Code excited linear prediction coding is an efficient technique for compressing speech sequences. Communications quality of speech can be obtained at bit rates below 8 Kb/s. However, relatively large coding delays are necessary to buffer the input speech in order to perform the LPC analysis. A low delay 8 Kb/s CELP coder is introduced in which the short term predictor is based on past synthesized speech. A new distortion measure that improves the tracking of the formant filter is discussed. Formal listening tests showed that the performance of the backward adaptive coder is almost as good as the conventional CELP coder

Leblanc, W. P.

Mahmoud, S. A.

Neumeyer, L. G.

English

NASA Technical Reports Server

N9 2-- i 83. :!,
A Low-Delay 8 Kb/s
Backward-Adaptive CELP Coder
L.G. Neumeyer, W.P. LeBlanc and S.A. Mahmoud
Dept. of Systems and Computer Engineering
Carleton University
Ottawa, Ontario, K 1S 5B6, Canada
Phone: 613-788-5753
Fax: 613-788-5727
ABSTRACT*
Code-excited linear prediction coding is an
efficient technique for compressing speech se-
quences. Communications quality of speech can
be obtained at bit rates below 8 Kb/s. How-
ever, relatively large coding delays are neces-
sary to buffer the input speech in order to per-
form the LPC analysis. In this paper we intro-
duce a low-delay 8Kb/s CELP coder in which
the short-term predictor is based on past syn-
thesized speech. A new distortion measure that
improves the tracking of the formant filter is dis-
cussed. Formal listening tests showed that the
performance of the backward-adaptive coder is
almost as good as the conventional CELP coder.
INTRODUCTION
Recent advances in linear prediction coding
have made it possible to achieve communica-
tions quality of speech at bit rates below 8 Kb/s.
Practical real-time implementations are possi-
ble due to efficient algorithms based on Code-
Excited Linear Prediction (CELP) [1]. In these
coders, the residual is vector quantized using an
analysis-by-synthesis search procedure. The ex-
citation vector (or codevector) is chosen from a
large codebook. All the codevectors are passed
through the synthesis filters and compared with
the original speech vector. The index of the
codevector that minimizes an objective distor-
tion measure between original and quantized
speech is sent through the channel. The parame-
ters of the synthesis filters (gain, long- and short-
term LPC coefficients, and pitch lag) are sent
* This work has been sponsored by the Telecommunication Research
Institute of Ontario (TRIO).
to the decoder as side information. Gain, pitch
lag, and long-term predictor coefficients can be
optimized using closed-loop procedures. Ide-
ally, the formant filter could also be optimized
in a closed-loop procedure but this would lead
to a mathematically untractable set of non-linear
equations [2]. Therefore, the short-term predic-
tor coefficients are calculated using an open-loop
solution based on the original speech. In order to
obtain a reliable linear prediction filter, approx-
imately 20 ms of speech samples are buffered.
The one-way delay of the coder, although highly
dependent on real-time implementations, could
be as high as 60 ms. The delay could be re-
duced by using only past speech (no buffering).
However, the linear prediction analysis would be
unreliable, resulting in poor speech quality. This
problem can be overcome by updating the LPC
parameters at a higher rate. This would require
more bits/sample, thereby increasing either the
total bit rate or the distortion.
In this paper, we present an 8 Kb/s CELP
coder in which the short-term linear prediction
parameters are updated in a backward-adaptive
manner. That is, the linear prediction analysis
is performed on past synthesized speech which
is available, assuming no transmission errors, at
both ends of the channel. Therefore, the LPC
parameters are not sent through the channel and
can be updated at high rates, even in a sample-
by-sample basis. Speech quality is as good as in
the conventional (or forward-adaptive) coder. A
new distortion measure is introduced to prevent
predictor mistracking.
A diagram of the encoder is shown in figure
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International Mobile Satellite Conference, Ottawa, t990
https://ntrs.nasa.gov/search.jsp?R=19920014940 2020-03-17T12:11:40+00:00Z
1. The synthesis filters are separated into their
zero-input and zero-state components. The min-
imum pitch is constrained to be always greater
than the block size. Therefore the transfer
function of the zero-state pitch synthesis filter
is unity. The weighting filter is moved from
its original location (filtering the error between
original and synthesized speech) to both of its
input branches.
zero input
zero input zero =late zero state
e_leb_k
Z_
I. 0 _ zero state zero state
i . i
-
I-Lc-1
l
Figure 1 CELP Encoder
CODER DESIGN
Backward adaptation
In pure backward-adaptive 16 Kb/s CELP
coders [3] [4] only the excitation vector index
is sent through the channel. The rest of the pa-
rameters are computed in a backward-adaptive
mode. The vector dimension (block of samples)
is 4-5 samples and the one-way delay is below 2
ms. Unfortunately, as the bit rate decreases the
quantization effects become more pronounced,
leading to poor filter tracking and to further dis-
tortion of the original speech. As a result, in
the BA-CELP coder only the short-term predic-
tor is computed in a backward-adaptive manner.
Pitch filter parameters and gain are optimized
in closed-loop procedures and sent through the
channel as side information. The three-tap pitch
filter plays an important role, not only in the fine
structure but also in the shape of the spectrum
of the reconstructed speech.
In our BA-CELP coder, all the parameters
are updated at the end of each block of sam-
pies. The bit allocation scheme is shown in table
1. The vector dimension is 26 samples and the
sampling rate is 8 Khz. Consequently, the total
delay (typically 4 times the vector dimension)
is around 13 ms. The short-term LPC analy-
sis is performed using the modified covariance
method. The length of the frame is four times
the vector dimension. Note that the frames are
highly overlapped and relatively short. This is
necessary to improve the tracking of the adaptive
filter, specially when rapid changes of the spec-
trum occur. The autocorrelation method proved
to be inefficient in this application. This is be-
cause the windowing process weights the error
in the middle of the frames higher than at the
edge of the frames. As a result, spectral match
is poor in regions of rapid spectrum variations.
Parameter bits/block Kbits/sec
Formant filter 0 0.0
Pitch filter 5 1.5
Pitch lag 7 2.2
Gain 5 1.5
Excitation vec. 9 2.8
Total 26 8.0
Table 1 Bit allocation and corresponding
bit rate. The vector dimension is 26
samples and the sampling rate is 8 Khz.
Perceptual weighting filter
Psychoacoustical studies show that the hu-
man auditory system can tolerate more errors in
the formants of the speech spectrum than in the
valleys. Therefore, we can obtain a more sub-
jective distortion measure by weighting the spec-
trum of the error. Regions of the error spectrum
that correspond to valleys between formants in
the speech spectrum are de-emphasized and re-
gions corresponding to the formants are empha-
sized. Using a weighting function W(z) we can
Internahonal Mobile Satelhte Conference, Ottawa, 1990
685
write,
2_
e_ = 2----_
o
(1)
where e_, is the noise-weighted mean-squared
error (NWMSE). A general weighting filter is
discussed in [3] and [51.
A(z/71)
W(z)- A(z/'_) ' 0<3,2<7x_<1 (2)
A good choice for the parameters is 71=0.9 and
3,2=0.4. Note that in conventional CELP coders
only one LPC analysis is necessary for the syn-
thesis and weighting filters. Conversely, the
backward-adaptive approach "requires" two sep-
arate LPC analyses. One based on reconstructed
speech for the synthesis filter and the other one
based on the original speech for the weighting
filter.
Mixed distortion
Further improvement in filter tracking can be
achieved by using a mixed distortion measure in
the excitation vector search procedure. The pro-
posed mixed distortion combines mean-squared
error with a subjectively meaningful LPC dis-
tortion measure.
Log-likelihood ratio distortion measure.
In linear prediction theory, the minimum
residual energy for a particular speech frame is
given by
a = ro - aTr (3)
where r is the correlation vector, ro is the en-
ergy of the segment and a is the optimum LPC
coefficient vector. If the same frame is passed
through a non-optimum inverse filter then the
residual energy fl must be greater than a,
/3 = ro -- 2fiTr + fiTRh _> a (4)
where R is the correlation matrix. Equality holds
when a = ft. The log-likelihood ratio (LLR)
distortion measure is defined as
dLLR(A(z),A(z)) : log (_) (5)
which is equivalent to the difference of the log-
arithmic prediction gains. The LLR distortion
measure has proved to be subjectively meaning-
ful [6][7].
Figure 2 shows the filtering operation. The
two input sequences are s(n) and g(n). The car-
responding pth order inverse filters are A(z) and
A(z). When one of the input sequences, say s(n)
is passed through the filters, the resulting resid-
ual energies are a and/3. A different distortion
would be obtained by using g(n) instead of s(n)
as the input sequence. This difference shows the
asymmetric nature of the likelihood ratio.
s(n)
s(n) _0t
Figure 2 Computation of the residual energies
in the log-likelihood ratio distortion measure.
Search procedure. The optimum excitation
vector is searched in two sequential steps. First,
a conventional search algorithm finds the best nc
excitation vectors that minimizes the NWMSE.
The best nc candidates are used in the second
stage in order to minimize the mixed distortion
measure.
The convolution of the l th codevector v(/)
with the impulse response of the weighted syn-
thesis filter can be written in matrix form as,
i (l) = aHv (l) (6)
where G is the gain, H is a lower triangular
toeplitz matrix containing the impulse response
in its first column and K is the vector dimen-
sion,
n
ha 0 0 " h! 1
hi ]-to 0 "'"
h2 hi ha '''
: : : .. --
hK-1 hK-2 hg-3 "'" o
(7)
686
International Mobile Satellite Conference, Ottawa, 1990
The NWMSE is given by,
= IIz- i(1)ll
= I}zl[ 2- 2Gzrnv (/) + a2v r (/) nTnv (/)(8)
Taking the derivative with respect to G we get
the minimum NWMSE and the optimum gain
for the l th codevector,
0e..__.y__= _2zTHv (l) + 2Gv z (1)HTHv(1) = 0
OG
zTHv (l)
Govt(1) = vT (1)nTHv(1)
(zTHv (l)) 2
(z)= IlzllZ- vT (1)HTHv(1)
(9)
In order to find the nc optimum excitation vec-
tors out of the L-level codebook it is necessary
to maximize the second term of the minimum
error:
(zTHv (l)) 2
find lopt =:_ max
_=o...L-a v T(/)HTHv (1) (10)
The computational complexity of the search is
reduced by using a shift-symmetric codebook
[81.
In the second stage of the search, the opti-
mum codevector is chosen out of the nc candi-
dates. The objective is to choose a codevector
that minimizes the distortion between the origi-
nal LPC model A(z) and the backward-adaptive
LPC model fi_(z) one vector into the future. The
original LPC model has already been computed
for the weighting filter. To calculate the corre-
sponding A(z) for each candidate, we compute
the next block of speech samples and perform
the LPC analysis on the updated synthesized
speech sequence. The mixed distortion is de-
fined as,
( ) ,(2(,) = .(i) A (z) A (z) +,7 logdmix _LLR
_w
i = 1...no
(11)
where e(mi'0 is the minimum NWMSE of the
candidates and 77is a parameter to be optimized
in subjective tests. In equation 1 l, as 7/goes to
infinity the mixed distortion measure becomes
equivalent to the NWMSE. On the other hand,
as r/approaches zero the LPC distortion of future
frames decreases at the cost of accuracy in the
current block of samples.
SIMULATION RESULTS
Computer simulations results were obtained
for the BA-CELP coder and for a conventional
forward-adaptive version. The conventional 8
Kb/s CELP coder computed the LPC analy-
sis on 20 ms of buffered speech. The auto-
correlation method was used to calculate the
LPC coefficients which were transformed to
linear-spectrum pairs and quantized. For the
BA-CELP coder we used the mixed distortion
parameters r/=l and nc=16. For these val-
ues, the NWMSE was greater than the mini-
mum in 20% of the speech blocks. The shift-
symmetric excitation codebook was optimized
using a 10-minute speech database.
Formal listening tests were conducted fol-
lowing the CcYvr recommendations in [9]. The
stimulus material contained six different sen-
tences spoken by different males and females.
Twenty listeners evaluated speech quality under
five different conditions, 2 coders and 3 refer-
ences. The reference conditions consisted of the
original speech (PCM 64 Kb/s) and speech cor-
rupted with random noise which has amplitude
proportional to the instantaneous signal ampli-
tude. The distorted speech is specified according
to the modulated noise reference unit (MNRU)
[10]. Mean opinion scores and 95% confidence
intervals are shown in table 2. According to our
results, speech quality in the forward-adaptive
coder is only 0.1 points in the MOS scale better
than the BA-CELP coder.
Condition Mean Error
PCM 64 Kb/s 4.24 0.15
Forward 3.42 0.20
Backward 3.33 0.19
MNRU 20 dB 2.39 0.18
MNRU 15 dB 1.68 0.17
Table 2 Mean opinion score test.
Mean and 95% confidence intervals.
International Mobile Satellite Conference, Ottawa, 1990
687
Figure 3 shows noise-weighted signal-to-
noise ratio as a function of r/for a 30 second seg-
ment of speech. The dashed line represents the
NWSNR for the conventional search (no LLR
distortion). Observe that for values of 7/between
0.2 and 3 the global NWSNR is greater than for
the regular search NWSNR. This shows how the
global NWMSE was reduced by using the sub-
optimal (in a NWMSE sense) mixed distortion
measure. In other words, an increase in the error
of one block of samples helps in filter tracking
and therefore improves the overall performance
of the coder. Figure 4 shows the log-likelihood
ratio distortion measure for different values of 7/.
20.4
20.2
20
g 19.8
19.6
19.4
19.2
19
.... NWSNR (E.t,_--mfimty)
o._ _ 115 2 ,;
But
Figure 3 Noise-weighted signal-to-noise ratio versus r/.
-- LI_ vs Eut
.... L LR (E_mafimt_)
0.5 I 1.5 2 2.5
F/at
Figure 4 Log-likelihood ratio distortion vs 7/.
CONCLUDING REMARKS
In this paper we discussed how a delay of
approximately 13 ms is achieved in the BA-
CELP. Based on subjective MOS tests, speech
quality has been found to be comparable to that
of conventional forward-adaptive CELP coders.
However, several LPC analyses are necessary
to compute the mixed distortion measure. The
number of candidates in the search procedure
determines the computational complexity of the
coder. Further reductions in complexity may be
possible by using recursive LPC algorithms in-
stead of block algorithms. To further reduce
the delay, future investigation would include
backward-adaptation of the remaining parame-
ters.
REFERENCES
[1] M. Schroeder and B. Atal, "Code-Excited
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689


A low-delay 8 Kb/s backward-adaptive CELP coder

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