This paper reports on the work proceeding with regard to the development of a real-time voice codec for the terrestrial and satellite mobile radio environments. The codec is based on a complexity reduced version of code-excited linear prediction (CELP). The codebook search complexity was reduced to only 0.5 million floating point operations per second (MFLOPS) while maintaining excellent speech quality. Novel methods to quantize the residual and the long and short term model filters are presented

Leblanc, Wilfrid P.

Mahmoud, S. A.

English

NASA Technical Reports Server

N88- 2575 1
REAL-TIME SPEECH ENCODING BASED ON
CODE-EXCITED LINEAR PREDICTION (CELP)
WILFRID P. LEBLANC, Carleton University, Canada;
S.A.MAHMOUD, Carleton University, Canada.
CARLETON UNIVERSITY
Department of Systems and Computer Engineering
V b b_Wi:t, UIIb_IIU
Canada
K1S 5B6
Tel: 1-613-564-6655, 1-613-564-2793
ABSTRACT
This paper reports on the work proceeding with regards to
the development of a real-time voice codec for the terrestrial and
satellite mobile radio environments. The codec is based on a com-
plexity reduced version of CELP. The codebook search complexity
has been reduced to only 0.5 MFLOPS (million floating point op-
erations per second) while maintaining excellent speech quality.
Novel methods to quantize the residual and the long and short
term model filters are presented.
INTRODUCTION
Since the introduction of CELP [Schroeder 1985], there has been considerable
interest in techniques to reduce its complexity, and efficien t techniques to encode
the long and short term model filters. In Schroeder's and Atal's classic paper,
the residual was quantized at only 2 kbps, with no quantization of the remaining
parameters (gain, long and short term predictor). It was believed that a high
quality voice codec, based on CELP, could be realized at an aggregate rate of 4.8
kbps.
However, the computational complexity of CELP is unwieldy, which hinders
the real-time implementation of such a technique. Various authors [Davidson 1986,
Trancoso 1986, Chen 1987] have addressed the complexity issue and have arrived
at marginally acceptable systems.
In this paper, we propose a new structure-- referred to as KELP-- which has
a greatly reduced complexity. We also discuss novel techniques to encode the long
and short term predictor parameters.
The original CELP algorithm is shown in Fig. 1, The filter A(z) is referred
to as the short term inverse filter and is given by [Markel 1976]
A(z) = 1 - _ akz -k
k=l
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where p is the predictor order and the ak's are the predictor parameters. The long
term inverse filter B(z), is given by
B(z) = 1- bkz-(M+k)
k_--q
where the bk are the long term predictor parameters and M is the pitch period.
The order is large but many of the coefficients are zero. The noise weighting filter
W(z) is just
W(z)- A(z)
A(z/'7)
where _ .._ 0.73.
]codebook_
|
|
|
t
t
|
/
1 Id(k) l 1 _
minimize
Fig. 1. The Original CELP Search Algorithm
The search complexity for the optimal excitation from the L level, K dimen-
sional codebook is just
C = LK(3p+2q+2)fs/K FLOPS
300 MFLOPS
for L = 21°, K = 40, p = 10, q = 1, and a sampling frequency (fs) of 8 kHz.
REDUCED COMPLEXITY CELP (KELP)
In this section we introduce a technique to greatly reduce the computational
complexity of the CELP algorithm while maintaining excellent speech quality.
As the first step, we move the location of W(z) and separate the zero state and
zero input responses of the long and weighted short term model filter (A(z/7)). If
the pitch period is greater than the vector dimension (M > K + q), the zero state
response of B(z) is unity. Thus, we may redraw the structure as shown in Fig.
2. Note that the ordering of G and A(z/7) is not important since we are dealing
with the zero state response only.
498
We note that the structures of Fig. 1 and Fig. 2 are not amenable to fast
search non-exhaustive algorithms. By moving the location of the codebook, and
quantizing x(k), a non-exhaustive (tree search) is possible. In addition, if the
denominator of W(z) is fixed, (as in [Kroon 1986]), no degradation would result.
With a variable denominator filter, degradation will result. However, A(z/",/) is
relatively flat and contains no pitch information. Thus, quantizing x(k) should
be very efficient. Forcing the codebook elements to the unit circle implies that
minimizing the mean squared error is equivalent to maximizing the correlation
K-1
G= Z
k=0
over the whole codebook. The modified search procedure is shown in Fig. 3. With
the search structured in this manner, we may use a non-exhaustive tree search for
the optimum excitation.
_. d(k:
t(k)
: zero state
[ ....................................... •
mininfize
_. d(k)/
zero state zero ill[Jut
maximize
Fig. 2. CELP, Modified Search Fig. 3. KELP
The search complexity for this structure is greatly reduced. For a full search
code the complexity (for the above parameters) is 8 MFLOPS. By using a binary
tree search, or a 32-32 tree search [Makhoul 1985], we obtain complexities of 160
KFLOPS, and 500 KFLOPS respectively. A 32-32 tree search is a good tradeoff
between computational complexity and memory requirements.
Typically the pitch predictor is optimized to minimize the open loop residual
energy. However, the input to the pitch predictor contains an appreciable amount
of quantization noise. By redefining the noise weighting filter we can circumvent
499
this problem. We redefine W(z) such that
A(z)B(z)
17¢'(z) = A(z/7)
The search procedure with the new noise weighting filter is shown in Fig. 4.
Note that the new noise weighting filter emphasizes the pitch information more
so than the original weighting filter. Perceptual quality was judged to be almost
equivalent.
I......
maximize
Fig. 4. KELP, Redefined Noise Weighting Filter
The memory complexity (34) and computational complexity (C) for the vari-
ous search procedures is shown in Table 1. The codebooks were optimized using a
closed loop Vector Quantizer (K-means) design algorithm [LeBlanc 1988, Makhoul
1985]. The bit rate for the residual with the above parameters is 2 kbps.
Table 1. Complexity of CELP and KELP
Codec 34 (KWords)
CELP 4O
KELP (full search)
KELP (32-32 search)
KELP (binary search)
4O
< 42
80
C (MFLOPS)
3OO
8
0.5
0.16
With the KELP structure, however, a new synthesis structure must be used.
The KELP synthesis structure is shown in Fig. 5.
QUANTIZATION OF THE SHORT TERM PREDICTOR
The short term predictor (p = 10) was calculated using a window size of
80 samples and a frame size of 160 samples (200% overlap). Every other frame
5OO
A(z/7) B(z) A(z)
zero state
Fig. 5. The KELP Synthesis Structure
is quantized. Intermediate frames are found by linear interpolation between two
adjacent frames.
The short term predictor is quantized based on the Line-Spectrum-Pairs [Ka-
bal 1986]. Each pair is quantized in a two dimensional vector quantizer. The mean
squared error was minimized during the design of the vector quantizers. Thirty-
two bits were allocated for quantizing the short term predictor, with a {6,7,7,6,6)
bit assignment. It was found that this assignment lead to a good perceptual qual-
ity. Furthermore, channel errors can be easily handled since the short term filter
is quantized on a block by block basis with no inherent memory.
With 32 bits allocated to the short term model filter we require a bit rate of
1.6 kbps.
QUANTIZATION OF THE LONG TERM PREDICTOR
The long term predictor is optimized based on minimizing the open loop
residual. It is updated every 10 msec.
The pitch predictor is chosen from a large codebook (128 levels) to mini-
mize the open loop residual error. The codebook is designed using the Inverse
Filter Matching Principle. The average residual error was minimized in the code-
book design process. Thus the distortion measure is a simple matrix multiply,
and the centroid calculation consists of averaging the covariance matrices in each
cell [LeBlanc 1988]. The codebook elements were stabilized as discussed in [Ra-
machandran, 1987].
The pitch period is quantized to seven bits and is in the range (20,147). Thus,
1.4 kbps is allocated to quantizing the long term model filter.
GAIN QUANTIZATION
The gain is quantized on a log-mse scale to five bits. A Lloyd-Max scalar
quantizer was used. The gain is updated every 5 msec. This leads to a rate of 1
kbps for the gain.
The resultant codec based on KELP (Fig. 4) has excellent speech quality.
The total bit rate using the aforementioned quantization procedures is 6 kbps.
By exploiting the intraframe memory of the various parameters, improved perfor-
mance could be realized at a corresponding increase in complexity. Note, however,
501
that the introduction of memory would lead to a degradation in the presence of
channel errors.
CONCLUSION
This paper introduced a novel method to greatly reduce the complexity of
the CELP algorithm while maintaining excellent speech quality. The structure
was modified into a form amenable to fast search non-exhaustive algorithms. The
computational complexity has been reduced to 0.5 MFLOPS with only a very
slight increase in memory requirements.
BIBLIOGRAPHY
J.D. Markel and A.H. Gray Jr., Linear Prediction of Speech, Springer-Verlag,
New York, New York, 1976.
J. Makhoul, S. Roucos, and H. Gish, "Vector Quantization in Speech Coding,"
Proceedings of the IEEE, Vol. 73, No. 11, November 1985.
M.R. Schroeder and B.S. Atal, "Code-Excited Linear Prediction (CELP): High
Quality Speech at Very Low Bit Rates," IEEE International Conference
on Acoustics Speech and Signal Processing, Tampa Florida, March 1985.
I.M. Trancoso and B.S. Atal, "Efficient Procedures for Finding the Optimum
Innovation in Stochastic Coders," IEEE International Conference on Acous-
tics Speech and Signal Processing, Tokyo Japan, 1986.
G. Davidson and A. Gersho, "Complexity Reduction Methods for Vector Ex-
citation Coding,', IEEE International Conference on Acoustics Speech and
Signal Processing, Tokyo Japan, 1986.
P. Kroon, R.J. Sluyter, and E.F. Deprettere, "A Low Complexity Regular Pulse
Coding Scheme With a Reduced Transmission Delay," IEEE International
Conference on Acoustics Speech and Signal Processing, Tokyo Japan, 1986.
J. Chen, G. Davidson, and K. Zeger, "Speech Coding for the Mobile Satellite
Experiment", IEEE International Conference On Communications, Seattle,
Washington, 1987.
P. Kabal and R. Ramachandran, "The Computation of Line Spectral Frequencies
Using Chebyshev Polynomials", IEEE Transactions On Acoustics Speech
and Signal Processing, Vol. ASSP-34, No. 6, December 1986.
R. Ramachandran and P. Kabal, "Stability and Performance Analysis of Pitch
Filters in Speech Coders", IEEE Transactions On Acoustics Speech and Sig-
nal Processing, Vol. ASSP-35, No. 7, July 1987.
W. LeBlanc, An Advanced Speech Coder Based on a Rate-Distortion Theory
Framework., Masters Thesis, To be published, Carleton University, Ottawa,
Canada, 1988.
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