec o
om each s age is he quan iza ion e o om he
p eceding s age.
In
[4]
he MSVQ is applied o he
quan iza ion o he LPC pa ame e s, and i is shown
ha , in he case o Euclidean dis ance measu es
such as he log-a ea a io, ha quan ize is e y
close o a heo e ically p edic ed asymp o ically
op imal
a .e
dis o ion ela ionship.
In
he scheme we p esen he mul is age s uc u e
has been used o de elop a con inuously adap i e
VQ. The objec i e o he adap i e algo i hm is o
upda e
he
las used
code ec o
Ci
in o de o
minimize he exponen ially weigh ed mse
Ei
de ined
as
E = L
pi
IIXi(n-j)-Ci(n+1
)112
i=O
(1)
whe e Xi(n-j) a e he
inpu
ec o s
p e iously
quan ized by
Cj.
The minimiza ion o (1) gi es
00
L
pi
Xi(n-j)
Ci(n+1)
=.~,;;j=:.,O
__
_
00
00
Ci(n+
1) =
(1-P)
[ L
pi
Xi(n-j) + Xi(n) ]
(2)
i=1
No e ha Xi(n) is he las inpu ec o x(n) and he
in ini e sum can be iden i ied as he p e ious
Ci,
so
we can exp ess he abo e equa ion as
Ci(n+
1) = P
Ci(n)
+
(1-P)
x(n)
Ci(n+
1) =
Ci(n)
+
(1-P)
(x(n) -
Ci(n))
(3)
o
Ci(n+
1) =
Ci(n)
+
(1-P)
e(n)
(4)
whe e e(n) is he quan iza ion e o .
This upda e equa ion is he well known Kohonen's
algo i hm,
used
o design wha he calls sel -
o ganizing ea u e maps [8],
i.
e., ec o quan ize s.
This algo i hm, as i appea s in (4), is no use ul o
adap ing he quan ize as i is used because he
ecei e
does
no known he alue
o
he
quan iza ion e o . Ne e heless in a MSVQ he
e o
o one s age is quan ized by he ollowing
s ages, he e o e, his quan ized e o is a ailable a
he decode and is used ins ead o he ac ual e o .
The esul ing upda ing equa ion is hen
Ci(n+1) =
Ci(n)
+ Jleq(n)
(5)
whe e
Jl=(1-P) is he s ep size and eq(n) is, in
gene al, he sum o he ou pu s o he ollowing
s ages.
In
he mos simple case, (2 s ages), he VQ
equa ions a e
Cj
=
q1(
X) (6)
eq
= q2( X -
Cj
)
(7)
z =
Ci
+
eq
(8)
whe e x is he inpu ec o , z he quan ized ec o ,
Ci
he
ou pu
o
he i s
quan ize
and
eq
he
con ibu ion o he second code book (Fig. 1
).
X .
..
VQ,.
c
• 1
•
•
+ e
eq
' I
l---------------------J
Figu e
1.
AMSVQ sys em
wi h
2 s ages
Then eq, ha is an es ima ion o he quan iza ion
e o o he i s codebook, is used o adap he i s
quan ize as equa ion
(5)
indica es.
As i is shown in
[6]
his algo i hm can also be
ob ained
applying
a
LMS- ype
minimiza ion
algo i hm o he
e o
a he ou pu o he i s
codebook. In ou simula ions we only adap ed he
i s
s age
ha
was
a
ull-sea ch
codebook.
Ne e heless, a simila algo i hm can be de i ed o
gain-shape
ec o
quan ize s and
o he
kind o
s uc u es as he ee-sea ched ec o quan ize
[9].
Al hough obus
o
a ia ions in he signal s a is ics
he abo e adap a ion make he
quan ize
mo e
sensi i e
o
channel e o s ha he con en ional
mul is age s uc u e. This p oblem can be educed
using a leakage ac o simila o ha used in he
I
. l
(
4
1
q
il
n
c
(
c
q
VII
w
V1
81
o
a
S1
1
:
n
:
e
s
e
11
d
LMS- ype algo i hms
o
p ac ical
ADPCM
schemes.
Then
(5)
is
modi ied o gi e:
Ci(n+1)
=
(1-y)
Ci(n)
+
1J.9q(n)
+YCio(n) (10)
whe e y is a small alue ha con ol he memo y o
he sys em
and
Cio
is
he ini ial (design) alue
o
he
code ec o
Cj.
3. CODEBOOK DESIGN
The codebook design app oach
is
simila o ha
used
in
con en ional mul is age
VQ
[1].
We
need
a
ep esen a i e speech aining se om di e en
speake s, bu hanks o he adap i e na u e
o
he
AMSVQ sys em he esul s
a e
no expec ed o
be
e y condi ioned
by
he elec ion o he aining
sequence.
S a ing wi h he i s codebook
and
using he
LBG
clus e ing algo i hm (7], he codebooks a e
cons uc ed
in
succession. The aining sequence
o he second codebook is ob ained
as
he i s
codebook quan iza ion e o .
The
p oblem
is
ha ,
o
ob ain his quan iza ion e o ,
we
need
he ou pu o
he second codebook o apply he adap a ion
algo i hm
(5)
o he i s codebook. As
eq
is
no
a ailable
o
ob ain his aining sequence, he ac ual
q·uan iza ion e o e is used o adap he i s
codebook (equa ion (4)). Fu he de ails
can
be
ound
in
[6].
4.
RESULTS
The AMSVQ sys em has been applied o he
quan iza ion o LPC pa ame e s wi h impo an
imp o emen s espec o he con en ional
mul is age s uc u e. Quan iza ion o he LPC
coe icien s has been ex ensi ely s udied.
Gene ally, he in e se sines o he e lec ion
coe icien s
o
he log-a ea a io alues a e
quan ized.
We
chose
he
log-a ea a io alues wi h
he
mse
dis o ion o ou expe imen s. The e o e,
we
will de ine he LAR-SNR
as
M N
L L i2(m)
LAR-SNR =
~M~m:::=;.:.~~i=..;.
1
---
L L ( i(m)-Vqi(m))2
m=1
i=1
whe e
Vi
is
he i- h log-a ea
a io.
Vec o quan ize s
ha e
p o en
o
be
e y e icien
in
encoding he p edic o pa ame e s. Ne e heless,
o high quali y coding, 24-30 bi s
a e
equi ed
and
a ull sea ch codebook become imp ac ical.
S uc u ed codebooks,
as
he mul is age, mus
be
1305
used o educe he complexi y. The de eloped
adap a ion algo i hm makes he subop imal
mul is age s uc u e e icien and obus agains
di e en speake s, languages
and
en i onmen s.
To design he quan ize s a aining speech
sequence o med
by
80
sen ences
o
7 emale
and
7 male speake s was used. And o es he
quan ize s
we
chose
24
sen ences o a di e en
male speake (no included
in
he aining
sequence).
The
silen segmen s (backg ound noise)
we e
no
p ocessed.
The speech signal
was
no p eemphasized
and
he
co ela ion me hod wi h a Hamming window
o
200
samples
(25
ms)
was used o ob ain en
log
a ea
pa ame e s e e y
160
samples
(20
ms).
4.1.
High- a e quan iza ion
The i s esul s
we
p esen ha e been ob ained
using a codebook o 8 codewo ds
(3
bi s/ ame)
in
he i s s age
and
3 codebooks
o
256
codewo ds
(8
bi s/ ame)
in
he second, hi d
and
ou h
s age. The
numbe o bi s o
each
ame
is
hus
27
(3+8+8+8)
and
a
50
ames/s, he bi
a e
equals
1350
bps.
To
ob ain a as adap a ion and obus ness agains
channel e o s, only he 8 codewo ds
o
he i s
quan ize we e adap ed.
Fi s
o
all,
we
s udied he pe o mance
o
a single
codebook o 8 codewo ds
(3
bi s) when i was
adap ed using he ac ual e o e ( o wa d
adap a ion). The esul s showed
an
inc ease
in
signal o noise a io (LAR-SNR)
o
mo e
o
2 dB o
alues o he s ep
size
be ween
0.1
and
1,
and
local
maximum we e obse ed nea
1J.=0.1
and
1J.=0.6,
so
hese alues and
IJ.=O
we e used o design h ee
di e en se s
o
codebooks.
V
SNR
-a-
0.0
-0.1
...
0.6
-1
+-----,.------,..-~- ---.,...-----i
0,00 0,02 0,04
0,06
0,08 0,10
11
Figu e
2.
Inc ease in
SNR
o
he
h ee
designed
AMSVQ
Then, he designed codebooks ha e been used o
quan ize he es
~eque~ce
wi h
di e ~n
alues ?
he s ep size ll·
F1g.
2 Illus a es he mc emen m
LAR-SNR espec o he
19
dB o he con en ional
(IJ.=O),
mul is age ec o quan ize . The bes esul s
1306
a e now ob ained wi h
).1.=0.4
and he AMSVQ
sys em designed o
).1.=0.1.
Ne e heless smalle
alues o he s ep size
as
).1.=0.1
o
).1.=0.01
gi e
also
a signi ican inc ease o he pe o mance
and
can
be
a good choice o p o iding obus ness agains
channel e o s.
4.2.
Low- a e quan iza ion
The
aim
o his expe imen
was
o
compa e he ull-
sea ch VQ wi h he AMSVQ.
Due
o
he complexi y
o he ull-sea ch scheme only 1 0 bi s pe ame
we e used.
We
ied di e en dis ibu ions o bi s
be ween he i s and he second s age. Fig. 3
compa es he LAR-SNR ob ained wi h
each
scheme
and in able I he complexi y o he ull-sea ch
and
he bes AMSVQ schemes is also shown .
A
28
37
46
55
64
73
82
Figu e 3. LAR-SNR o some AMSVQ schemes wi h
di e en bi dis ibu ions and he Full-sea ch VQ (A).
Scheme bi s/ ame Comp. Cos LAR-SNR
VQ
10 1024 11,52
AMSVQ 3+7 136 12,53
AMSVQ 2+8 260 12,62
Table I. Compu a ional cos and LAR-SNR o some 10
bi s VQ schemes.
4.3.
Speech coding
The de eloped AMSVQ o he
LPC
pa ame e s
has
been in eg a ed
in
a CELP
and
a Mul iPulse code .
As, i was expec ed, he esul s show ha
an
inc ease
'in
LAR-SNR gi es also
an
inc ease
in
he
global pe o mance o he code
and
bo h speech
quali y
and
SNR
is
imp o ed (Table
11).
bi s/ ame CELP Mul i pulse
00
10,57 14,50
AMSVQ-27 10,00 13,30
MSVQ-27 9,65 12,90
AMSVQ-19 9,38 12,80
MSVQ-19 9,15 12,20
Table II. SNR o di e en code s and some LPC VQ schemes
5.
CONCLUSIONS
The applica ion o he de eloped adap a ion
algo i hm o he mul iple s age ec o quan ize
allows
o
inc ease he pe o mance
and
educe
he
complexi y o p e ious VQ-based schemes. This
algo i hm is e y simple and equi es
no
addi ional
bi s. The quan ize is con inuously edesigned
and
i
is less sensible o he chosen aining sequence.
Ne e heless, one o he mos impo an esul s is
he inc ease in obus ness ac oss di e en
speake s, languages and en i onmen s ha he
adap a ion algo i hm p o ides.
The esul s show ha he AMSVQ inc eases he
pe o mance o con en ional mul is age quan ize s
and can
be
a good choice o coding he LPC
coe icien s wi h high quali y.
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Makhoul,
S.
Roucos,
and
H.
Gish. "Vec o
Quan iza ion
in
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73,
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M.R.
Sch oede , and
B.S.
A al. "Code-exci ed
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a
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941-944, Ma ch 1985.
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B.H.
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597-600, No embe 1982.
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M.
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G.
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IEEE
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225·228, Lisboa, Ap il 1989.
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Y.
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[9]
J.A. Rod guez-Fonollosa. "Cuan i icaci6n
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[10] J.R. Fonollosa,
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J.A. Rod guez-Fonollosa.
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Vec o
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1
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l
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e
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