AN ADPCM WITE AN EXPONENTIAL POWER ESTIMATOR BASED PREDICTOR
George Mathew,
S. V. Narasimhan
and
FOR SPEECE CODING
A. P. Shivaprasad
Dept. of Electrical Communication Engg.,
Indian Institute of Science,
ABSTRACT
The application of Exponential Power
Estimation ( E P E ) technique to realize
computationally simple predictor adaptation
algorithm has been investigated.
An ADPCM
system which employs the EPE-based adaptive
predictor provides a computational advantage
of 2N multiplications (N being the predictor
o r d e r ) a n d o n e d i v i s i o n per i t e r a t i o n
compared to the ADPCM which employs a block
power estimator based adaptive predictor.
Performance comparison has been done with two
conventional ADPCM systems at different bit
rates and channel conditions, using different
quantizer characteristics.
The results
indicate that the proposed ADPCM performs
identical to the conventional ones at 32 kbps
(kilo bits per second) and better than them
at 16 kbps.
1. INTRODUCTION
In speech coding, it is known that the
Differential Pulse Code Modulation (DPCM)
schemes provide reduction in the bandwidth
requirement (by removing the redundancy) as
c o m p a r e d to the P u l s e C o d e M o d u l a t i o n
schemes, for a specified quality. To achieve
adequate dynamic range and good subjective
quality, however, it is necessary to adapt
the parameters of the quantizer and predictor
of the DPCM syst.em, to the input signal
characteristics.
Several algorithms have
been developed for adapting the quantizer and
predictor, most of which suffer from high
computational complexity and are hence not
easily implementable.
Attempts have been
done to reduce this computatonal complexity
and the algorithms reported in [8161211] are
examples in this direction.
Among the various algorithms available
for predictor adaptation [ 7 ] , the Least Mean
Square (LMS) gradient adaptive algorithm is
the simplest from the computational point of
view.
I n t h e L M S a l g o r i t h m , at e a c h
iteration, the predictor coefficients are
updated by moving a small step on the mean
s q u a r e p r e d i c t i o n e r r o r s u r f a c e in t h e
direction opposite to that of the gradient of
the surface
To ensure convergence, the
s t e p s i z e i s l i m i t e d by t h e m a x i m u m
eigenvalue ( l m a x ) of the autocorrelation
[a].
matrix of the input siqnal.
However, for
computational simplicity, product of the
input signal power and the predictor order,
which i s e q u a l t o the t r a c e of t h e
correlation matrix, is used instead of lmaX.
Bangalore-560 012,
complexity contributes to the complexity of
the A D P C M system.
In this paper, the
p e r f o r m a n c e o f a n ADPCM s y s t e m w h o s e
predictor coefficients are adapted based on
the LMS algorithm which makes use of the
Exponential Power Estimator (EPE) [l] for
estimating the signal power is studied. The
use of EPE algorithm, which obtains the power
estimate without any multiplications or
divisions and expresses it in the form 2i, i
being an integer, renders the adaptation
algorithm
computationally
simple.
Performance comparison is done with two
conventionally used predictor adaptation
schemes.
In the following sections, the EPE
algorithm, predictor adaptation and results
and
discussion
are
presented.
2. EXPONENTIAL POWER ESTIMATION
T h e d e s i r e d f e a t u r e s of a power
estimator are the following:
1) The estimate should follow the significant
changes
in
the
input
signal
characteristics,
2) The estimation should not introduce any
a d d i t i o n a l c o m p u t a t i o n s in t e r m s of
multiplications or divisions, and
3 ) Use of this estimate should not lead to
further complexity.
Based on these features, the conventional
Block and Recursive power etimators [l] are
not only complex by themselves but also make
the a d a p t i v e a l g o r i t h n q u i t e complex.
However, the EPE estimator, whose features
were introduced in the previous section, is
not only simple from the computational point
of view but also has a fast response due to
its e x p o n e n t i a l n a t u r e ( a s a g a i n s t the
additive nature of the conventional ones).
The basic principle of the EPE algorithm is
to track the envelope of the sequence x2(n)
and the algorithm is given below:
1. Compute N(n) = l ~ ( n ) 1 2 - k ( ~ - ~ ) / a
2.
T(n) = T(n-l)(l + 21T)
if N ( n ) > 1
= T(n-l)(l - 2DT)
if N(n) < 1
= T(n-1)
otherwise.
where ,
x(n)
Thus, the input siqnal power is important in
preeictor adaptation a n d i t s estimqtion
T(n)
- input signal,
estimated,
- an internal
whose power is to be
variable wnich is
updated to t r a c ~tnp envelope of
34.3.1
682
INDIA.
CH2766 - 4/89/0000 - 0682 0 1989 IEEE
i(n)
ITIDT
sequence x2(n)
-- anthe
integer variable,
negative integer constants which
c o n t r o l t h e a m o u n t s of i n c r e m e n t
(T(n-l)2IT)
and
decrement
( T ( r 1 - 1 ) 2 ~ ~ )in T(n) and hence the
speed of updating,
integer part of (.) and
max
limits of T(n).
- -
T,,,in,
T m a x is c h o s e n d e p e n d i n g u p o n t h e
maximum input signal level ( 1 Xmaxl = 2Tmax)
and then Tmin is decided by the dynamic range
Tmin).
(DR) requirement as DR(dB) = 6(Tmax
The values of I T and DT are chosen depending
upon t h e r e q u i r e d r e s p o n s e r a t e o f t h e
algorithm and t h e ratio of increment to
decrenient (I/D) in T( n).
-
4. RESULTS AND DISCUSSION
Performance of the three ADPCM systems
(E-, B- and S- A D P C M S ) m e n t i o n e d i n t h e
previous section have been evaluated for real
speech input under ideal ( n o i s e f r e e ) and
noisy channel conditions, at bit rates of 1 6
pip0
and 32 kbps.
The sentence used is
be an t o rust while new" (male voice) and is
& i ~ t e a ? o ~
E.,
sampled at 8 kHz.
and digitized into 1 2 bits, thus resulting in
an i n p u t s i g n a l r a n g e o f (-2048, 2048).
Segmented Signal t o Noise Ratio (SEGSNR) with
nonoverlapping eegmeQt.9 of length 1 6 0 samples
is u s e d a s t h e p e r f o r m a n c e measure.
Both
uniform and nonuniform (Gaussian) [ 5 ]
quantizer characteristics have been used for
the prediction error quantization. Quantizer
adaptation is done based on the principle of
robust a d a p t i v e q u a n t i z a t i o n [4] so a s t o
m a k e t h e q u a n t i z e r r o b u s t t o c h a n n e l bit
errors.
3. PREDICTOR ADAPTATION
The LMS algorithm used for updating t h e
predictor (linear) coefficients of the ADPCM
system (Fig. 1) is given byt
aj(n+l) = a;(n)
where ,
X(n)
aj(n)
+
2 w
--------
- input
- jth
signal t o the predictor,
predictor
c o e f f i c i e n t at
the nth instant,
8
a,(n)X(n-j)t
-
N
predictor
outputt
quantized prediction errort
input signal power estimate,
predictor order
and
0 < d-, < 1.
The power estimate Px(n) is obtained using
the EPE algorithm given in section 2.
The
performance of the EPE based ADPCM has been
compared with two conventional ADPCM systems
given below:
3.1
Block Power Estimator
based
ADPCM
B-ADPCM 1
k e r e t t h e p o w e r e s t i m a t e P p ( n ) is
obtained using the conventional block power
rotimator given by
whrrr
N1
K
,
- block length of the data used for
- astimation,
a positive constant to keep the
estimate away from zero during the
silence periods.
3.2
Sign-Siqn LMS based ADPCM (S-ADPCM)
Here, t h e predictor c o e f f i c i e n t s a r e
updated using the Sign-Sign LMS algorithm [SI
given by
aj(n) + X sgn(eq(n)) sgn(X(n-j))
aj(n+l)
where sgn(.) is the signum function and
O < x < 1
and
l:jLN
-
T h e ADPCM system parameters a s used in
the s i m u l a t i o n s t u d y a r e g i v e n below:
Predictor:
T m a x = 11:
Dynamic Range = 60 dB;
T m i n = 1; I/D = 4: IT
-5; DT = -7;
O b =9'2
at 3 2 kbps and&
=8'2
at 16 kbps: A = 2-11 and K = 10;
N = 4 and NI = 4.
Quantizer:
D y n a m i c R a n g e = 60 d B ; M a x i m u m s t e p
s i z e = 1000; Minimum s t e p size = 1 and
t h e leakage factor = 63/64.
Figs. 2 and 3 s h o w t h e i d e a l c h a n n e l
performance of E-r B- and S- ADPCM systems
using uniform and nonuniform quantizers at
the bit r a t e s o f 3 2 and 1 6 kbps.
The
p e r f o r m a n c e of E-ADPCM is i d e n t i c a l t o SADPCM and slightly inferior t o 8-ADPCM at 3 2
kbps (fig. 2).
However, E-ADPCM has a small
edge over S-ADPCM and is identical t o 8-ADPCM
at 1 6 kbps (fig. 3).
4 and 5 illustrate the
Figs.
corresponding results for noisy channel
conditions.
These results are obtained by
doing t h e s i m u l a t i o n for 2 0 independent
random number sequences for every bit error
rate (BER) and then averaging the results.
The differen2 BER considered are
and 10'
The BER of low5 correspond t o
As c a n b e
t h e i d e a l c h a n n e l condition.
observed from fig. 4, t h e performance of EADPCM is better than S-ADPCM but inferior t o
B-ADPCM at 32 kbps. However, at 1 6 kbps, its
p e r f o r m a n c e is s u p e r i o r t o b o t h B- and sADPCM systems.
.
F u r t h e r , it c a n be s e e n t h a t t h e
nonuniform quantizer provides about 1.5 d B
SEGSNR improvement over the uniform one at
32kbps (figs. 2 and 4), whereas they perform
a l i k e at 1 6 kbps.
The reason for this
behaviour can be attributed t o the nature of
the threshold levels of these quantizers.
T h e observations noted above have been
found t o be true for other speech sentences
also.
Table I compares the computational
34.3.2
683
requirements of the three ADPCM systems.
It
can be seen that the E-ADPCM has an advantage
of 2N m u l t i p l i c a t i o n s and o n e d i v i s i o n
compared to the B-ADPCM.
However, the SADPCM i s c o m p u t a t i o n a l l y l e s s c o m p l e x
compared :o the E-ADPCM.
These results and the further studies
aimed at the application of EPE for speech
coding to realize computationally simple
adaptation algorithms for predictor and
quantizer prove that an ADPCM based on the
EPE algorithm is best suited for low bit rate
applications [3].
CONCLUSIONS
An ADPCM which uses t.he Exponential
Power Estimation (EPE) technique for updating
its predictor coefficients has been studied
for real speech input at the bit rate of
1G and 32 kbps, usinq uniform and nonuniform
robust adaptive quantizers, under ideal and
noisy channel conditions. The proposed ADPCM
has an improved performance at 16 kbps and
identical performance at 32 kbps, compared to
the c o n v e n t i o n a l s y s t e m s c o n s i d e r e d .
F u r t h e r , t h e use of EPE p r o v i d e s a
computational advantaqe of 2N multiplications
and one division over tnp ADPCM that uses the
block power estimator.
The fact that the EADPCM system with sucn sipnificant reduction
in computational complexity performs better
or identical to the higher complex R-ADPCM
s y s t e m , b r i n g s c u t t n e e f f i c i e n c y and
simplicity of the EPE technique.
REFERENCES
1. M. B e l l a n g e r
and
C. C. E v c i , " A n
Efficient Step-size Adaptation Technique for
LMS Adaptive Filters," Proc. IEEE Int. Conf.
Acoustics, Speech and Signal Processing,
pp.1153-1156, 1965.
2. W. R. Daummer, X. MaitrerP. Mermelstein
and I. Tokizawa, "Overview of the ADPCM
Coding Algorithm," Proc. IEEE Int. Conf.
Global Telecommun., pp.774-777, 1984.
3 . George Mathew, "Application of Exponential
Power Estimatpr for Speech Coding," Master of
Science (Engg.) Thesis, Dept. of E C E l
I I Sc Bangalore, July 1989.
4. D. J. Goodman
and R. M. Wilkinson, " A
Robust Adaptive Quantizer," IEEE Trans.
Commun., vol.COM-23, pp.1362-1365, Nov. 1975.
5. J. M a x ,
"Quantizing
for
Distortion," IRE Trans. Inform.
vol.IT-6, pp.7-12, March 1960.
Minimum
Theory,
6. D. W. Petr,
"32 KBPS ADPCM-DLQ Coding for
Network Applications," Proc. IEEE Int. Conf.
Global Telecommun., pp.239-243,1982.
7. R. C. R e i n i n q e r and J. D .
Gibson,
"Backward Adaptive Lattice 3nd Transversal
Predictors in ADPCM," IEEE Trans. Commun. ,
vol.COM-33, pp.74-82, June 1985.
8. J. M. Roulin, G. Eonnerot,J. L. Jeandot
and R. Lacroix, " A 60 Channel PCM-ADPCM
Converter," IEEE Trans. Commur.. I vol..CON-30,
pp.567-573, April 19G2.
9. E. Widrow, J. M.
McCoo1, N. G. Larimore
and C. R . J o h n s o n Jr.,
" S t a t i o n a r y and
Nbnstationary Learninq Characteristics of Lb!S
Adapt i v e F i 1 t e r ," P r c c
I E E E , vo 1 . 6 4 ,
pp.1151-1162, Aug. 1976
.
Table
.
1
Computational Requirements of E-, B- and S- ADPCM systems
Type of
Operation
E-ADPCM
Exponentiations
1
Divisions
0
Multiplications
684
S-ADPCM
1
4N+B+1
2N+1
I
8-ADPCM
1
2N+B+1
Additions
34.3.3
-_
N+B+1
3N
I
2N
I
I
si.
-1
0
7
UNIFORM QUANTIZER
~
*
i
-40.00
i
-20.00
0.00
20.00
40
UNIFORM QUANTIZER
I
v
1
i
1
I
-30.00
-50.00
-10.00
10.00
30.00
0
0
In
NONUNIFORM QUANTIZER
N
-50.00
FIG.2
-30.00
-10.00
10.00
INPUT LEVEL IN OB
NONUNIFORM QUAP(T1ZER
30.
LD
I D E A L CHANNEL AT 32 KBPS
30.00
-30.00
-10.00
10.00
INPUT LEVEL IN OB
-50.00
FIG.3
I D E A L CHANNEL AT 16 KBPS
0
9
2
UNIFORM QUANTIZER
N
(U
UNIFORM QUANTIZER
m
0
20
U?
2
:
m
m
W
0)
0
0
-
-3
-5.00
-4.20
-3.40
-1.8
-2.60
0
I
-5.00
I
-4.20
I
-3.40
-2.60
-1.80
0
9
1
NONUNIFORM QUANTIZER
CD,
N
0
W
m
0
0
ua
1
-5.00
FIG.4
1
I
I
1
-3.40
-1.8
-2.60
BIT ERROR RATE IN LOG (BER)
-4.20
NOISY CHANNEL AT 32 KBPS
0
: E-ADPCM,
A
2
B-ADPCMt
?
L
U
-5.00
FiG.5
,
-4.20
l
-3.40
l
-2.60
l
-1.80
BIT ERROR RATE IN LOG (BER)
NOISY CHANNEL AT 16 KBPS
+: S-ADPCM
34.3.4
685